CN118053515A

CN118053515A - DNN-TL-GA-based metal cluster structure optimization method and optimization system

Info

Publication number: CN118053515A
Application number: CN202410124840.2A
Authority: CN
Inventors: 杨祁; 刘清宇; 何圣贵
Original assignee: Institute of Chemistry CAS
Current assignee: Institute of Chemistry CAS
Priority date: 2024-01-29
Filing date: 2024-01-29
Publication date: 2024-05-17

Abstract

The invention relates to the field of machine learning, and discloses an optimization method and an optimization system for a metal cluster structure based on DNN-TL-GA. The method comprises the following steps: according to the initial structure of the metal cluster, a first sample set is generated by adopting a GA and a first DFT local optimization method; training the pre-trained DNN by using the first sample set to obtain a first DNN model; according to the offspring structure of the former S generation of the DFT local optimization, adopting GA and a first DNN model to obtain offspring structures of the S+1st to T generation of the DNN local optimization; and selecting Q low-energy structures from the progeny structures of the former S generation of DFT local optimization and the progeny structures of the S+1st to T generation of DNN local optimization to obtain the global optimal structure of the metal cluster. According to the invention, more representative low-energy samples on the potential energy surface can be obtained, the potential energy surface global searching capability is better, the cluster structure optimizing efficiency is improved, and new Pt ₁₆ and Pt ₁₇ clusters global optimal structures are searched, so that the potential energy surface global searching capability is better.

Description

DNN-TL-GA-based metal cluster structure optimization method and optimization system

Technical Field

The invention relates to the field of machine learning, in particular to an optimization method and an optimization system for a metal cluster structure based on DNN-TL-GA (Deep Nueral Network-TRANSFER LEARNING-Genetic Algorithm, deep neural network-transfer learning-genetic algorithm).

Background

Metal clusters are widely studied because of their unique structural and physicochemical characteristics, and the structure of the metal clusters determines their characteristics, so that studying the globally optimal structure of the metal clusters (i.e., the geometric configuration with the lowest energy on the potential energy surface of the metal clusters) is the basis for studying other properties of the metal clusters. One efficient way to predict the structure of metal clusters is to use global optimization techniques, which generally consist of two parts: global search and local optimization. Generally, the difference of global optimization techniques mainly depends on a global search method, and a search algorithm is generally adopted to perform global search; density functional theory (Density Functional Theory, DFT) is a common method of local optimization of metal cluster structures, the most time-consuming step in the global optimization process being the local optimization based on DFT methods, as this involves time-consuming electronic structure calculations.

Disclosure of Invention

The invention aims to provide an optimization method and an optimization system for a metal cluster structure based on DNN-TL-GA, which are based on the method for global optimization of the metal cluster structure by combining DNN and migration learning, and can acquire more representative low-energy samples on a potential energy surface and have better potential energy surface global searching capability by using a genetic algorithm to sample and global search on the potential energy surface of the metal cluster structure, so that the optimization efficiency of the metal cluster structure is further improved.

In order to achieve the above object, a first aspect of the present invention provides a method for optimizing a metal cluster structure based on DNN-TL-GA, the method comprising: generating a first sample set by adopting a genetic algorithm and a first DFT local optimization method according to an initial structure of a metal cluster, wherein the first sample set comprises a progeny structure of a former S generation of DFT local optimization and corresponding energy; training a pre-trained DNN by using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-size metal cluster by adopting a migration learning method; according to the offspring structure of the former S generation of the DFT local optimization, adopting the genetic algorithm and the first DNN model to obtain offspring structures of the S+1st to T generation of the DNN local optimization; and selecting Q structures from the offspring structures of the former S generation of the DFT local optimization and the offspring structures of the S+1st to T generation of the DNN local optimization, wherein the energy of the Q structures is lower than that of other structures.

Preferably, the generating the first sample set includes: generating an initial offspring structure of the former S generation by adopting the genetic algorithm according to the initial structure of the metal cluster; and processing the offspring structure of the initial preceding S generation by adopting the first DFT local optimization method.

Preferably, the obtaining the offspring structures of the s+1st to T-th generations of the local optimization of the DNN includes: generating initial S+1st generation to T generation offspring structures by adopting the genetic algorithm according to the previous S generation offspring structures locally optimized by DFT; and locally optimizing the offspring structures from the initial S+1st generation to the T generation by adopting the first DNN model.

Preferably, after the step of obtaining the offspring structures of the s+1st to T-th generations of the DNN local optimization is performed, the optimization method further includes: generating a second sample set according to the progeny structure of the previous S generation of the DFT local optimization and the progeny structures of the (S+1) -th generation to the (T) -th generation of the DNN local optimization by adopting the genetic algorithm, the first DNN model and a second DFT local optimization method, wherein the second sample set comprises the progeny structures of the (T+1) -th generation to the (U) -th generation of the DFT local optimization and corresponding energy; processing the first DNN model by adopting the transfer learning method to obtain a second DNN model to be trained, and training the second DNN model to be trained by using the first sample set and the second sample set to obtain a second DNN model; according to the progeny structure of the previous S generation of the DFT local optimization, the progeny structure of the s+1th to T generation of the DNN local optimization, and the progeny structure of the t+1th to U generation of the DFT local optimization, the genetic algorithm and the second DNN model are adopted to obtain the progeny structures of the u+1th to V generation of the DNN local optimization, and the selecting Q structures includes: and selecting the Q structures from the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the S+1st generation to the T generation of the DNN local optimization, the offspring structures of the T+1st generation to the U generation of the DFT local optimization and the offspring structures of the U+1st generation to the V generation of the DNN local optimization.

Preferably, the generating the second sample set includes: generating the initial generation-T+1th to generation-U generation structures by adopting the genetic algorithm according to the generation structure of the DFT locally optimized generation-S and the generation structures of the DNN locally optimized generation-S+1th to generation-T; pre-optimizing the offspring structures from the initial T+1st generation to the U generation by adopting the first DNN model; and processing the pre-optimized offspring structure by adopting the second DFT local optimization method.

Preferably, the obtaining the offspring structures of the (u+1) -th generation and the (V) -th generation of the local optimization of the DNN comprises: generating the offspring structures of the (U+1) -th generation and the (V) th generation by adopting the genetic algorithm according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization and the offspring structures of the (T+1) -th generation and the U generation of the DFT local optimization; and adopting the second DNN model to locally optimize the offspring structures from the (U+1) th generation to the (V) th generation.

