CN113987806B - Atmosphere mode optimization method based on proxy model - Google Patents
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Abstract
The invention is applicable to the field of agent models, and provides an atmosphere mode optimization method based on an agent model, which discloses an atmosphere mode parameter optimization method based on the agent model, and the field of parameter optimization is designed, and the method comprises the following steps: determining a parameter range, sampling, simulating the results of each sample by using an atmospheric mode, taking Root Mean Square Error (RMSE) as an evaluation standard of an atmospheric mode output result, fitting a functional relation between the sample and the mode result by constructing a proxy model, searching an optimal value of the proxy model by using a PSO particle swarm algorithm, carrying out verification in the atmospheric mode, and continuously and iteratively updating the proxy model until the final parameter tuning result is output according to the tuning requirement. The invention reduces the resource expenditure by applying the thought of the agent model to the parameter tuning of the atmosphere mode; meanwhile, the time consumption of the mode tuning is reduced, and the efficiency of the atmosphere mode parameter tuning is improved.
Description
Technical Field
The invention belongs to the field of agent models, and particularly relates to an atmosphere mode optimization method based on an agent model.
Background
The atmosphere mode is one of important components of the earth system mode, is an important tool for exploring weather rules and predicting weather changes, and simulates various physical and chemical changes of the earth through a nonlinear equation set; on the subgrid scale, some physical processes are represented in the form of parameters, so that the determination of the values of such parameters is critical in the running process of a mode, and small changes can cause great deviation of results, so that the adjustment of the values of the parameters is one of important conditions for the running stability and accuracy of the mode.
The parameter selection problem can be abstracted into a traditional parameter optimization problem, and research at home and abroad carries out a great deal of research and provides various optimization algorithms according to the characteristics and parameter meanings of the atmospheric mode, but the operation of the atmospheric mode is extremely high in cost, and from the scientific point of view, the atmospheric mode needs 3-5 years of integral stabilization time from a starting state to an equilibrium state; from the application point of view of the optimization algorithm, convergence conditions meeting the requirements are usually achieved, at least ten or more rounds of iteration are required. In such high overhead scenarios, the time overhead of iteratively obtaining the optimal solution by the optimization algorithm is often unacceptable.
The proxy model is an analysis model with small calculation amount, but the calculation result is similar to the calculation analysis result of the high-precision model. The method has wide application in a plurality of engineering fields, on one hand, the time cost of parameter tuning can be greatly reduced by using the proxy model, on the other hand, more efficient optimization algorithms can be applied to the parameter tuning of the atmosphere mode,
Aiming at the problems in the related technology, the research of applying the agent model to the optimization of the atmosphere mode parameters has not been developed at present.
Disclosure of Invention
The embodiment of the invention aims to provide an atmosphere mode optimization method based on a proxy model, and aims to solve the problem that the application of the proxy model to the research of atmosphere mode parameter tuning is not developed at present.
The embodiment of the invention is realized in such a way that the atmosphere mode optimization method based on the agent model comprises the following steps:
step one: determining optimal parameters and optimization targets, and determining upper and lower limits according to the selected parameters;
step two: sampling within a parameter range by utilizing Latin hypercube sampling;
Step three: the parameter samples obtained in the second step are sequentially brought into a parameter input list of the atmospheric mode, the atmospheric mode is started to be executed, after the atmospheric mode corresponding to each sampling value is executed, an output file of the atmospheric mode is read, the change of different samples to an optimization target is obtained, and the change level of each sample to the mode is judged by using Root Mean Square Error (RMSE);
step four: constructing a proxy model by using the data obtained in the third step;
Step five: searching an optimal solution of the agent model by using a particle swarm algorithm;
Step six: bringing the parameters represented by the solution in the fifth step back to the atmosphere mode to obtain a new set of values, and adding the set of values to a solution set for constructing a proxy model to update the proxy model;
Step seven: judging whether the result in the step six meets the optimization requirement, if not, respectively adding the parameters in the step six and the RMSE simulated by the atmospheric mode into the sample set S and the RMSE simulated by the air mode, updating the proxy model, and repeating the steps four to six;
step eight: and when the RMSE obtained in the step six meets the optimization standard, ending the tuning process, and outputting the parameters obtained at the moment, wherein the parameters are the final tuning realization result.
According to a further technical scheme, according to the second step, latin hypercube sampling is performed as follows:
Step 201: firstly, determining the number N of samples, namely the number of samples to be extracted;
step 202: dividing the interval (0, 1) into N sections equally;
Step 203: randomly extracting a value for each of the N segments;
step 204: mapping the extracted value into a standard normal distribution sample through an inverse function of the standard normal distribution;
step 205: and (5) disturbing the sampling sequence to obtain a final sampling result.
According to a further technical scheme, according to the third step, the method for calculating the RMSE comprises the following steps:
Where N represents the result of the nth set of samples, the value range is between 1 and N, m represents the total number of grid points of the optimization area, y i represents the result of the target simulated in the ith grid point mode, and y o,i represents the value of the observed data in the ith grid point.
According to a further technical scheme, according to the fourth step, the method of the proxy model is as follows:
401: the polynomial proxy model is exemplified by a second order polynomial, and the expression is as follows:
wherein, beta represents a coefficient to be estimated, and d is the number of parameters;
402: the Kriging proxy model has the expression:
y＝f(x)Tβl+zl(x)，l＝1，2，...，q
where β is a regression coefficient of a polynomial, the polynomial f (x) may be of any order, z (x) is a random process, and its mean E [ z (x) ]=0;
403: the RBF proxy model has the expression:
Wherein i=1 to n represent response values of the sample points i, ω i represents an i-th sample point weight coefficient, r i is a euclidean distance between a to-be-measured point and the i-th sample point, r i＝∥y-yi∥,φ(ri) is a mirror function, and typically is a Guass function: phi (r) = -r 2/c2, where c is a coefficient.
According to a further technical scheme, according to the fifth step, the particle swarm algorithm comprises the following steps:
Step 5.1: randomly initializing each particle;
step 5.2: calculating the adaptive value of each particle, wherein the adaptive value in the problem is a proxy model Output results of (2);
step 5.3: acquiring an individual optimal value of the particle, and updating the individual optimal value of the particle if the adaptive value of the particle obtained in the step 5.2 is better than the original optimal value of the particle;
step 5.4: acquiring a global optimal value of the particle, and if the adaptive value of the particle obtained in the step 5.3 is better than the global optimal value, updating the global optimal value;
Step 5.5: the speed and position of each are updated as follows:
vi＝vi+c1*rand*(pbesti-xi)+c2*rand*(gbest-xi)
xi＝xi+vi
Wherein v i represents the speed of the ith particle, c 1 and c 2 are self-learning factors and population learning factors, are two constants, rand is a random number between 0 and 1, pbest i is the individual optimum value of the ith particle, gbest is the global optimum value of the particle, and x i represents the current position of the ith particle;
step 5.6: judging whether convergence conditions are met, and if not, returning to the step 5.2;
step 5.7: and obtaining an optimal solution.
According to a further technical scheme, according to the second step, the hierarchical sampling mode is random hierarchical sampling.
According to a further technical scheme, according to the fifth step, the solution of the agent model is the optimal solution.
The embodiment of the invention provides an atmosphere mode optimization method based on a proxy model, which discloses an atmosphere mode parameter optimization method based on the proxy model, and relates to the field of parameter optimization, comprising the following steps of: determining a parameter range, sampling, simulating the results of each sample by using an atmospheric mode, taking Root Mean Square Error (RMSE) as an evaluation standard of an atmospheric mode output result, fitting a functional relation between the sample and the mode result by constructing a proxy model, searching an optimal value of the proxy model by using a PSO particle swarm algorithm, carrying out verification in the atmospheric mode, and continuously and iteratively updating the proxy model until the final parameter tuning result is output according to the tuning requirement. According to the invention, the thought of the agent model is applied to parameter tuning of the atmospheric mode, so that the times of executing the atmospheric mode are effectively reduced, the resource expenditure is reduced, and the economic benefit is improved while the high-efficiency optimization algorithm is ensured; meanwhile, the time consumption of the mode tuning is reduced, and the efficiency of the atmosphere mode parameter tuning is improved.
Drawings
FIG. 1 is a schematic diagram of an optimization process according to an embodiment of the present invention;
fig. 2 is a schematic diagram of searching an optimal solution of a proxy model in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Specific implementations of the invention are described in detail below in connection with specific embodiments.
As shown in fig. 1 and 2, an atmospheric mode optimization method based on a proxy model according to an embodiment of the present invention includes the following steps:
step one: determining optimal parameters and optimization targets, and determining upper and lower limits according to the selected parameters;
step two: sampling within a parameter range by utilizing Latin hypercube sampling;
Step three: the parameter samples obtained in the second step are sequentially brought into a parameter input list of the atmospheric mode, the atmospheric mode is started to be executed, after the atmospheric mode corresponding to each sampling value is executed, an output file of the atmospheric mode is read, the change of different samples to an optimization target is obtained, and the change level of each sample to the mode is judged by using Root Mean Square Error (RMSE);
step four: constructing a proxy model by using the data obtained in the third step;
Step five: searching an optimal solution of the agent model by using a particle swarm algorithm;
Step six: the parameters represented by the optimal solution in the fifth step are brought back to the atmosphere mode to obtain a new group of values, and the group of values are added to a solution set for constructing the proxy model to update the proxy model;
Step seven: judging whether the result in the step six meets the optimization requirement, if not, respectively adding the parameters in the step six and the RMSE simulated by the atmospheric mode into the sample set S and the RMSE simulated by the air mode, updating the proxy model, and repeating the steps four to six;
step eight: and when the RMSE obtained in the step six meets the optimization standard, ending the tuning process, and outputting the parameters obtained at the moment, wherein the parameters are the final tuning realization result.
In the embodiment of the invention, the invention discloses an atmosphere mode parameter optimization method based on a proxy model, which belongs to the field of design parameter optimization and comprises the following steps of: determining a parameter range, sampling, simulating the results of each sample by using an atmospheric mode, taking Root Mean Square Error (RMSE) as an evaluation standard of an atmospheric mode output result, fitting a functional relation between the sample and the mode result by constructing a proxy model, searching an optimal value of the proxy model by using a PSO particle swarm algorithm, carrying out verification in the atmospheric mode, and continuously and iteratively updating the proxy model until the final parameter tuning result is output according to the tuning requirement. According to the invention, the thought of the agent model is applied to parameter tuning of the atmospheric mode, so that the times of executing the atmospheric mode are effectively reduced, the resource expenditure is reduced, and the economic benefit is improved while the high-efficiency optimization algorithm is ensured; meanwhile, the time consumption of the mode tuning is reduced, and the efficiency of the atmosphere mode parameter tuning is improved.
As shown in fig. 1 and 2, as a preferred embodiment of the present invention, according to step two, the step of latin hypercube sampling is as follows:
Step 201: firstly, determining the number N of samples, namely the number of samples to be extracted;
step 202: dividing the interval (0, 1) into N sections equally;
Step 203: randomly extracting a value for each of the N segments;
step 204: mapping the extracted value into a standard normal distribution sample through an inverse function of the standard normal distribution;
step 205: and (5) disturbing the sampling sequence to obtain a final sampling result.
As shown in fig. 1 and 2, as a preferred embodiment of the present invention, according to step three, the RMSE calculation method is as follows:
Where N represents the result of the nth set of samples, the value range is between 1 and N, m represents the total number of grid points of the optimization area, y i represents the result of the target simulated in the ith grid point mode, and y o,i represents the value of the observed data in the ith grid point.
As shown in fig. 1 and 2, as a preferred embodiment of the present invention, according to the fourth step, the method of the proxy model is as follows:
401: the polynomial proxy model is exemplified by a second order polynomial, and the expression is as follows:
wherein, beta represents a coefficient to be estimated, and d is the number of parameters;
402: the Kriging proxy model has the expression:
y＝f(x)Tβl+zl(x)，l＝1，2，...，q
where β is a regression coefficient of a polynomial, the polynomial f (x) may be of any order, z (x) is a random process, and its mean E [ z (x) ]=0;
403: the RBF proxy model has the expression:
Wherein i=1 to n represent response values of the sample points i, ω i represents an i-th sample point weight coefficient, r i is a euclidean distance between a to-be-measured point and the i-th sample point, r i＝∥y-yi∥,φ(ri) is a mirror function, and typically is a Guass function: phi (r) = -r 2/c2, where c is a coefficient.
As shown in fig. 1 and 2, as a preferred embodiment of the present invention, according to the fifth step, the particle swarm algorithm is as follows:
Step 5.1: randomly initializing each particle;
step 5.2: calculating the adaptive value of each particle, wherein the adaptive value in the problem is a proxy model Output results of (2);
step 5.3: acquiring an individual optimal value of the particle, and updating the individual optimal value of the particle if the adaptive value of the particle obtained in the step 5.2 is better than the original optimal value of the particle;
step 5.4: acquiring a global optimal value of the particle, and if the adaptive value of the particle obtained in the step 5.3 is better than the global optimal value, updating the global optimal value;
Step 5.5: the speed and position of each are updated as follows:
vi＝vi+c1*rand*(pbesti-xi)+c2*rand*(gbest-xi)
xi＝xi+vi
Wherein v i represents the speed of the ith particle, c 1 and c 2 are self-learning factors and population learning factors, are two constants, rand is a random number between 0 and 1, pbest i is the individual optimum value of the ith particle, gbest is the global optimum value of the particle, and x i represents the current position of the ith particle;
step 5.6: judging whether convergence conditions are met, and if not, returning to the step 5.2;
step 5.7: and obtaining an optimal solution.
As shown in fig. 1 and 2, as a preferred embodiment of the present invention, the sampling is performed in a random manner according to the second step.
As shown in fig. 1 and 2, as a preferred embodiment of the present invention, according to step five, the solution of the proxy model is the optimal solution.
In the embodiment of the invention, according to the embodiment of the invention, an atmosphere mode parameter tuning method based on a proxy model is provided, a Kriging proxy model is used, an atmosphere mode is used as an example, an atmosphere mode CAM5.3 of CESM1.3 is used as an example, global total precipitation is used as an optimization target, and the whole optimization process is described in fig. 1, and each optimization step is as follows:
Step one: determining global optimization targets as total precipitation, selecting the following six parameters, and determining upper and lower limits according to parameter meanings:
The parameter list and range are as follows:
| Parameter name | Default value | Lower limit of | Upper limit of |
| cldfrc_rhminl | 0.8975 | 0.80 | 0.99 |
| micro_mg_dcs | 5*10^-6 | 1*10^-6 | 5*10^-6 |
| zmconv_dmpdz | -1.0*10^-3 | -2.0*10^-3 | -0.2*10^-3 |
| zmconv_tau | 3600 | 1800 | 28800 |
| zmconv_c0_ocn | 0.03 | 0.001 | 0.1 |
| micro_mg_ai | 700 | 350 | 1400 |
Table 1 list of parameters and ranges
Step two: samples are sampled by using a pull Ding Chao cube sample, in an embodiment, 6 parameters are total, the number of samples is 10 times that of the parameters, 60 groups of samples are total, each sample can be regarded as a 6-dimensional vector, and each parameter in each sample is a sample value obtained randomly according to a sampling rule.
Step three: the 60 sets of samples were each brought into CAM mode, the present example chosen was the f2000_cam5 example, ne30 resolution, and the observed data used the re-analysis dataset of ERA5, and the root mean square error RMSE was calculated for each of these 60 sets of samples relative to the re-analysis data.
Step four: and constructing a Kriging proxy model F (x-A) by using the sample set S and the root mean square error set RMSE to obtain a fitting estimation relation about parameters and root mean square errors.
Step five: the PSO particle swarm optimization algorithm is utilized to find the optimal solution of the agent model F (x-A), a set of optimal solutions is obtained through the process shown in the figure 2, the optimal solutions comprise a set of 6-dimensional vectors, parameter values representing the situation that the optimal solutions are obtained by 6 parameters, and RMSE estimated by the agent model F (x-A) is obtained by the parameters.
And step six, re-substituting the parameter value of the optimal solution obtained in the step five into the CAM5.3 to obtain a real simulation result, and calculating the set of results and the Root Mean Square Error (RMSE) of the analysis data.
Step seven: and D, judging whether the result in the step six meets the optimization requirement, if not, respectively adding the parameters in the step six and the RMSE simulated by the CAM5.3 into the sample set S and the root mean square error set RMSE in the step four, updating the proxy model, and repeating the steps four to six.
Step eight: and when the RMSE obtained in the step six meets the optimization standard, ending the tuning process, and outputting the parameters obtained at the moment, wherein the parameters are the final tuning realization result.
The embodiment of the invention provides an atmosphere mode optimization method based on a proxy model, and the invention discloses an atmosphere mode parameter optimization method based on the proxy model, which belongs to the field of design parameter optimization and comprises the following steps: determining a parameter range, sampling, simulating the results of each sample by using an atmospheric mode, taking Root Mean Square Error (RMSE) as an evaluation standard of an atmospheric mode output result, fitting a functional relation between the sample and the mode result by constructing a proxy model, searching an optimal value of the proxy model by using a PSO particle swarm algorithm, carrying out verification in the atmospheric mode, and continuously and iteratively updating the proxy model until the final parameter tuning result is output according to the tuning requirement. According to the invention, the thought of the agent model is applied to parameter tuning of the atmospheric mode, so that the times of executing the atmospheric mode are effectively reduced, the resource expenditure is reduced, and the economic benefit is improved while the high-efficiency optimization algorithm is ensured; meanwhile, the time consumption of the mode tuning is reduced, and the efficiency of the atmosphere mode parameter tuning is improved.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (6)
1. The atmosphere mode optimization method based on the agent model is characterized by comprising the following steps of:
step one: determining optimal parameters and optimization targets, and determining upper and lower limits according to the selected parameters;
step two: sampling within a parameter range by utilizing Latin hypercube sampling;
Step three: the parameter samples obtained in the second step are sequentially brought into a parameter input list of the atmospheric mode, the atmospheric mode is started to be executed, after the atmospheric mode corresponding to each sampling value is executed, an output file of the atmospheric mode is read, the change of different samples to an optimization target is obtained, and the change level of each sample to the mode is judged by using Root Mean Square Error (RMSE);
step four: constructing a proxy model by using the data obtained in the third step;
Step five: searching an optimal solution of the agent model by using a particle swarm algorithm;
Step six: bringing the parameters represented by the solution in the fifth step back to the atmosphere mode to obtain a new set of values, and adding the set of values to a solution set for constructing a proxy model to update the proxy model;
Step seven: judging whether the result in the step six meets the optimization requirement, if not, respectively adding the parameters in the step six and the RMSE simulated by the atmospheric mode into the sample set S and the RMSE simulated by the air mode, updating the proxy model, and repeating the steps four to six;
step eight: and when the RMSE obtained in the step six meets the optimization standard, ending the tuning process, and outputting the parameters obtained at the moment, wherein the parameters are the final tuning realization result.
2. The proxy model-based atmosphere pattern optimization method according to claim 1, wherein according to step two, the step of latin hypercube sampling is as follows:
Step 201: firstly, determining the number N of samples, namely the number of samples to be extracted;
step 202: dividing the interval (0, 1) into N sections equally;
Step 203: randomly extracting a value for each of the N segments;
step 204: mapping the extracted value into a standard normal distribution sample through an inverse function of the standard normal distribution;
step 205: and (5) disturbing the sampling sequence to obtain a final sampling result.
3. The agent model-based atmosphere pattern optimization method according to claim 1, wherein according to step three, the RMSE calculation method is as follows:
where N represents the result of the nth set of samples, the value range is between 1 and N, m represents the total number of grid points of the optimization area, y i represents the result of the target simulated in the ith grid point mode, and y 0,i represents the value of the observed data in the ith grid point.
4. The atmosphere pattern optimization method based on the proxy model according to claim 1, wherein according to the fourth step, the method of the proxy model is as follows:
401: the polynomial proxy model is a second order polynomial, and the expression is as follows:
wherein, beta represents a coefficient to be estimated, and d is the number of parameters;
402: the Kriging proxy model has the expression:
y＝f(x)Tβl+zl(x)，l＝1，2，...，q
where β is a regression coefficient of a polynomial, the polynomial f (x) may be of any order, z (x) is a random process, and its mean E [ z (x) ]=0;
403: the RBF proxy model has the expression:
Wherein i=1 to n represent response values of the sample points i, ω i represents an i-th sample point weight coefficient, r i is a euclidean distance between a to-be-measured point and the i-th sample point, r i＝//y-yi//,φ(ri) is a mirror function, and typically is a Guass function: phi (r) = -r 2/c2, where c is a coefficient.
5. The agent model-based atmosphere pattern optimization method according to claim 1, wherein according to step five, the particle swarm algorithm steps are as follows:
Step 5.1: randomly initializing each particle;
step 5.2: calculating the adaptive value of each particle, wherein the adaptive value in the problem is a proxy model Output results of (2);
step 5.3: acquiring an individual optimal value of the particle, and updating the individual optimal value of the particle if the adaptive value of the particle obtained in the step 5.2 is better than the original optimal value of the particle;
step 5.4: acquiring a global optimal value of the particle, and if the adaptive value of the particle obtained in the step 5.3 is better than the global optimal value, updating the global optimal value;
Step 5.5: the speed and position of each are updated as follows:
vi＝vi+c1*rand*(pbesti-xi)+c2*rand*((gbest-xi)
xi＝xi+vi
wherein v i represents the speed of the ith particle, c 1 and c 2 are self-learning factors and population learning factors, are two constants, rand is a random number between 0 and 1, pbest i is the individual optimum value of the ith particle, gbest is the global optimum value of the particle, xi represents the current position of the ith particle;
step 5.6: judging whether convergence conditions are met, and if not, returning to the step 5.2;
step 5.7: and obtaining an optimal solution.
6. The atmosphere pattern optimization method based on the proxy model according to claim 1, wherein according to step five, the solution of the proxy model is an optimal solution.
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