CN115270593A - Multi-physical-field model separation type solving method based on deep learning - Google Patents

Multi-physical-field model separation type solving method based on deep learning Download PDF

Info

Publication number
CN115270593A
CN115270593A CN202210556874.XA CN202210556874A CN115270593A CN 115270593 A CN115270593 A CN 115270593A CN 202210556874 A CN202210556874 A CN 202210556874A CN 115270593 A CN115270593 A CN 115270593A
Authority
CN
China
Prior art keywords
neural network
equation set
loss function
physical
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210556874.XA
Other languages
Chinese (zh)
Inventor
仲林林
吴冰钰
王逸凡
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southeast University
Original Assignee
Southeast University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southeast University filed Critical Southeast University
Priority to CN202210556874.XA priority Critical patent/CN115270593A/en
Publication of CN115270593A publication Critical patent/CN115270593A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Artificial Intelligence (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Computing Systems (AREA)
  • Medical Informatics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Computer Hardware Design (AREA)
  • Geometry (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Biomedical Technology (AREA)
  • Biophysics (AREA)
  • Computational Linguistics (AREA)
  • General Health & Medical Sciences (AREA)
  • Molecular Biology (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a deep learning-based multi-physical field model separation type solving method which can be used for numerical calculation of a multi-physical field equation set. The invention comprises the following steps: establishing a multi-physical field equation set model, and taking physical laws contained in the multi-physical field equation set as prior information of the deep neural network; establishing a deep learning separated neural network based on a multi-physical field equation set model; constructing a loss function by taking an equation, corresponding boundary conditions and initial conditions as the basis, and selecting neural network parameters which accord with model complexity; the neural network training solves the numerical solution of the multi-physical field equation set, new loss function values are continuously obtained during the training, and after the new loss function values converge to a given threshold value, the training is finished, so that the problem of low precision when the high-dimensional problem is solved by the traditional method is solved.