Preferably, after the step of obtaining the offspring structures of the u+1th to V th generations of the DNN local optimization is performed, the optimization method further includes: generating a third sample set according to the progeny structure of the former S generation of the local optimization of the DFT, the progeny structure of the s+1st to T generation of the local optimization of the DNN, the progeny structure of the t+1st to U generation of the local optimization of the DFT and the progeny structure of the u+1st to V generation of the local optimization of the DNN by adopting the genetic algorithm, the second DNN model and a third DFT local optimization method, wherein the third sample set comprises the progeny structure of the v+1st to W generation of the local optimization of the DFT and corresponding energy; processing the second DNN model by adopting the transfer learning method to obtain a third DNN model to be trained, and training the third DNN model to be trained by using the first sample set, the second sample set and the third sample set to obtain a third DNN model; obtaining the progeny structures of the (w+1) -th generation and the (X) -th generation of the DNN local optimization by adopting the genetic algorithm and the third DNN model according to the progeny structures of the former S generation of the DFT local optimization, the progeny structures of the (s+1) -th generation and the (U) -th generation of the DNN local optimization, the progeny structures of the (u+1) -th generation and the (V) -th generation of the DNN local optimization and the progeny structures of the (v+1) -th generation and the (W) -th generation of the DFT local optimization, wherein the Q-th structure comprises: and selecting the Q structures from the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the S+1st generation to the T generation of the DNN local optimization, the offspring structures of the T+1st generation to the U generation of the DFT local optimization, the offspring structures of the U+1st generation to the V generation of the DNN local optimization, the offspring structures of the V+1st generation to the W generation of the DFT local optimization and the offspring structures of the W+1st generation to the X generation of the DNN local optimization.

Preferably, after the step of selecting the Q structures is performed, the optimization method further includes: processing the Q structures by adopting a fourth DFT local optimization method to obtain a global optimal structure of the metal cluster, wherein the precision of the fourth DFT local optimization method is higher than the precision of the following steps: the first DFT local optimization method, the second DFT local optimization method, or the third DFT local optimization method.

Through the technical scheme, the method creatively adopts a genetic algorithm and a first DFT local optimization method according to the initial structure of the metal cluster to generate a first sample set; training the pre-trained DNN by using the first sample set to obtain a first DNN model; then, according to the offspring structure of the former S generation of the DFT local optimization, adopting the genetic algorithm and the first DNN model to obtain offspring structures of the S+1st to T generation of the DNN local optimization; and finally, selecting Q low-energy structures from the offspring structures of the former S generation of the DFT local optimization and the offspring structures of the S+1st to T generation of the DNN local optimization. Therefore, on the basis of the DNN combined with the migration learning global optimization metal cluster structure method, the genetic algorithm is used for sampling and global searching on the potential energy surface of the metal cluster structure, more representative low-energy samples on the potential energy surface can be obtained, and the potential energy surface global searching capability is better, so that the optimization efficiency of the metal cluster structure is further improved.

A second aspect of the present invention provides an optimization system for a metal cluster structure, the optimization system comprising: the generation device is used for generating a first sample set by adopting a genetic algorithm and a first DFT local optimization method according to the initial structure of the metal cluster, wherein the first sample set comprises a progeny structure of a former S generation of DFT local optimization and corresponding energy; the model acquisition device is used for training the pre-trained DNN by using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing the trained DNN model of the small-size metal cluster by adopting a migration learning method; the structure acquisition device is used for acquiring the S+1st to T generation of the offspring structure of the DNN local optimization by adopting the genetic algorithm and the first DNN model according to the offspring structure of the former S generation of the DFT local optimization; and structure selection means for selecting Q structures from among the S-generation offspring structures before the DFT local optimization and the s+1-generation to T-generation offspring structures DNN local optimization, wherein the Q structures have lower energy than other structures.

Specific details and benefits of the optimization system for a metal cluster structure provided in the embodiments of the present invention can be found in the above description of the optimization method applicable to a metal cluster structure based on DNN-TL-GA, and will not be repeated here.

A third aspect of the present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method for optimizing a DNN-TL-GA based metal cluster structure.

A fourth aspect of the invention provides a computer program product comprising a computer program which, when executed by a processor, implements the method of optimizing a DNN-TL-GA based metal cluster structure.

Additional features and advantages of the invention will be set forth in the detailed description which follows.

Drawings

The accompanying drawings are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain, without limitation, the embodiments of the invention. In the drawings:

FIG. 1 is a flow chart of a method for optimizing DNN-TL-GA based metal cluster structures according to one embodiment of the invention;

FIG. 2 is a flow chart of a method for optimizing DNN-TL-GA based metal cluster structures according to one embodiment of the invention;

FIG. 3 is a flow chart of a method for optimizing DNN-TL-GA based metal cluster structures according to an embodiment of the invention;

FIG. 4 is a schematic diagram of a process for optimizing a DNN-TL-GA-based metal cluster structure according to an embodiment of the invention;

FIG. 5 is a globally optimal structure diagram of Pt _9-17 metal clusters optimized by a DNN-TL-GA based metal cluster structure optimization method according to an embodiment of the invention; and

FIG. 6 is a global optimum block diagram of Rh ₂V₇ ^- metal clusters optimized by a DNN-TL-GA based metal cluster structure optimization method according to one embodiment of the invention.

Detailed Description

The following describes specific embodiments of the present invention in detail with reference to the drawings. It should be understood that the detailed description and specific examples, while indicating and illustrating the invention, are not intended to limit the invention.

FIG. 1 is a flow chart of a method for optimizing a DNN-TL-GA based metal cluster structure according to an embodiment of the invention. As shown in fig. 1, the optimization method may include: step S101, generating a first sample set by adopting a genetic algorithm and a first DFT local optimization method according to an initial structure of a metal cluster, wherein the first sample set comprises a progeny structure of a former S generation of DFT local optimization and corresponding energy; step S102, training a pre-trained DNN by using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-size metal cluster by adopting a migration learning method; step S103, according to the offspring structure of the former S generation of the DFT local optimization, adopting the genetic algorithm and the first DNN model to obtain offspring structures from the S+1st generation to the T generation of the DNN local optimization; and step S104, selecting Q structures from the progeny structures of the former S generation of the DFT local optimization and the progeny structures of the S+1st to T generation of the DNN local optimization, wherein the energy of the Q structures is lower than that of other structures.

The respective steps (steps S101 to S104) described above are explained and explained below.

Before performing step S101, the elemental composition, size, charge, and multiplicity of the metal clusters to be optimized may be set in advance; then, N metal cluster initial structures are generated, wherein the value range of N can be 10-100.

Wherein, the element composition of the metal cluster can be any metal element; the element types can be one, two and three; the metal clusters are not limited in charge and may be neutral metal clusters, anionic metal clusters, and cationic metal clusters.