Description

Multi-physical-field model separation type solving method based on deep learning
Technical Field
The invention relates to the technical field of artificial intelligence and multi-physical-field modeling, in particular to a multi-physical-field model separation type solving method based on deep learning.
Background
The multi-physical field system is a coupling system with more than one physical field variable, in the multi-physical field, all physical fields are mutually superposed and mutually influenced, and the research on the multi-physical field is to research the relationship among a plurality of physical attributes of interaction. For example, natural convection heat transfer studies the relationship between pressure field, velocity field, temperature field, and magnetohydrodynamics studies the relationship between magnetic field, electric field, fluid field. As a research field across subjects, the multi-physics field covers various subjects including mathematics, physics, engineering, electromagnetism, and the like. When a multi-physical field model is established, a corresponding partial differential equation is established according to each physical field, and finally the equations are simultaneously established to form a multi-physical field equation set.
Numerical simulation is a common method for solving a multi-physics model and a multi-physics equation set behind the multi-physics model, and comprises finite difference, finite element, finite volume method and the like. However, such conventional methods all have certain defects, for example, the results depend on grid division, and the problem of low precision exists when solving a high-dimensional problem. The deep neural network is used as a strong nonlinear mapping tool and has great potential for solving a multi-physics field equation set. When it is desirable to use as little computational resources as possible, a separate deep neural network can be used to solve the multi-physics field equation set.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides a multi-physical-field model separation type solving method based on deep learning, and solves the problem of low precision when a high-dimensional problem is solved by using a traditional method.
(II) technical scheme
In order to achieve the purpose, the invention is realized by the following technical scheme: a multi-physical-field model separation type solving method based on deep learning specifically comprises the following steps:
the method comprises the following steps: establishing a multi-physical field equation set model, and taking physical laws contained in the multi-physical field equation set as prior information of the deep neural network;
step two: establishing a deep learning separated neural network based on a multi-physical field equation set model;
step three: constructing a loss function by taking an equation and corresponding boundary conditions and initial conditions as the basis, selecting parameters (including but not limited to the number of layers, the number of neurons and the learning rate of the neural network, and the parameters can be obtained by automatic machine learning) such as the number of layers of the neural network which accords with the complexity of the model, and obtaining the parameters by the automatic machine learning;
step four: and (3) training the neural network to solve the numerical solution of the multi-physical-field equation set, continuously obtaining a new loss function value during training, and finishing the training when the value is converged to a given threshold value.
Preferably, in the first step, the corresponding multiple physical field equation set model is established according to a specific problem; the corresponding multi-physics field equation set model is rewritten into the following general formula:
Figure BDA0003652569730000021
the boundary conditions are as follows:
Figure BDA0003652569730000022
the initial conditions were:
Figure BDA0003652569730000023
where X (X, t) is an input quantity, X is a space quantity, t is an amount of time, um (m =1,2, …, N) is a solution to the system of equations, the specific meaning depending on the type of the corresponding multiphysics equation, Nm[·；λm]Is a non-linear calculation parameterized by mIn the case of a hybrid vehicle,
Figure BDA0003652569730000024
is the corresponding boundary value, betamIs the corresponding initial value.
Preferably, in the second step, a type of the deep neural network is selected, and a separate deep neural network is constructed according to the multiphysics equation set, wherein the type of the neural network is not fixed, and includes but is not limited to a feedforward neural network, a convolutional neural network, and a cyclic neural network.
Preferably, n neural networks are constructed according to the selected neural network type, the independent variables of the equation set are used as the input quantity of each neural network according to the multi-physical field equation set, and the solved quantity of the equation set is respectively used as the output quantity of each neural network according to the multi-physical field equation set.
Preferably, in step three, a sufficiently smooth activation function is selected, a loss function is constructed according to the multiphysics equation set, the boundary condition and the initial condition, the number of layers of the neural network and the number of neurons in each layer which meet the complexity of the model are selected, and the parameters can be obtained through automatic machine learning.
Preferably, the first part of the loss function is constructed from the respective multiphysics equations
Figure BDA0003652569730000031
Constructing a second part of the loss function based on the boundary conditions
Figure BDA0003652569730000032
Constructing a third part of the loss function based on the initial conditions
Figure BDA0003652569730000033
Separately constructing loss functions of each neural network
Figure BDA0003652569730000034
Preferably, the
Figure BDA0003652569730000035
The calculation formula is as follows:
Figure BDA0003652569730000036
where Nf is the number of sample points in the computational domain and Ψ is the activation function;
the above-mentioned
Figure BDA0003652569730000037
The calculation formula is as follows:
Figure BDA0003652569730000038
where Nb is the number of sample points in the boundary domain and Ψ is the activation function;
the above-mentioned
Figure BDA0003652569730000039
The calculation formula is as follows:
Figure BDA00036525697300000310
where Ni is the number of sample points in the boundary domain and Ψ is the activation function.
Preferably, the fourth step comprises the following steps:
s1, training a neural network once to obtain an output value;
s2, calculating a loss function value of the first neural network;