Specifically, the bond length distribution algorithm (Bond length distribution algorithm, BLDA) can be used to randomly generate the initial structure of the metal cluster, but the initial structure random generation method commonly used in algorithms such as basin jumping and simulated annealing can also be used.

Step S101, according to an initial structure of a metal cluster, a genetic algorithm and a first DFT local optimization method are adopted to generate a first sample set.

Wherein the first sample set includes a progeny structure of a previous S generation of DFT local optimization and corresponding energy.

For step S101, the generating a first sample set includes: generating an initial offspring structure of the former S generation by adopting the genetic algorithm according to the initial structure of the metal cluster; and processing the offspring structure of the initial preceding S generation by adopting the first DFT local optimization method.

Before the genetic algorithm generates each new structure, the structures of all the previous generations are subjected to energy sequencing, and then the structures with low energy are selected for operations such as crossing and mutation to generate new structures. Wherein the structure is checked by key length and unreasonable structures are deleted. For the 1-10 generations, the 2 nd generation is based on the first 1 generation, the 3 rd generation is based on the first 2 generations, … …, and the 1-10 generations of structures (the purpose is to generate diversified structures) are sequentially generated, of course, S in the present embodiment is not limited to the first 10 generations, and the number 10 is merely used as an example. The genetic algorithm may be referred to as an existing algorithm, which is not an improvement point of the present application, and will not be described herein. For example, the genetic algorithm may be used to generate the first 10 (e.g., 1-10) generation of offspring structures, which includes a total of T ₁ offspring structures, according to the N metal cluster initial structures generated as described above, each structure being locally optimized by M steps of DFT using a small basis set to generate T ₁ ×m structures/energy samples (e.g., sample set 1 shown in fig. 4), where M may have a value in the range of 5 to 30.

Therefore, the genetic algorithm is used for sampling and global searching on the potential energy surface of the metal cluster structure, more representative low-energy samples on the potential energy surface can be obtained, and the potential energy surface has better global searching capacity, so that the global optimal structure of the metal cluster can be obtained more efficiently.

Step S102, training the pre-trained DNN by using the first sample set, so as to obtain a first DNN model.

The pretrained DNN is obtained by processing a trained DNN model of a small-size metal cluster by adopting a migration learning method.

Specifically, the migration learning method is utilized to perform migration learning on a trained DNN model of a small-size (less atomic number) metal cluster so as to obtain a pre-trained DNN of the metal cluster to be optimized, and because the migration learning can migrate knowledge of a source task learned by the neural network to related but different target tasks, the neural network of the target tasks can be trained well with less data. For example, the pre-trained neural network of Pt ₉ was learned from the Pt ₈ trained neural network migration. The pre-trained DNN is then trained to DNN model 1 with better performance using sample set 1, as shown in fig. 4. It should be noted that the metal clusters in the present application are larger than the small-sized metal clusters with the trained DNN model, but are not limited to the same elements of both metal clusters.

And step S103, obtaining the S+1st to T generation of offspring structures of DNN local optimization by adopting the genetic algorithm and the first DNN model according to the previous S generation offspring structures of DFT local optimization.

For step S103, the obtaining the offspring structures from the s+1st generation to the T generation of the DNN local optimization includes: generating initial S+1st generation to T generation offspring structures by adopting the genetic algorithm according to the previous S generation offspring structures locally optimized by DFT; and locally optimizing the offspring structures from the initial S+1st generation to the T generation by adopting the first DNN model.

For example, the genetic algorithm is used to generate offspring structures of 11 th to 100 th generations based on the original (initial) first 10 th generation offspring structures. Specifically, before each generation of new structure is generated by the genetic algorithm, the structures of all the previous generations are subjected to energy sequencing, and then the structures with low energy are selected for crossover, mutation and other operations to generate the new structure. For the 11-100 generations, the 11 th generation is based on the first 10 generations, and the 12 th generation is based on the first 11 generations, … …, and the 11-100 generations of structures (aiming at generating diversified structures) are sequentially generated.

Then, DNN model 1 (DNN model 1 can also be used in combination with a preset structure optimization algorithm) is adopted to replace a DFT method to locally optimize a new structure generated by a genetic algorithm (namely, fit a potential energy surface of a metal cluster structure). The preset structure optimization algorithm may be a Limited memory BFGS (Limited-memory broyden-fletcher-goldfarb-shanno, L-BFGS) algorithm, newton's method, or BFGS. DNN is very effective in fitting complex potential energy planes, and the well-fitted potential energy planes can be effectively used for local optimization of the metal cluster structure, so that a neural network method and a small amount of training samples are used for fitting the potential energy planes of the metal cluster structure, the calculation time in the optimization of the metal cluster structure is reduced, and the calculation cost is greatly reduced.

Step S104, selecting Q structures from the S generation of the previous generation of the DFT local optimization and the S+1 generation to T generation of the DNN local optimization.

Wherein the energy of the Q structures is lower than the energy of the other structures. Wherein, the value range of Q can be 5-35.

Specifically, energy sequencing is performed on all the locally optimized structures generated in the generation P (the value range of P can be 50-200, for example, 100) of the genetic algorithm, Q low-energy structures are selected (for example, if the structure with the lowest energy is at the 1 st, the structure with the next energy is at the 2 nd, and other structures are ranked in turn according to the energy reduction mode), the top Q is selected), then DFT optimization is performed on the base group with higher replacement precision, and finally the globally optimal structure of the metal cluster is obtained.

DNN has a stronger complex potential energy surface fitting capability, but requires a large number of training samples. If the overall optimized metal cluster structure method of DNN combined with TL (DNN-TL) is adopted, the problems of low potential energy surface sampling efficiency and low overall searching capacity exist, and a large amount of training samples and calculation time are needed. The embodiment provides a method for globally optimizing a metal cluster structure by combining DNN with TL and GA (DNN-TL-GA), namely, a genetic algorithm is used for sampling and globally searching on a potential energy surface of the metal cluster structure, so that more representative low-energy samples on the potential energy surface can be obtained, and better global searching capacity of the potential energy surface is possessed, and the method is favorable for obtaining a globally optimal structure of the metal cluster more efficiently. Compared with a global optimization metal cluster structure method combining DNN and TL, the method reduces training samples by about half, can save about 70-80% of calculation time, and further improves the optimization efficiency of the metal cluster structure.

In the embodiment, the first sample set is adopted to train DNN once to obtain a first DNN model, and then the model is adopted to replace a DFT method to locally optimize a new structure generated by a genetic algorithm so as to accelerate the local optimization speed of a metal cluster structure. In the next embodiment, in order to increase the number of low-energy samples, a genetic algorithm is used to regenerate a plurality of offspring structures, two sample sets (a first sample set and a second sample set) are used to train DNN twice to obtain a second DNN model, and then the model is used to replace the DFT method to locally optimize a new structure generated by the genetic algorithm, so as to accelerate the local optimization speed of the metal cluster structure.