s3, updating the weight of the neural network by using a gradient optimization algorithm;
s4, repeating the steps S1-S3a times, changing the step 42 into calculating the loss function value of a second neural network, repeating the steps S1-S3a times, and so on until the loss functions of n neural networks are trained, wherein a is more than or equal to 1;
s5, repeating the steps 41-44, and observing the loss function value of the neural network until the loss function value is reduced to a given threshold value;
s6, observing the L2 norm error value of the neural network until the error value is reduced to a given threshold value, wherein the L2 norm is the distance between two points in the feature space, and if a point A (x) exists in the space1,y1)，B(x2,y2) Then A, B two points have an L2 norm error of:
Figure BDA0003652569730000041
and S7, obtaining the output of the neural network, namely the numerical solution of the corresponding multi-physical field equation.
Preferably, the update method of the neural network weight is that the gradient optimization algorithm updates only the weight of the neural network corresponding to the loss function.
Preferably, the update method of the neural network weights updates the weights of all the neural networks by a gradient optimization algorithm.
(III) advantageous effects
After the scheme is adopted, the invention utilizes the separated neural network architecture to solve the accurate solution of the multi-physical field equation set, solves the defect that the conventional numerical calculation method depends on grid division and high-order solution needs a large amount of iteration, can effectively train a corresponding mapping set from limited data samples, and solves the problem of low accuracy in the traditional method for solving the high-dimensional problem.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a neural network for solving a 1-dimensional transient arc model in an implementation;
FIG. 3 is a diagram illustrating a comparison of neural network training results and finite element method calculations in an exemplary embodiment;
FIG. 4 is a diagram illustrating a comparison between the neural network training results and the finite element method calculations in an exemplary embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Examples
As shown in fig. 1 to 4, the present invention provides a method for solving a multi-physics model by a separation method based on deep learning, which specifically includes the following steps:
the method comprises the following steps: establishing a multi-physical field equation set model, and taking physical laws contained in the multi-physical field equation set as prior information of the deep neural network;
step two: establishing a deep learning separated neural network based on a multi-physical field equation set model;
step three: constructing a loss function based on an equation and corresponding boundary conditions and initial conditions, selecting parameters (including but not limited to the number of layers, the number of neurons and learning rate of the neural network, and the parameters can be obtained by automatic machine learning) such as the number of layers of the neural network which accord with the complexity of the model, and obtaining the parameters by the automatic machine learning;
step four: and (3) training the neural network to solve the numerical solution of the multi-physical-field equation set, continuously obtaining a new loss function value during training, and finishing the training when the value is converged to a given threshold value.
Further, in the step one, establishing a corresponding multi-physics field equation set model according to a specific problem; the corresponding multi-physics field equation set model is rewritten into the following general formula:
Figure BDA0003652569730000061
the boundary conditions are as follows:
Figure BDA0003652569730000062
the initial conditions were:
Figure BDA0003652569730000063
where X (X, t) is an input quantity, X is a space quantity, t is an amount of time, um (m =1,2, …, N) is a solution to the system of equations, the specific meaning depending on the type of the corresponding multiphysics equation, Nm[·；λm]Is a non-linear operator parameterized by lambdam,
Figure BDA0003652569730000064
is the corresponding boundary value, betamIs the corresponding initial value.
Further, in step two, a type of the deep neural network is selected, and a separate deep neural network is constructed according to the multi-physics field equation set, wherein the type of the neural network is not fixed, and the neural network comprises but is not limited to a feedforward neural network, a convolution neural network and a circular neural network.
Furthermore, n neural networks are constructed according to the selected neural network type, the independent variables of the equation set are used as the input quantity of each neural network according to the multi-physical field equation set, and the solved quantity of the equation set is respectively used as the output quantity of each neural network according to the multi-physical field equation set.
Further, in the third step, a fully smooth activation function is selected, a loss function is constructed according to the multi-physics field equation set, the boundary condition and the initial condition, the number of the layers of the neural network and the number of the neurons in each layer which meet the complexity of the model are selected, and the parameters can be obtained through automatic machine learning.
Further, a first portion of the loss function is constructed from the respective multiphysics equations
Figure BDA0003652569730000065
Constructing a second part of the loss function based on the boundary conditions
Figure BDA0003652569730000071
Constructing a loss function from each initial conditionThird part of (2)
Figure BDA0003652569730000072
Separately constructing loss functions of each neural network
Figure BDA0003652569730000073
Further, the
Figure BDA0003652569730000074
The calculation formula is as follows:
Figure BDA0003652569730000075
where Nf is the number of sample points in the computational domain and Ψ is the activation function;
the above-mentioned
Figure BDA0003652569730000076
The calculation formula is as follows:
Figure BDA0003652569730000077
where Nb is the number of sample points in the boundary domain and Ψ is the activation function;
the above-mentioned
Figure BDA0003652569730000078
The calculation formula is as follows:
Figure BDA0003652569730000079
where Ni is the number of sample points in the boundary domain and Ψ is the activation function.
Further, the fourth step includes the following steps:
s1, training a neural network once to obtain an output value;
s2, calculating a loss function value of the first neural network;
s3, updating the weight of the neural network by using a gradient optimization algorithm;
step S4, after repeating the steps S1-S3a times, changing the step 42 into calculating the loss function value of a second neural network, repeating the steps S1-S3a times, and so on until the loss functions of n neural networks are trained, wherein a is more than or equal to 1;
s5, repeating the steps 41-44, and observing the loss function value of the neural network until the loss function value is reduced to a given threshold value;
s6, observing the L2 norm error value of the neural network until the error value is reduced to a given threshold value, wherein the L2 norm is the distance between two points in the feature space, and if a point A (x) exists in the space1,y1)，B(x2,y2) Then A, B two points have an L2 norm error of:
Figure BDA0003652569730000081
and S7, obtaining the output of the neural network, namely the numerical solution of the corresponding multi-physical field equation.
Further, the updating method of the neural network weight is that the gradient optimization algorithm updates only the weight of the neural network corresponding to the loss function.
Further, the updating method of the neural network weight updates the weights of all the neural networks for the gradient optimization algorithm
As shown in fig. 1-2, an embodiment of the present invention provides a method for solving a multi-physical field model by a separation method based on deep learning, in which a 1-dimensional transient arc is used as a research object, and a numerical solution of a 1-dimensional transient arc equation is calculated by a separation method.
The method shows a flow chart of a 1-dimensional transient arc multi-physics field model separation type solving method based on deep learning, and the method comprises the following steps:
(1) Establishing a multi-physical field equation set model of the 1-dimensional transient electric arc;
(11) Establishing a 1-dimensional arc equation model based on a mass conservation equation, an energy conservation equation and an ohm's law equation:
Figure BDA0003652569730000082
Figure BDA0003652569730000083
the equation group separates two physical fields of a speed field and a temperature field;
(12) The corresponding 1-dimensional transient arc equation model is rewritten into the following general form:
Figure BDA0003652569730000084
Figure BDA0003652569730000085
the boundary conditions are as follows:
T|r＝R＝Tb
Figure BDA0003652569730000091
where ρ is the density, t is the time, r is the arc radius, vrIs the arc velocity, CpIs the specific heat, T is the temperature, σ is the electrical conductivity, g is the arc conductance, k is the thermal conductivity, EradIs the loss of energy, T, by radiationbFor a given boundary temperature value for R = R, the parameters λ representing the plasma properties are: σ, k, Erad。
(2) Establishing a deep learning-based separate neural network framework based on the multi-physics field equation set in the step (1), wherein the deep learning-based separate neural network framework is shown in figure 2;
(21) Selecting a neural network type, such as a feed-forward neural network;
(22) Constructing a coupling type deep neural network according to a multi-physical field equation set;
(221) Constructing two neural networks based on the neural network type selected in the step (21);
(222) According to the multi-physical field equation set, taking independent variables r and t of the equation set as input quantities of each neural network;
(223) According to the multi-physical-field equation set, the solution quantity T of the equation set is used as an output value of a first neural network, and the solution quantity v of the equation set is used as an output value of a second neural network.
(3) Constructing a loss function by taking Cheng Dengshi and corresponding boundary conditions and initial conditions as a basis, and selecting parameters such as the layer number of the neural network which accords with the complexity of the model;
(31) Selecting an activation function, such as the Huber function:
Figure BDA0003652569730000092
(32) Constructing a loss function according to a multi-physical field equation set, boundary conditions and initial conditions;
(321) Constructing a first portion of a loss function from each of the multiple physical field equations
Figure BDA0003652569730000093
The calculation formula is as follows:
Figure BDA0003652569730000101
Figure BDA0003652569730000102
where Nf is the number of sample points in the computational domain and Ψ is the huber function;
(322) Constructing a second part of the loss function based on the boundary conditions
Figure BDA0003652569730000103
The calculation formula is as follows:
Figure BDA0003652569730000104
Figure BDA0003652569730000105
where Nb is the number of samples in the boundary domain;
(323) Constructing a third part L of the loss function from the initial conditionsiThere is no initial condition in the case of a 1-dimensional transient arc, so Li =0;
(324) Constructing a loss function of each neural network:
Figure BDA0003652569730000106
Figure BDA0003652569730000107
(33) The number of layers of the neural network and the number of neurons in each layer are selected as appropriate.
(4) The neural network training solves the numerical solution of the multi-physical field equation set, new loss function values are continuously obtained during the training, and after the new loss function values converge to a certain threshold value, the training is finished, so that the deep neural network solution of the multi-physical field equation set model is realized;
(41) Training the neural network once to obtain an output value;
(42) Calculating a loss function value of the first neural network;
(43) Updating the weight of the neural network corresponding to the loss function by using a gradient optimization algorithm;
(44) Repeating the steps 41-43a times, changing the step 42 into calculating the loss function value of the second neural network, repeating the steps 41-43a times, and so on until the loss functions of the n neural networks are trained;
(45) Repeating steps 41-44, and observing the loss function value of the neural network until the loss function value of the neural network drops to a given threshold value;
(46) Observing the error value of the L2 norm of the neural network until the error value drops to a given threshold, wherein the L2 norm is the distance between two points in the feature space if a point A (x) exists in the space1,y1)，B(x2,y2) Then A, B two points have an L2 norm error of:
Figure BDA0003652569730000111
the output of the neural network, i.e. the numerical solution corresponding to the multi-physical field equation, is obtained as the result of solving the temperature and the speed when t =0.5s as shown in fig. 3 and 4.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.