As shown in fig. 2, after the step of obtaining the offspring structures of the s+1st to T-th generations of the DNN local optimization (i.e. step S103), the optimization method further includes: step S105, generating a second sample set by adopting the genetic algorithm, the first DNN model and a second DFT local optimization according to the progeny structure of the former S generation of the DFT local optimization and the progeny structures of the (S+1) -T generation of the DNN local optimization, wherein the second sample set comprises the progeny structures of the (T+1) -U generation of the DFT local optimization and corresponding energy; step S106, processing the first DNN model by adopting the migration learning method to obtain a second DNN model to be trained, and training the second DNN model to be trained by using the first sample set and the second sample set to obtain a second DNN model; and step S107, obtaining the offspring structures of the (U+1) -th generation and the (V) -th generation of the DNN local optimization by adopting the genetic algorithm and the second DNN model according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization and the offspring structures of the (T+1) -th generation and the U-th generation of the DFT local optimization.

Accordingly, the selecting Q structures (i.e. step S104) specifically includes: step S108, selecting the Q structures from the first DFT locally optimized generation-preceding S generation of structures, the first DNN locally optimized generation-preceding S+1st to generation-T generation of structures, the second DFT locally optimized generation-t+1st to generation-U generation of structures and the second locally optimized generation-U+1st to generation-V structures.

The respective steps (steps S105 to S108) described above are explained and explained below.

Step S105, generating a second sample set according to the progeny structure of the previous S generation of the DFT local optimization and the progeny structures of the s+1st to T generation of the DNN local optimization by using the genetic algorithm, the first DNN model and a second DFT local optimization method.

Wherein the second sample set comprises the T+1st to U generation offspring structures and corresponding energies of DFT local optimization.

For step S105, the generating the second sample set includes: generating the offspring structures of the T+1th to the U generation by adopting the genetic algorithm according to the offspring structure of the previous S generation locally optimized by DFT and the offspring structures of the S+1th to the T generation locally optimized by DNN; pre-optimizing the offspring structures from the T+1th generation to the U generation by adopting the first DNN model; and processing the pre-optimized offspring structure by adopting the second DFT local optimization method.

The specific procedure for steps S101-S103 is detailed in the description above, except that the values of S, T are adjustable.

The genetic algorithm can be used to generate the initial offspring structures of 101 th-110 th generation (for example, the previous 100 th generation) according to the generated offspring structures of the previous T generation, wherein the offspring structures comprise T ₂ offspring structures in total, each structure is pre-optimized by DNN model 1, then M-step DFT local optimization is carried out on the pre-optimized structure to obtain T ₂ xM structures/energy samples (wherein the value range of M can be 5-30), and the samples are combined with sample set 1 to form sample set 2 (shown in figure 4), wherein the method comprises the following steps ofSamples.

And S106, processing the first DNN model by adopting the migration learning method to obtain a second DNN model to be trained, and training the second DNN model to be trained by using the first sample set and the second sample set to obtain the second DNN model.

Specifically, the initialization parameters are obtained by migrating the parameters of the DNN model 1, and the parameters of the DNN model 2 are initialized by using the obtained initialization parameters, and because the migration learning can migrate the knowledge of the source task learned by the neural network to the related but different target tasks, the neural network of the target tasks can be trained well with less data. The initialized DNN model 2 is then trained to a better performing DNN model 2 using sample set 2, as shown in fig. 4.

And step S107, obtaining the offspring structures of the (U+1) -th generation and the (V) -th generation of the DNN local optimization by adopting the genetic algorithm and the second DNN model according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization and the offspring structures of the (T+1) -th generation and the U-th generation of the DFT local optimization.

For step S107, the obtaining the locally optimized offspring structures from the u+1st generation to the V generation includes: generating the offspring structures of the (U+1) -th generation and the (V) th generation by adopting the genetic algorithm according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization and the offspring structures of the (T+1) -th generation and the U generation of the DFT local optimization; and adopting the second DNN model to locally optimize the offspring structures from the (U+1) th generation to the (V) th generation.

For example, the genetic algorithm is used to generate offspring structures of 111 th to 180 th generations according to the offspring structures of the previous 110 th generation. Then, DNN model 2 (DNN model 2 can be combined with a preset structure optimization algorithm) is adopted to replace a DFT method to locally optimize a new structure generated by the genetic algorithm. The preset structure optimization algorithm can be an L-BFGS algorithm, a Newton method or a BFGS method.

And S108, selecting the Q structures from the previous S generation of the structure of the DFT local optimization, the S+1st to T generation of the structure of the DNN local optimization, the T+1st to U generation of the structure of the DFT local optimization and the U+1st to V generation of the structure of the DNN local optimization.

Specifically, energy sequencing is performed on all the locally optimized structures generated in the generation P (the value range of P can be 50-200, for example, 180) of the genetic algorithm, Q low-energy structures are selected (for example, if the structure with the lowest energy is at the 1 st, the structure with the next energy is at the 2 nd, and other structures are ranked in turn according to the energy reduction mode), the top Q is selected), DFT optimization is performed on the base group with higher replacement precision, and finally the globally optimal structure of the metal cluster is obtained.

In the embodiment, two sample sets (the first sample set and the second sample set) are adopted to train DNN twice to obtain a second DNN model, and then the model is adopted to replace a DFT method to locally optimize a new structure generated by a genetic algorithm so as to accelerate the local optimization speed of a metal cluster structure. In the next embodiment, in order to further increase the number of low-energy samples, a genetic algorithm is used to regenerate a plurality of offspring structures, three sample sets (a first sample set, a second sample set and a third sample set) are used to train DNN three times to obtain a third DNN model, and then the model is used to replace the DFT method to locally optimize a new structure generated by the genetic algorithm so as to accelerate the local optimization speed of the metal cluster structure.

As shown in fig. 3, after the step of obtaining the descendant structure of the u+1st to V generation of the DNN local optimization (i.e., step 107) is performed, the optimization method further includes: step S109, generating a third sample set according to the progeny structure of the previous S generation of the DFT local optimization, the progeny structure of the s+1st to T generation of the DNN local optimization, the progeny structure of the t+1st to U generation of the DFT local optimization, and the progeny structure of the u+1th to V generation of the DNN local optimization, by using the genetic algorithm, the second DNN model, and a third DFT local optimization method, wherein the third sample set includes the progeny structure of the v+1st to W generation of the DFT local optimization and the corresponding energy; step S110, processing the second DNN model by adopting the transfer learning method to obtain a third DNN model to be trained, and training the third DNN model to be trained by using the first sample set, the second sample set and the third sample set to obtain a third DNN model; and step S111, according to the progeny structure of the former S generation of the DFT local optimization, the progeny structure of the (S+1) th generation to the (T) th generation of the DNN local optimization, the progeny structure of the (T+1) th generation to the (U) th generation of the DFT local optimization, the progeny structure of the (U+1) th generation to the (V) th generation of the DNN local optimization and the progeny structure of the (V+1) th generation to the (W) th generation of the DFT local optimization, acquiring the progeny structure of the (W+1) th generation to the (X) th generation of the DNN local optimization by adopting the genetic algorithm and the third DNN model.

The selecting Q structures (i.e., step S104 or S108) specifically includes: step S112 is to select the Q structures from the previous S generation of the structure of the DFT local optimization, the s+1st to T generation of the structure of the progeny of the DNN local optimization, the t+1st to U generation of the structure of the progeny of the DFT local optimization, the u+1st to V generation of the structure of the progeny of the DNN local optimization, the v+1st to W generation of the structure of the progeny of the DFT local optimization, and the w+1st to X generation of the structure of the progeny of the DNN local optimization.

The respective steps (steps S109 to S112) described above are explained and explained below.

Step S109, generating a third sample set according to the progeny structure of the previous S generation of the DFT local optimization, the progeny structure of the s+1st to T generation of the DNN local optimization, the progeny structure of the t+1st to U generation of the DFT local optimization, and the progeny structure of the u+1st to V generation of the DNN local optimization, by using the genetic algorithm, the second DNN model, and a third DFT local optimization method.

Wherein the third sample set comprises the V+1st to W generation offspring structures and corresponding energies of DFT local optimization.

For step S109, the generating a third sample set includes: generating initial offspring structures from the V+1th generation to the W th generation by adopting the genetic algorithm according to the offspring structures of the previous V generation; pre-optimizing the offspring structures from the initial generation V+1 to the generation W by adopting the second DNN model; and processing the pre-optimized offspring structure by adopting the third DFT local optimization method.

The specific procedures for steps S101-S103, S105-S107 are described in detail above, except that the values of S, T, U, V are adjustable. For example, s=5, t=10, u=15, v=20.

The genetic algorithm can be used to generate the initial 21 st-25 th generation offspring structures, which comprise T ₃ offspring structures, according to the generated offspring structures of the previous V generation (for example, the previous 20 th generation), each structure is pre-optimized by DNN model 2, then M-step DFT local optimization is carried out on the pre-optimized structure to obtain T ₃ xM structures/energy samples (wherein the value range of M can be 5-30), and the samples are combined with sample set 2 to form sample set 3 (shown in figure 4), which comprisesSamples. Wherein, T ₁、T₂ and T ₃ have the following relationship: t ₁>T₂≥T₃.

Each "sample set" in the present application is made up of a number of data pairs of metal cluster structure (i.e., cartesian coordinates) and energy (i.e., each sample data in the sample set is made up of cartesian coordinates and energy). The DFT local optimization process is to continuously adjust the structure of the metal clusters toward the direction of energy decrease until the energy converges to a local minimum.

Step S110, processing the second DNN model by using the migration learning method to obtain a third DNN model to be trained, and training the third DNN model to be trained by using the first sample set, the second sample set and the third sample set to obtain a third DNN model.

Specifically, the initialization parameters are obtained by migrating the parameters of the DNN model 2, and the parameters of the DNN model 3 are initialized by using the obtained initialization parameters, and the neural network of the target task can be trained well by less data because the migration learning can migrate the knowledge of the source task learned by the neural network to the related but different target task. The initialized DNN model 3 is then trained to a better performing DNN model 3 using the sample set 3, as shown in fig. 4.

And step S111, according to the progeny structure of the former S generation of the DFT local optimization, the progeny structure of the (S+1) th generation to the (T) th generation of the DNN local optimization, the progeny structure of the (T+1) th generation to the (U) th generation of the DFT local optimization, the progeny structure of the (U+1) th generation to the (V) th generation of the DNN local optimization and the progeny structure of the (V+1) th generation to the (W) th generation of the DFT local optimization, acquiring the progeny structure of the (W+1) th generation to the (X) th generation of the DNN local optimization by adopting the genetic algorithm and the third DNN model.

For step S111, the obtaining the offspring structures from the w+1st generation to the X-th generation of the DNN local optimization includes: generating offspring structures from the W+1th generation to the X generation by adopting the genetic algorithm according to the offspring structure of the previous W generation; and locally optimizing the W+1st generation to X generation offspring structures by adopting the third DNN model.

For example, the genetic algorithm is used to generate the offspring structures of the 26 th to 50 th generations according to the offspring structures of the first 25 th generations. Then, DNN model 3 (DNN model 3 can be combined with a preset structure optimization algorithm) is adopted to replace a DFT method to locally optimize a new structure generated by the genetic algorithm. The preset structure optimization algorithm can be an L-BFGS algorithm, a Newton method or a BFGS method.

And step S112, selecting the Q structures from the previous S generation of the structure of the DFT local optimization, the S+1st to T generation of the structure of the offspring of the DNN local optimization, the T+1st to U generation of the structure of the offspring of the DFT local optimization, the U+1st to V generation of the structure of the offspring of the DNN local optimization, the V+1st to W generation of the structure of the offspring of the DFT local optimization and the W+1st to X generation of the structure of the offspring of the DNN local optimization.

Specifically, energy sequencing is performed on all the locally optimized structures generated in the generation P (the value range of P can be 50-200, for example, 50) of the genetic algorithm, Q low-energy structures are selected (for example, if the structure with the lowest energy is at the 1 st, the structure with the next energy is at the 2 nd, and other structures are ranked in turn according to the energy reduction mode), the top Q is selected), then DFT optimization is performed on the base group with higher replacement precision, and finally the globally optimal structure of the metal cluster is obtained.

In one embodiment, after the step of selecting the Q structures (i.e., step S104, step S108, or step S112) is performed, the optimization method further includes: and processing the Q structures by adopting a fourth DFT local optimization method to obtain a global optimal structure of the metal cluster.

The precision of the fourth DFT local optimization method is higher than that of the following: the first DFT local optimization method, the second DFT local optimization method, or the third DFT local optimization method.

Specifically, after performing energy sequencing on all the locally optimized structures generated by iterating the genetic algorithm for P times and selecting Q low-energy structures, DFT optimization can be performed by using a base group with higher precision, and finally, a global optimal structure of the metal cluster is obtained. Because only a few structures are processed by DFT with high precision, the globally better metal cluster structure can be obtained under the condition of not affecting the local optimization rate of the metal cluster structure.

In particular, the DNN-binding TL and GA global optimized metal cluster architecture approach is described below. The method comprises the following steps.

Step 1: setting the element composition, size, charge and multiplicity of the metal clusters to be optimized;

step 2: generating N metal cluster random initial structures;

Step 3: generating T ₁ offspring structures by using a genetic algorithm, wherein each structure is locally optimized by using M steps of DFT by using a small base group to generate T ₁ multiplied by M structures/energy samples (sample set 1);

step 4: obtaining a pre-training deep neural network of a metal cluster to be optimized by using a transfer learning method;

Step 5: training the pre-trained deep neural network into a deep neural network model 1 with better performance by using the sample set 1;

Step 6: the deep neural network model 1 combines a local optimization algorithm to replace a DFT method to locally optimize a new structure generated by a genetic algorithm;

Step 7: in order to increase the number of low-energy samples, a genetic algorithm is used for regenerating T ₂ offspring structures, each structure is pre-optimized by a deep neural network model 1, then M-step DFT optimization is carried out on the pre-optimized structure to obtain T ₂ xM structures/energy samples, and the samples are combined with a sample set 1 to form a sample set 2, wherein the method comprises the following steps of A sample number;

Step 8: initializing parameters of the deep neural network model 2, obtaining the parameters through migrating the parameters of the deep neural network model 1, and then training the initialized deep neural network model 2 into the deep neural network model 2 with better performance by using the sample set 2;

Step 9: the deep neural network model 2 is combined with a structure optimization algorithm to locally optimize a new structure generated by a genetic algorithm;

step 10: in order to further increase the number of low-energy samples, the genetic algorithm generates T ₃ offspring structures, each structure is pre-optimized by the deep neural network model 2, then M-step DFT optimization is carried out on the pre-optimized structure to obtain T ₃ ×M structures/energy samples, and the samples and the sample set 2 are combined to form a sample set 3, wherein the sample set 3 comprises A sample number;

Step 11: initializing parameters of the deep neural network model 3, which are obtained by migrating the parameters of the deep neural network model 2, and then training the initialized deep neural network model 3 into a deep neural network model 3 with better performance by using the sample set 3;

step 12: the genetic algorithm continuously generates a new metal cluster structure in the subsequent iteration, and the deep neural network model 3 is combined with the structure optimization algorithm to completely replace the DFT method to locally optimize the new metal cluster structure.

Step 13: and (3) carrying out energy sequencing on all the locally optimized structures generated by the iteration P times of the genetic algorithm, selecting Q low-energy structures, then carrying out DFT optimization on the base group with higher conversion accuracy, and finally obtaining the global optimal structure of the metal cluster.

Example 1

The atomic species was set to Pt, the atomic number was 9, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 10 offspring structures were co-generated, each structure was locally optimized with a 5-step DFT (using TPSSh functional and def2-SVP basis set), yielding 50 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₉ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 5 offspring structures were co-generated, each structure was locally optimized with a 5-step DFT (using TPSSh functional and def2-SVP basis set) to generate 25 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 75 samples).

In the 21-25 generations of genetic algorithm, 5 offspring structures were co-generated, each structure was locally optimized with a 5-step DFT (using TPSSh functional and def2-SVP basis set) to generate 25 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 100 samples).

The maximum algebra of the genetic algorithm is 150, about 100 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and a Pt ₉ metal cluster global optimal structure and zero correction energy-1074.0958 Hartree are obtained. Spin multiplex 3,5 and 7 operate in the same procedure as described above.

Example 2

The atomic species was set to Pt, the atomic number was 10, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 10 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set), yielding 100 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₁₀ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 5 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 50 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 150 samples).

In the 21-25 generations of genetic algorithm, 5 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 50 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 200 samples).

The maximum algebra of the genetic algorithm is 150, about 300 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and a Pt ₁₀ metal cluster global optimal structure and zero correction energy-1193.4881 Hartree are obtained. Spin multiplex 3,5 and 7 operate in the same procedure as described above.

Example 3

The atomic species was set to Pt, the atomic number was 11, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 40 offspring structures were generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set), yielding 400 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₁₁ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 3 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 30 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 430 samples).

In the 21-25 generations of genetic algorithm, 2 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 20 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 450 samples).

The maximum algebra of the genetic algorithm is 150, about 100 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and a Pt ₁₁ metal cluster global optimal structure and zero correction energy-1312.8484 Hartree are obtained. Spin multiplex 3,5 and 7 operate in the same procedure as described above.

Example 4

The atomic species was set to Pt, atomic number was 12, charge was 0, spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm 47 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 470 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₁₂ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 10 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 100 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 570 samples).

In the 21-25 generations of genetic algorithm, 8 offspring structures were co-generated, each structure was locally optimized with a 10-step DFT (using TPSSh functional and def2-SVP basis set) to generate 80 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 650 samples).

The maximum algebra of the genetic algorithm is 150, about 1400 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and a Pt ₁₂ metal cluster global optimal structure and zero correction energy-1432.2231 Hartree are obtained. Spin multiplex 3, 5 and 7 operate in the same procedure as described above.

Example 5

The atomic species was set to Pt, the atomic number was 13, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 15 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set), yielding 300 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₁₃ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 12 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 240 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 540 samples).

In the 21-25 generations of genetic algorithm, 10 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 200 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 540 samples).

The maximum algebra of the genetic algorithm is 150, about 940 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and the Pt ₁₃ metal cluster global optimal structure and zero correction energy-1551.6044 Hartree are obtained. Spin multiplex 3, 5 and 7 operate in the same procedure as described above.

Example 6

The atomic species was set to Pt, the atomic number was 14, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 24 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set), yielding 480 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₁₄ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 8 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 160 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 640 samples).

In the 21-25 generations of genetic algorithm, 5 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 100 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 740 samples).

The maximum algebra of the genetic algorithm is 150, about 1060 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and the Pt ₁₄ metal cluster global optimal structure and zero correction energy-1670.9858 Hartree are obtained. Spin multiplex 3, 5 and 7 operate in the same procedure as described above.

Example 7

The atomic species was set to Pt, the atomic number was 15, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

The pretrained neural network of Pt ₁₅ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 12 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 240 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 720 samples).

In the 21-25 generations of genetic algorithm, 9 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 180 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 900 samples).

The maximum algebra of the genetic algorithm is 150, about 900 structures are generated, 10 low-energy structures are selected, then TPSSh functional is kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and the Pt ₁₅ metal cluster global optimal structure and zero correction energy-1790.3518 Hartree are obtained. Spin multiplex 3, 5 and 7 operate in the same procedure as described above.

Example 8

The atomic species was set to Pt, the atomic number was 16, the charge was 0, the spin severity was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 38 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set), yielding 760 structure/energy samples (sample set 1).

The pretrained neural network of Pt ₁₆ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 25 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 500 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 1260 samples).

In the 21-25 generations of genetic algorithm, 17 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set) to generate 340 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 1600 samples).

The maximum algebra of the genetic algorithm is 150, about 1230 structures are generated in total, 15 low-energy structures are selected, then TPSSh functional functions are kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and the Pt ₁₆ metal cluster global optimal structure and zero correction energy-1909.7376 Hartree are obtained. Spin multiplex 3, 5 and 7 operate in the same procedure as described above.

Example 9

The atomic species was set to Pt, the atomic number was 17, the charge was 0, the spin severity was 1, and the size of the initial population of metal clusters was 40.

In the first 5 generations of genetic algorithm, 74 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis set), yielding 1480 structures/energy samples (sample set 1).

The pretrained neural network of Pt ₁₇ is obtained by the transition learning of the neural network trained by Pt ₈.

In the 11-15 generations of genetic algorithm, 12 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (employing TPSSh functional and def2-SVP basis set) to generate 240 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 1720 samples).

In the 21-25 generations of genetic algorithm, 14 offspring structures were generated, each structure was locally optimized with a 20-step DFT (using TPSSh functional and def2-SVP basis), 280 structure/energy samples were generated, and these samples were combined with sample set 2 to generate sample set 3 (containing about 2000 samples).

The maximum algebra of the genetic algorithm is 150, 700 structures are generated in total, 15 low-energy structures are selected, then TPSSh functional functions are kept unchanged, DFT optimization is carried out on def2-TZVP base groups with higher conversion accuracy, and a Pt ₁₇ metal cluster global optimal structure and zero correction energy-2029.1219 Hartree are obtained. Spin multiplex 3,5 and 7 operate in the same procedure as described above.

Example 10

The atomic species were set to Rh and V, rh atomic number was 2, V atomic number was 7, charge was-1, spin-multiple was 1, and the size N of the initial population of metal clusters was 20.

In the first 5 generations of genetic algorithm, 52 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSS functional, where Rh uses the SDD basis set and V uses the SVP basis set) to generate 1040 structure/energy samples (sample set 1).

The pre-training neural network of Rh ₂V₇ ^- is obtained by the transfer learning of the neural network trained by Rh ₃V₆ ^-.

In the 11-15 generations of genetic algorithm, 15 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSS functional, where Rh uses the SDD basis set and V uses the SVP basis set) to generate 300 structure/energy samples, which were combined with sample set 1 to generate sample set 2 (containing about 1340 samples).

In the 21-25 generations of genetic algorithm, 10 offspring structures were co-generated, each structure was locally optimized with a 20-step DFT (using TPSS functional, where Rh uses the SDD basis set and V uses the SVP basis set) to generate 200 structure/energy samples, which were combined with sample set 2 to generate sample set 3 (containing about 1540 samples).

The maximum algebra of the genetic algorithm is 150, about 1070 structures are generated in total, 15 low-energy structures are selected, TPSS functional is kept unchanged, and the TZVP base group with higher V conversion precision is subjected to DFT optimization to obtain the Rh ₂V₇ ^- metal cluster global optimal structure and zero correction energy-6829.5077 Hartree. Spin multiplex 3, 5 and 7 operate in the same procedure as described above.

The present invention searches for a more stable Pt ₁₆ and Pt ₁₇ metal cluster structure (as shown in fig. 5, where M represents how severe) and Rh ₂V₇ ^- metal cluster structure (as shown in fig. 6) than reported in the prior art, indicating that the present invention has good global optimization capabilities.

Wherein S, T, U, V, W, X, Q are integers.

In summary, the invention creatively adopts a genetic algorithm and a first DFT local optimization method to generate a first sample set according to the initial structure of the metal cluster; training the pre-trained DNN by using the first sample set to obtain a first DNN model; then, according to the offspring structure of the former S generation of the DFT local optimization, adopting the genetic algorithm and the first DNN model to obtain the offspring structures of the S+1st to T generation of the local optimization; and finally, selecting Q low-energy structures from the offspring structures of the former S generation of the DFT local optimization and the offspring structures of the S+1st to T generation of the local optimization. Therefore, on the basis of the method for globally optimizing the metal cluster structure by combining DNN with TL, the invention uses the genetic algorithm to sample and globally search the potential energy surface of the metal cluster structure, so that more representative low-energy samples on the potential energy surface can be obtained and the potential energy surface global search capability is better, thereby further improving the optimizing efficiency of the metal cluster structure.

An embodiment of the present invention provides an optimization system for a metal cluster structure, the optimization system including: the generation device is used for generating a first sample set by adopting a genetic algorithm and a first DFT local optimization method according to the initial structure of the metal cluster, wherein the first sample set comprises a progeny structure of a former S generation of DFT local optimization and corresponding energy; the model acquisition device is used for training the pre-trained DNN by using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing the trained DNN model of the small-size metal cluster by adopting a migration learning method; the structure acquisition device is used for acquiring the S+1st to T generation of the offspring structure of the DNN local optimization by adopting the genetic algorithm, the first DNN model and a preset structure optimization algorithm according to the offspring structure of the former S generation of the DFT local optimization; and structure selection means for selecting Q structures from among the S-generation offspring structures before the DFT local optimization and the s+1-generation to T-generation offspring structures DNN local optimization, wherein the Q structures have lower energy than other structures.

An embodiment of the present invention provides a computer readable storage medium having a computer program stored thereon, which when executed by a processor implements the method for optimizing a DNN-TL-GA based metal cluster structure.

An embodiment of the invention provides a computer program product comprising a computer program which, when executed by a processor, implements the method for optimizing a DNN-TL-GA based metal cluster structure.

The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the specific details of the above embodiments, and various simple modifications can be made to the technical solution of the present invention within the scope of the technical concept of the present invention, and all the simple modifications belong to the protection scope of the present invention.

In addition, the specific features described in the above embodiments may be combined in any suitable manner, and in order to avoid unnecessary repetition, various possible combinations are not described further.

Those skilled in the art will appreciate that all or part of the steps in implementing the methods of the embodiments described above may be implemented by a program stored in a storage medium, including instructions for causing a single-chip microcomputer, chip or processor (processor) to perform all or part of the steps of the methods of the embodiments described herein. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.

Moreover, any combination of the various embodiments of the invention can be made without departing from the spirit of the invention, which should also be considered as disclosed herein.

Claims

1. A method for optimizing a metal cluster structure based on DNN-TL-GA, comprising:

Generating a first sample set by adopting a genetic algorithm and a first DFT local optimization method according to an initial structure of a metal cluster, wherein the first sample set comprises a progeny structure of a former S generation of DFT local optimization and corresponding energy;

Training a pre-trained DNN by using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-size metal cluster by adopting a migration learning method;

according to the offspring structure of the former S generation of the DFT local optimization, adopting the genetic algorithm and the first DNN model to obtain offspring structures of the S+1st to T generation of the DNN local optimization; and

And selecting Q structures from the offspring structures of the former S generation of the DFT local optimization and the offspring structures of the S+1st to T generation of the DNN local optimization, wherein the energy of the Q structures is lower than that of other structures.

2. The optimization method of claim 1, wherein the generating the first sample set comprises:

generating an initial offspring structure of the former S generation by adopting the genetic algorithm according to the initial structure of the metal cluster; and

And processing the offspring structure of the initial previous generation by adopting the first DFT local optimization method.

3. The optimization method according to claim 1, wherein the obtaining the offspring structures of the s+1st to T generation of the DNN local optimization includes:

generating initial S+1st generation to T generation offspring structures by adopting the genetic algorithm according to the previous S generation offspring structures locally optimized by DFT; and

And adopting the first DNN model to locally optimize the offspring structures from the initial S+1st generation to the T generation.

4. The optimization method according to any one of claims 1 to 3, characterized in that after the step of obtaining the offspring structures of the s+1st to T-th generations of the DNN local optimization is performed, the optimization method further comprises:

Generating a second sample set according to the progeny structure of the previous S generation of the DFT local optimization and the progeny structures of the (S+1) -th generation to the (T) -th generation of the DNN local optimization by adopting the genetic algorithm, the first DNN model and a second DFT local optimization method, wherein the second sample set comprises the progeny structures of the (T+1) -th generation to the (U) -th generation of the DFT local optimization and corresponding energy;

Processing the first DNN model by adopting the transfer learning method to obtain a second DNN model to be trained, and training the second DNN model to be trained by using the first sample set and the second sample set to obtain a second DNN model;

Obtaining the offspring structures of the (U+1) -th generation and the (V) -th generation of the DNN local optimization by adopting the genetic algorithm and the second DNN model according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization and the offspring structures of the (T+1) -th generation and the U-th generation of the DFT local optimization,

The selecting Q structures includes: and selecting the Q structures from the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the S+1st generation to the T generation of the DNN local optimization, the offspring structures of the T+1st generation to the U generation of the DFT local optimization and the offspring structures of the U+1st generation to the V generation of the DNN local optimization.

5. The optimization method of claim 4, wherein the generating the second sample set comprises:

Generating initial T+1th to U generation offspring structures by adopting the genetic algorithm according to the DFT locally optimized former S generation offspring structure and DNN locally optimized S+1th to T generation offspring structures;

pre-optimizing the offspring structures from the initial T+1st generation to the U generation by adopting the first DNN model; and

And processing the pre-optimized offspring structure by adopting the second DFT local optimization method.

6. The optimization method according to claim 4, wherein the obtaining the offspring structures of the u+1th to V th generations of the DNN local optimization includes:

Generating the offspring structures of the (U+1) -th generation and the (V) th generation by adopting the genetic algorithm according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization and the offspring structures of the (T+1) -th generation and the U generation of the DFT local optimization; and

And adopting the second DNN model to locally optimize the offspring structures from the (U+1) th generation to the (V) th generation.

7. The optimizing method according to claim 4, characterized in that, after the step of obtaining the offspring structures of the u+1th to V th generations of the DNN partial optimization is performed, the optimizing method further comprises:

Generating a third sample set according to the progeny structure of the former S generation of the local optimization of the DFT, the progeny structure of the s+1st to T generation of the local optimization of the DNN, the progeny structure of the t+1st to U generation of the local optimization of the DFT and the progeny structure of the u+1st to V generation of the local optimization of the DNN by adopting the genetic algorithm, the second DNN model and a third DFT local optimization method, wherein the third sample set comprises the progeny structure of the v+1st to W generation of the local optimization of the DFT and corresponding energy;

Processing the second DNN model by adopting the transfer learning method to obtain a third DNN model to be trained, and training the third DNN model to be trained by using the first sample set, the second sample set and the third sample set to obtain a third DNN model;

obtaining the offspring structures of the (W+1) -th generation and the (X) -th generation of the DNN local optimization by adopting the genetic algorithm and the third DNN model according to the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the (S+1) -th generation and the T generation of the DNN local optimization, the offspring structures of the (U+1) -th generation and the V generation of the DNN local optimization and the offspring structures of the (V+1) -th generation and the W generation of the DFT local optimization,

The selecting Q structures includes: and selecting the Q structures from the offspring structures of the former S generation of the DFT local optimization, the offspring structures of the S+1st generation to the T generation of the DNN local optimization, the offspring structures of the T+1st generation to the U generation of the DFT local optimization, the offspring structures of the U+1st generation to the V generation of the DNN local optimization, the offspring structures of the V+1st generation to the W generation of the DFT local optimization and the offspring structures of the W+1st generation to the X generation of the DNN local optimization.

8. The optimization method of claim 7, wherein after performing the step of selecting the Q structures, the optimization method further comprises: processing the Q structures by adopting a fourth DFT local optimization method to obtain a global optimal structure of the metal cluster,

9. A system for optimizing a DNN-TL-GA based metal cluster structure, the system comprising:

The generation device is used for generating a first sample set by adopting a genetic algorithm and a first DFT local optimization method according to the initial structure of the metal cluster, wherein the first sample set comprises a progeny structure of a former S generation of DFT local optimization and corresponding energy;

The model acquisition device is used for training the pre-trained DNN by using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing the trained DNN model of the small-size metal cluster by adopting a migration learning method;

The structure acquisition device is used for acquiring the S+1st to T generation of the offspring structure of the DNN local optimization by adopting the genetic algorithm and the first DNN model according to the offspring structure of the former S generation of the DFT local optimization; and

And the structure selection device is used for selecting Q structures from the progeny structures of the former S generation of the DFT local optimization and the progeny structures of the S+1st to T generation of the DNN local optimization, wherein the energy of the Q structures is lower than that of other structures.

10. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a computer program which, when executed by a processor, implements the method for optimizing a DNN-TL-GA based metal cluster structure according to any one of claims 1 to 8.

11. A computer program product, characterized in that the computer program product comprises a computer program which, when executed by a processor, implements the method for optimizing a DNN-TL-GA based metal cluster structure according to any one of claims 1 to 8.