Claims (10)

1. A multi-physical-field model separation type solving method based on deep learning is characterized by comprising the following steps:
the method comprises the following steps: establishing a multi-physical field equation set model, and taking physical laws contained in the multi-physical field equation set as prior information of the deep neural network;
step two: establishing a deep learning separated neural network based on a multi-physical field equation set model;
step three: constructing a loss function by taking an equation, corresponding boundary conditions and initial conditions as the basis, and selecting neural network parameters which accord with model complexity;
step four: and (3) training the neural network to solve the numerical solution of the multi-physical-field equation set, continuously obtaining a new loss function value during training, and finishing the training when the value is converged to a given threshold value.
2. The method for solving the multi-physics field model separation formula based on the deep learning of claim 1, is characterized in that: the establishing of the multi-physical field equation set model, taking the physical laws contained in the multi-physical field equation set as the prior information of the deep neural network, specifically comprises:
establishing a corresponding multi-physical field equation set model according to a specific problem; the corresponding multi-physics field equation set model is rewritten into the following general formula:
Figure FDA0003652569720000011
the boundary conditions are as follows:
Figure FDA0003652569720000012
the initial conditions were:
Figure FDA0003652569720000013
where X (X, t) is an input quantity, X is a space quantity, t is an amount of time, um (m =1,2, …, N) is a solution to the system of equations, the specific meaning depending on the type of the corresponding multiphysics equation, Nm[·；λm]Is a non-linear operator parameterized by lambdam,
Figure FDA0003652569720000021
is the corresponding boundary value, betamIs the corresponding initial value.
3. The method for solving the multi-physics field model separation formula based on the deep learning of claim 1, is characterized in that: the method for establishing the deep learning separated neural network based on the multi-physics field equation set model specifically comprises the following steps:
selecting a type of deep neural network, and constructing a separated deep neural network according to the multi-physical field equation set, wherein the type of the neural network is not fixed and includes but is not limited to a feedforward neural network, a convolution neural network and a cyclic neural network. For a one-dimensional equation, a feedforward neural network is generally selected; for a two-dimensional equation, a convolutional neural network may be selected; while a recurrent neural network is generally chosen for equations with time-varying terms.
4. The method for solving the multi-physics model separating formula based on the deep learning of claim 3, wherein: the architecture of the separated deep neural network is as follows: constructing n neural networks according to the selected neural network types, taking the independent variable of the equation set as the input quantity of each neural network according to the multi-physical field equation set, and taking the solution quantity of the equation set as the output quantity of each neural network respectively according to the multi-physical field equation set.
5. The method for solving the multi-physics model separation formula based on the deep learning of claim 1, wherein: the method for constructing the loss function by taking the equation, the corresponding boundary condition and the initial condition as the basis and selecting the neural network parameters conforming to the model complexity specifically comprises the following steps:
and selecting a fully smooth activation function, constructing a loss function according to the multi-physics field equation set, the boundary condition and the initial condition, selecting the number of the neural network layers and the number of neurons of each layer which meet the complexity of the model, and obtaining the parameters through automatic machine learning.
6. The method for solving the multi-physics field model separation formula based on the deep learning of claim 5, is characterized in that: according to the equation of each multi-physical fieldConstructing a first part of a loss function
Figure FDA0003652569720000022
Constructing a second part of the loss function based on the boundary conditions
Figure FDA0003652569720000031
Constructing a third part of the loss function based on the initial conditions
Figure FDA0003652569720000032
Separately constructing loss functions for each neural network
Figure FDA0003652569720000033
7. The method for solving the multi-physics field model separation formula based on the deep learning of claim 6, is characterized in that: the above-mentioned
Figure FDA0003652569720000034
The calculation formula is as follows:
Figure FDA0003652569720000035
where Nf is the number of sample points in the computational domain and Ψ is the activation function;
the above-mentioned
Figure FDA0003652569720000036
The calculation formula is as follows:
Figure FDA0003652569720000037
where Nb is the number of sample points in the boundary domain and Ψ is the activation function;
the above-mentioned
Figure FDA0003652569720000038
The calculation formula is as follows:
Figure FDA0003652569720000039
where Ni is the number of sample points in the boundary domain and Ψ is the activation function.
8. The method for solving the separating type of the multi-physics field model based on the deep learning of claim 1, wherein the neural network training is used for solving the numerical solution of the multi-physics field equation set, new loss function values are continuously obtained during the training, and after the new loss function values converge to a given threshold value, the training is finished, specifically comprising the following steps:
s1, training a neural network once to obtain an output value;
s2, calculating a loss function value of a first neural network;
s3, updating the weight of the neural network by using a gradient optimization algorithm;
step S4, after repeating the steps S1-S3a times, changing the step 42 into calculating the loss function value of a second neural network, repeating the steps S1-S3a times, and so on until the loss functions of n neural networks are trained, wherein a is more than or equal to 1;
s5, repeating the steps S1-S4, and observing the loss function value of the neural network until the loss function value is reduced to a given threshold value;
s6, observing the L2 norm error value of the neural network until the error value is reduced to a given threshold value, wherein the L2 norm is the distance between two points in the feature space, and if a point A (x) exists in the space1,y1)，B(x2,y2) Then A, B two points have an L2 norm error of:
Figure FDA0003652569720000041
9. the method for solving the multi-physics field model separation formula based on the deep learning of claim 8, wherein: the updating method of the neural network weight is that the gradient optimization algorithm only updates the weight of the neural network corresponding to the loss function.
10. The method for solving the multi-physics field model separation formula based on the deep learning of claim 8, wherein: the updating method of the neural network weight is used for updating the weights of all the neural networks by a gradient optimization algorithm.
CN202210556874.XA 2022-05-19 2022-05-19 Multi-physical-field model separation type solving method based on deep learning Pending CN115270593A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210556874.XA CN115270593A (en) 2022-05-19 2022-05-19 Multi-physical-field model separation type solving method based on deep learning

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210556874.XA CN115270593A (en) 2022-05-19 2022-05-19 Multi-physical-field model separation type solving method based on deep learning

Publications (1)

Publication Number Publication Date
CN115270593A true CN115270593A (en) 2022-11-01

Family

ID=83759954

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210556874.XA Pending CN115270593A (en) 2022-05-19 2022-05-19 Multi-physical-field model separation type solving method based on deep learning

Country Status (1)

Country Link
CN (1) CN115270593A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116777010A (en) * 2023-08-25 2023-09-19 之江实验室 Model training method and task execution method and device
CN117057238A (en) * 2023-08-15 2023-11-14 天津大学 Combustor stable combustion blunt body design method based on physical information operator network model

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117057238A (en) * 2023-08-15 2023-11-14 天津大学 Combustor stable combustion blunt body design method based on physical information operator network model
CN117057238B (en) * 2023-08-15 2024-04-19 天津大学 Combustor stable combustion blunt body design method based on physical information operator network model
CN116777010A (en) * 2023-08-25 2023-09-19 之江实验室 Model training method and task execution method and device
CN116777010B (en) * 2023-08-25 2023-12-19 之江实验室 Model training method and task execution method and device

Similar Documents

Publication Publication Date Title
CN115270593A (en) Multi-physical-field model separation type solving method based on deep learning
CN108284442A (en) A kind of mechanical arm flexible joint control method based on fuzzy neural network
CN113190688B (en) Complex network link prediction method and system based on logical reasoning and graph convolution
CN111127246A (en) Intelligent prediction method for transmission line engineering cost
Liu et al. A fault diagnosis intelligent algorithm based on improved BP neural network
CN111292525A (en) Traffic flow prediction method based on neural network
CN112255095A (en) Soil stress-strain relation determining method
CN106981097A (en) A kind of T spline surface approximating methods based on subregion Local Fairing weight factor
CN104050505A (en) Multilayer-perceptron training method based on bee colony algorithm with learning factor
Mousavi et al. Robust filtering of extended stochastic genetic regulatory networks with parameter uncertainties, disturbances, and time-varying delays
CN111738412A (en) Big data exception mining method, system and storage medium for incomplete network
CN111638648A (en) Distributed pulse quasi-synchronization method with proportional delay complex dynamic network
CN101893852B (en) Multi-target modeling method for complex industrial process
CN115146527A (en) Multi-physical-field model coupling solving method based on deep learning
Zhang et al. Distributed consensus-based boundary observers for freeway traffic estimation with sensor networks
Zhu et al. Structural safety monitoring of high arch dam using improved ABC-BP model
Singh et al. Identification and control of a nonlinear system using neural networks by extracting the system dynamics
CN111079279A (en) Multi-scale topological optimization design method for multi-configuration lattice structure
Bouaziz et al. Evolving flexible beta basis function neural tree for nonlinear systems
CN107563103B (en) Consistency filter design method based on local conditions
CN114329320A (en) Partial differential equation numerical solution method based on heuristic training data sampling
CN106022482A (en) Method for decoupling bed temperature and bed pressure of circulating fluidized bed by use of improved fuzzy neural network
Sóbester et al. Genetic programming approaches for solving elliptic partial differential equations
CN114254416A (en) Soil stress-strain relation determination method based on long-term and short-term memory deep learning
CN113657029A (en) Efficient approximate optimization method for aircraft driven by heterogeneous data

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination