A thermophysical property calculation method and system based on partial derivative regular constraint multi-model symbolic regression fusion

Abstract

The present application relates to a kind of based on partial derivative regular constraint multi-model symbolic regression fusion thermophysical property calculation method and system. Obtain the target thermophysical property data of target material under different physical models;Objectify target thermophysical property, and construct candidate physical characteristics based on the output result of multiple low-precision physical models and its associated features;Candidate physical characteristics are converted to reference scale, and the candidate physical characteristics in feature space are used as input, the result of target high-precision physical model is used as target value, and candidate correction formula is generated using symbolic regression method, and target correction formula is determined from candidate correction formula according to prediction error, formula complexity and partial derivative regular constraint;The prediction result output by target correction formula is processed by partial derivative regular constraint, and the correction prediction result of target material is obtained.The present application reduces the number of times of calling target high-precision physical model, improves the explainability and continuous variation rationality of thermophysical property prediction result.

Description

Technical Field

[0001] This invention relates to the field of material property prediction and interpretable machine learning technology, and in particular to a high-precision thermophysical property calculation method and system based on the output results of multiple low-precision physical models, symbolic regression correction, and partial derivative canonical constraints. Background Technology

[0002] With the development of computational materials science and artificial intelligence-aided materials design, using computational models to predict the thermodynamic properties and finite-temperature-dependent properties of materials under different temperatures and pressures has become an important means of material screening, performance evaluation, and service behavior analysis. For material systems such as ferroelectric materials, semiconductor materials, high-temperature ceramic materials, thermal barrier coating materials, and alloy materials, the variation of thermophysical properties with temperature and pressure directly affects the phase stability, mechanical response, and service reliability of the materials.

[0003] In existing finite-temperature property calculations, the target high-precision physical model can typically account for anharmonic phonons, electronic excitations, volume changes, or other finite-temperature effects, resulting in relatively reliable predictions. However, these models have complex calculation processes and high computational costs, making them difficult to apply intensively across a large number of materials, multiple phase structures, multiple temperature points, and multiple pressure points. In contrast, lower-precision physical models such as static calculation models, harmonic calculation models, and quasi-harmonic calculation models have lower computational costs and are suitable for generating denser state point data, but their physical approximation is higher, and the calculation results often show systematic or local deviations from the results of the target high-precision physical model.

[0004] To reduce the number of calls to the target high-precision physical model, existing technologies can employ machine learning, multi-fidelity modeling, or data-driven correction methods to establish a mapping relationship between low-precision model results and high-precision model results. However, some methods typically rely on a single low-precision physical model as input, making it difficult to fully utilize the complementary information between multiple low-precision physical models; while some machine learning correction models can improve prediction errors, the internal relationships of the models are not intuitive enough, making it difficult to directly output concise explicit correction formulas.

[0005] Symbolic regression methods can search for explicit mathematical expressions from candidate features, making them suitable for establishing interpretable correction relationships between low-precision physical model results and target high-precision physical model results. However, existing symbolic regression correction methods typically focus more on fitting errors and formula complexity at discrete state points. They lack sufficient constraints on the changing trends of continuous variables such as temperature and pressure, and are prone to unreasonable local fluctuations. Summary of the Invention

[0006] The purpose of this invention is to address the problems in current thermal property calculation schemes, such as high cost of calling up the target high-precision physical model, insufficient utilization of information from a single low-precision model, and unreasonable fluctuations in the direction prediction of continuous variables. This invention provides a high-precision thermal property calculation method and system based on the symbolic regression fusion of multiple low-precision physical models under partial derivative canonical constraints.

[0007] The objective of this invention can be achieved through the following technical solutions: As a first aspect of the present invention, a method for calculating thermal properties based on partial derivative canonical constraint multi-model symbolic regression fusion is provided, the steps of which include: Acquire target thermal property data of the target material at multiple temperature and pressure states, generated by different physical models, wherein the physical models include multiple low-precision physical models and at least one target high-precision physical model; Match the target thermal property data generated by different physical models at the same state point to form a model calibration dataset; The target thermal properties in the model calibration dataset are objectified to construct a symbolic regression modeling object; candidate physical features are constructed based on the output results of multiple low-precision physical models and the correlation features between models, and the candidate physical features are transformed to the dimensionless symbolic regression feature space through a reference scale. Using candidate physical features in the dimensionless symbolic feature space as input, and the target thermal property results generated by the target high-precision physical model as the target value, candidate correction formulas are generated using the symbolic regression method. The target correction formula is determined from the candidate correction formulas based on the prediction error, formula complexity, and the partial derivative regularization term of the prediction result in the temperature direction, pressure direction, or temperature-pressure neighborhood direction. The prediction results generated by the target correction formula are subjected to partial derivative canonical constraint processing to obtain the target thermal property prediction results of the target material.

[0008] As a preferred technical solution, the method obtains the target thermal property data results generated by the high-precision physical model of the target at at least some state points, as well as the target thermal property data results generated by the low-precision physical model at each temperature state point and pressure state point. State points for which low-precision physical model results have been obtained but high-precision physical model results for the target have not been obtained are marked as state points to be predicted.

[0009] As a preferred technical solution, the target thermal properties include one or more of the following: Gibbs free energy, entropy, heat capacity, coefficient of thermal expansion, elastic constant, dielectric constant, and thermal conductivity; As a preferred technical solution, the low-precision physical model includes multiple types of static calculation models, simple harmonic calculation models, quasi-harmonic calculation models, or few-factor temperature effect models; the target high-precision physical model includes multi-factor calculation models or full-factor calculation models, and the target high-precision physical model has higher calculation accuracy or more complete physical effects than the low-precision physical model.

[0010] As a preferred technical solution, the target thermal properties are objectified, as follows: When the target thermal property is in scalar form, the scalar thermal property is used as the object of symbolic regression modeling. When the target thermal property is in matrix or tensor form, the components of the matrix or tensor thermal property or the finite temperature-related physical quantities derived from the matrix or tensor thermal property are used as the objects of symbolic regression modeling.

[0011] As a preferred technical solution, the candidate physical features include: the output value of the low-precision physical model; the difference, ratio or relative deviation between the output values ​​of different low-precision physical models; and the combined features between the output value of the low-precision physical model and the temperature, pressure, volume, energy difference, free energy difference or phase structure information of the state point.

[0012] As a preferred technical solution, the method of generating candidate correction formulas using symbolic regression is as follows: Based on the candidate operator set, the upper limit of formula complexity, and the upper limit of the number of features, a symbolic regression method is used to search for an explicit mathematical expression between the target thermal properties generated by the low-precision physical model and the target thermal properties generated by the high-precision physical model, which serves as a candidate correction formula; the symbolic regression method includes one or more of SISSO, genetic programming symbolic regression, or sparse regression symbolic regression.

[0013] As a preferred technical solution, the candidate correction formulas are sorted and screened using an evaluation function that includes prediction error, formula complexity, and partial derivative regularization term to obtain the target correction formula.

[0014] As a preferred technical solution, the partial derivative regularization term includes one or more of the following: temperature direction partial derivative regularization term, pressure direction partial derivative regularization term, or temperature-pressure neighborhood direction partial derivative regularization term. Organize adjacent state points according to temperature direction, pressure direction, or temperature-pressure neighborhood direction; construct partial derivative regularization terms based on the first-order difference, second-order difference, local partial derivative, or local rate of change of the predicted values ​​of adjacent state points. When the partial derivative regularization term exceeds the preset range of change, or when the overall change trend of the state point is inconsistent with that of the adjacent state points, the candidate correction formula is penalized, its ranking is reduced, or it is eliminated, and / or the prediction results of the candidate correction formula are marked as abnormal, locally smoothed, abnormally corrected, or missing information is filled.

[0015] As a second aspect of the present invention, a thermal property calculation system based on partial derivative canonical constraint multi-model symbolic regression fusion is provided. The system executes the thermal property calculation method based on partial derivative canonical constraint multi-model symbolic regression fusion as described above, including: The data acquisition unit is used to acquire the target thermal property data of the target material generated by different physical models at multiple temperature and pressure state points. A data processing unit is used to match the target thermal property data to form a model calibration dataset; The feature construction unit is used to objectify the target thermal properties and construct candidate physical features based on the output results of multiple low-precision physical models and their associated features. A scaling unit is used to transform the candidate physical features to a dimensionless symbolic regression feature space through a reference scale. The symbolic regression unit is used to generate candidate correction formulas based on candidate physical features in the dimensionless symbolic feature space and the target thermal property results of the high-precision physical model of the target using the symbolic regression method. The formula selection unit is used to determine the target correction formula based on the prediction error, formula complexity, and partial derivative canonical constraints. The partial derivative canonical constraint unit is used to perform partial derivative canonical constraint processing on the prediction results generated by the target correction formula based on the prediction results of adjacent state points. The result output unit is used to output the predicted results of the target thermal properties of the target material.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The embodiments of the present invention can integrate complementary information from multiple low-precision physical models, obtain explicit correction formulas through symbolic regression, and reduce abnormal fluctuations without physical basis between adjacent state points by using partial derivative canonical constraints. This reduces the number of times the target high-precision physical model is called, while improving the interpretability and rationality of continuous changes in the thermal property prediction results. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a high-precision thermal property calculation method based on symbolic regression fusion of multiple low-precision physical models under partial derivative canonical constraints, provided in an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram comparing the Gibbs free energy sign regression correction prediction result of the HfO2 material system with the target high-precision calculation result in an embodiment of the present invention.

[0019] Figure 3This is a schematic diagram comparing the sign regression correction prediction results of the elastic constants of the HfO2 material system with the target high-precision calculation results in an embodiment of the present invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0021] Example 1 This invention proposes a high-precision thermal property calculation method using symbolic regression fusion of multiple low-precision physical models under partial derivative canonical constraints. The method uses the outputs of multiple low-precision physical models as input and the target high-precision physical model as the correction target. An explicit correction formula is obtained through symbolic regression, and partial derivative canonical constraints are applied to the prediction results based on adjacent state points. Figure 1 The method described herein includes the following steps.

[0022] Step S101: Obtain the target thermophysical property data of the target material.

[0023] Specifically, acquiring target thermal property data includes: determining the target material, phase structure, temperature range, pressure range, target thermal property, multiple low-precision physical models and at least one target high-precision physical model, and acquiring the corresponding target thermal property results at multiple temperature state points and multiple pressure state points to form a temperature-pressure state point set, acquiring the low-precision physical model results and target high-precision physical model results at at least some state points, and marking the state points for which the target high-precision physical model results were not obtained as state points to be predicted.

[0024] The target material can be a material system that requires finite temperature property calculations; the target thermal properties include one or more of Gibbs free energy, entropy, heat capacity, coefficient of thermal expansion, elastic constant, dielectric constant, or thermal conductivity; the low-precision physical model includes one or more of static calculation models, harmonic calculation models, quasi-harmonic calculation models, or few-factor temperature effect models; the target high-precision physical model includes multi-factor calculation models or full-factor calculation models.

[0025] In one implementation, the target thermal property data is represented as A(T,p;m), where T represents temperature, p represents pressure, m represents the physical model, and A represents the target thermal property. If some state points have obtained low-precision physical model results but not the target high-precision physical model results, these state points are marked as state points to be predicted.

[0026] Step S102: Organize the target thermal property data accordingly to form a model calibration dataset.

[0027] Specifically, the output results of different models are matched according to the target material, phase structure, temperature state point, pressure state point, and physical model type. A correspondence is established between multiple low-precision physical model results and the target high-precision physical model result at the same state point. The model calibration dataset includes multiple low-precision physical model output results, state point information, and the corresponding target high-precision physical model output results for the same target material, phase structure, and state point.

[0028] In one implementation, the target thermal property outputs, temperature, pressure, and phase structure information of multiple low-precision physical models are used as input data, and the target high-precision physical model results obtained at at least some state points are used as target values ​​to form model calibration samples.

[0029] Step S103: Objectify the target thermal properties.

[0030] Specifically, objectification includes using one or more components of scalar thermal properties, matrix or tensor thermal properties, or finite temperature-related physical quantities derived from them as symbolic regression modeling objects. When the target thermal property is in scalar form, the scalar thermal property is used as the symbolic regression modeling object; when the target thermal property is in matrix or tensor form, the components of the matrix or tensor thermal property, or finite temperature-related physical quantities derived from the matrix or tensor thermal property, are used as symbolic regression modeling objects.

[0031] Step S104: Construct candidate physical features based on the output results of multiple low-precision physical models.

[0032] Specifically, candidate physical features include low-precision physical model output values, differences, ratios, or relative deviations between different low-precision physical model output values, and combined features between the low-precision physical model output values ​​and the temperature, pressure, volume, energy difference, free energy difference, or phase structure information of the state point.

[0033] Step S105: Perform a reference scale transformation on the candidate physical features to obtain a dimensionless symbolic regression feature space for symbolic regression.

[0034] Specifically, the reference scale can be determined based on reference temperature, reference pressure, reference volume, reference energy, reference target thermal property values ​​or training set statistics. The reference scale transformation of candidate physical features includes normalization, dimensionless processing or standardization processing, and the candidate physical features are entered into the dimensionless sign regression feature space.

[0035] Step S106: Establish candidate correction formulas using symbolic regression.

[0036] Specifically, the candidate physical features in the dimensionless symbolic regression feature space are used as input, and the target thermal properties of the target high-precision physical model obtained at at least some state points are used as target values. The symbolic regression method is used to search for an explicit mathematical expression between the low-precision physical model results and the target high-precision physical model results.

[0037] In one implementation, the candidate correction formula can be expressed as: Target high-precision physical model prediction result = low-precision model baseline result + correction term Among them, the low-precision model benchmark result can be selected from the output result of a single low-precision physical model, or it can be obtained by combining the output results of multiple low-precision physical models; the correction term is obtained by the symbolic regression method based on the candidate physical features.

[0038] During the symbolic regression search process, based on the candidate operator set, upper limit of formula complexity, upper limit of feature number, and prediction error index, an explicit mathematical expression is searched between the low-precision physical model result and the target high-precision physical model result, and this expression is used as a candidate correction formula. The symbolic regression method includes one or more of SISSO, genetic programming symbolic regression, or sparse regression symbolic regression.

[0039] Step S107: Determine the target correction formula based on the preset screening conditions.

[0040] Specifically, a comprehensive evaluation is performed on each candidate correction formula. Let the first... r The candidate formulas are f r Its screening score is: Among them, E( f r C( ) represents the prediction error, which can be calculated using the mean absolute error or root mean square error. It characterizes the difference between the predicted value of the candidate formula and the result of the target high-precision model. f r The formula complexity can be determined by the number of formula terms, the number of variables, the number of operators, or the expression hierarchy. P sel ( f r The partial derivative anomaly penalty term is used in the formula screening stage to evaluate the reasonableness of candidate formulas in terms of temperature, pressure, or neighborhood directions. If there are sudden jumps, oscillations, or trend reversals in the predicted values ​​of adjacent state points, the partial derivative anomaly penalty term is increased, reducing the ranking or eliminating the candidate. Finally, candidate formulas with lower screening scores, lower complexity, and reasonable trends are selected as the target correction formulas.

[0041] Step S108: Apply partial derivative canonical constraints to the output of the target correction formula. After the target formula is determined, its initial prediction results are... Make corrections to obtain Y : in, D This indicates the degree of deviation between the corrected result and the initial result. P out (Y) This is a partial derivative smoothing constraint term for the output stage, which can be obtained from the first-order difference, second-order difference, local partial derivative, or rate of change of the predicted values ​​of adjacent temperature points, pressure points, or neighborhood points. It is used to suppress abnormal fluctuations in the output results and improve the rationality of continuous changes through labeling, smoothing, correction, or completion.

[0042] Step S109: Output the corrected prediction results for the target material.

[0043] Specifically, the correction prediction results include the predicted values ​​of the target high-precision physical model results, the target correction formula, the prediction error index, and the evaluation results of the partial derivative canonical constraint.

[0044] Through steps S101 to S109, this embodiment can utilize the complementary information of multiple low-precision physical models to obtain corrected prediction results with explicit expression, continuous change trend, and reasonable partial derivative changes.

[0045] Example 2 This invention also provides a high-precision thermal property calculation system for symbolic regression fusion of multiple low-precision physical models under partial derivative canonical constraints. The system includes a data acquisition unit, a data processing unit, a feature construction unit, a scale conversion unit, a symbolic regression unit, a formula filtering unit, a partial derivative canonical constraint unit, and a result output unit. These units can be connected sequentially or interact via a data interface.

[0046] The data acquisition unit is used to acquire the target material's thermophysical property data at different temperature and pressure states and under different physical models. Specifically, the physical model includes multiple low-precision physical models and at least one high-precision physical model of the target material.

[0047] The data processing unit is used to match and process the target thermophysical property data acquired by the data acquisition unit to form a model calibration dataset. Specifically, the data processing unit establishes a correspondence between multiple low-precision physical model results and the target high-precision physical model results under the same target material, the same phase structure, and the same state point.

[0048] The feature construction unit is connected to the data processing unit and is used to determine the symbolic regression modeling object based on the model calibration dataset, generate candidate physical features based on the output results of multiple low-precision physical models and the correlation features between models, and output the candidate physical features to the scale conversion unit.

[0049] The scale transformation unit is used to perform reference scale transformation on candidate physical features to obtain a dimensionless symbolic regression feature space.

[0050] The symbolic regression unit is used to receive the dimensionless symbolic regression feature space output by the scaling unit, and take the candidate physical features in the dimensionless symbolic regression feature space as input, the target thermal property result of the target high-precision physical model as the target value, search for an explicit mathematical expression between the low-precision physical model result and the target high-precision physical model result, and generate one or more candidate correction formulas.

[0051] The formula screening unit is used to evaluate and screen the candidate correction formulas generated by the symbolic regression unit. Specifically, the formula screening unit sorts the candidate correction formulas according to their prediction error, formula complexity, and the partial derivative regularization term of the prediction result in the temperature direction, pressure direction, or temperature-pressure neighborhood direction, and determines the target correction formula from them.

[0052] The partial derivative canonical constraint unit is used to perform partial derivative canonical constraint processing on the prediction results output by the target correction formula. Specifically, the partial derivative canonical constraint unit organizes the prediction results of adjacent temperature state points, adjacent pressure state points, or temperature-pressure neighborhood state points into pseudo-time series or local neighborhoods, and identifies abnormal fluctuations based on the difference, local partial derivative, or local rate of change of the predicted values ​​of adjacent state points.

[0053] The result output unit is used to output the correction prediction results of the target material. The correction prediction results include one or more of the following: correction prediction value, target correction formula, prediction error index, curve or surface of target thermophysical properties changing with temperature and pressure, abnormal fluctuation marker, and partial derivative canonical constraint evaluation results.

[0054] Example 3 This embodiment uses the HfO2 material system as an example to illustrate the implementation of the present invention. HfO2 is only used to illustrate the specific application of the present invention and does not limit the scope of applicable materials of the present invention.

[0055] In this embodiment, the target material is HfO2, the target phase structure includes oI and oIII phases, and the target thermophysical properties include Gibbs free energy and elastic constants. The low-precision physical model includes a static calculation model, a harmonic calculation model, and a quasi-harmonic calculation model, while the target high-precision physical model includes a quasi-self-consistent phonon calculation model.

[0056] The samples in the HfO2 model calibration dataset include phase structure, temperature, pressure, low-precision physical model output, target high-precision physical model output, volume, free energy difference, elastic constant difference, and target thermophysical property type or component identifier.

[0057] In one implementation, the reference scale includes a reference temperature T. ref Reference pressure p ref Reference volume V ref Reference Gibbs free energy G ref and reference elastic constant C ref The corresponding dimensionless characteristics include: T norm =T / T ref ;p norm =p / p ref V norm =V / V ref ;ΔF norm =(F scp -F ha ) / G ref ;ΔC norm =(C QHA -C static ) / C ref One or more of them.

[0058] In one implementation, the Gibbs free energy correction formula is expressed as: G high =G low +G ref × f (T norm V norm ,ΔF norm ) Among them, G high The Gibbs free energy G of a quasi-self-consistent phonon qscp G low It can be the quasi-harmonic Gibbs free energy G qha G ref Represents the free energy reference scale. f This represents the dimensionless correction function obtained from symbolic regression. For phases oI and oIII, a unified correction model can be established, or separate phase-resolved correction models can be established.

[0059] For example, the comparison between the corrected prediction results and the high-precision calculation results of the target for the unified Gibbs free energy correction model of HfO2 is as follows: Figure 2 As shown, the target correction formula obtained from symbolic regression is expressed as: G qscp =G qha +G ref×(8.15208212937e -06 +8.40610848427×V norm ×ΔF norm +0.00017390511296×T norm 2 -8.20814272771×ΔF norm ) Among them, G qscp G represents the predicted value of the quasi-self-consistent phonon Gibbs free energy. qha V represents the quasi-harmonic Gibbs free energy. norm T represents the dimensionless characteristic of volume. norm ΔF represents the dimensionless characteristic of temperature. norm This indicates the dimensionless characteristic of the free energy difference.

[0060] For modeling elastic constants, one or more elastic constant components can be used as modeling objects, and low-precision elastic constants, static elastic constants, elastic constant differences, relative ratios, and combinations of the above features with temperature, pressure, or volume can be constructed. Elastic constants can be corrected using absolute value models or relative value models with respect to static elastic constants.

[0061] In one implementation, the formula for correcting the elastic constant component is expressed as: C high =C low +C ref ×g(T norm V norm ,ΔC norm ) Among them, C high The quasi-self-consistent phonon elastic constant C qscp C low The quasi-harmonic elastic constant C qha C ref denoted by the elastic constant reference scale, g represents the dimensionless correction function obtained from the sign regression.

[0062] For example, the comparison between the corrected prediction results and the high-precision calculation results of the target for the unified elastic constant absolute value correction model of HfO2 is as follows: Figure 3 As shown, the elastic constant component C can be... ii As the modeling object, the target correction formula obtained from symbolic regression is expressed as: C qscp =C qha +C ref ×(0.00207819101014-0.25705365429×ΔC norm ×Tnorm +0.0299305892874×T norm 2 +0.00925099089309×(ΔC norm -T norm )) Among them, C qscp C represents the predicted value of the quasi-self-consistent phonon elastic constant. qha C represents the quasi-harmonic elastic constant. ref ΔC represents the reference scale for the elastic constant. norm T represents the dimensionless characteristic of the difference in elastic constants. norm This indicates the dimensionless characteristic of temperature. The above C... ii It can represent the diagonal components in the elastic constant matrix; for C ij C jj For other components, or for phase-resolved models of the oI and oIII phases, corresponding explicit correction formulas can be established in the same way.

[0063] In the HfO2 example data, when using the unified Gibbs free energy correction model, the mean absolute error of the quasi-self-consistent phonon Gibbs free energy prediction relative to the target high-precision calculation result can reach 10. -4 The magnitude of eV / fu indicates that the symbolic regression correction formula can approximate the target high-precision physical model results while maintaining the explicit expression.

[0064] After obtaining the correction results for the Gibbs free energy or elastic constant, the prediction results for the same phase structure are arranged according to the temperature direction, pressure direction, or temperature-pressure state point neighborhood, and the local partial derivatives or local rates of change are calculated based on the differences in prediction results between adjacent state points. When the local partial derivatives or local rates of change exceed the preset range, the corresponding results are marked for abnormal fluctuations, smoothed, or a new candidate correction formula is selected.

[0065] Through the above HfO2 embodiments, the present invention can generate corrected prediction results that are close to the results of the quasi-self-consistent phonon calculation model based on the output results of the static calculation model, the harmonic calculation model and the quasi-harmonic calculation model, and can be used to predict finite temperature properties such as Gibbs free energy and elastic constant.

[0066] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0067] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion, characterized by the following steps: include: Acquire target thermal property data of the target material at multiple temperature and pressure states, generated by different physical models, wherein the physical models include multiple low-precision physical models and at least one target high-precision physical model; Match the target thermal property data generated by different physical models at the same state point to form a model calibration dataset; The target thermal properties in the model calibration dataset are objectified to construct a symbolic regression modeling object; candidate physical features are constructed based on the output results of multiple low-precision physical models and the correlation features between models, and the candidate physical features are transformed to the dimensionless symbolic regression feature space through a reference scale. Using candidate physical features in the dimensionless symbolic feature space as input, and the target thermal property results generated by the target high-precision physical model as the target value, candidate correction formulas are generated using the symbolic regression method. The target correction formula is determined from the candidate correction formulas based on the prediction error, formula complexity, and the partial derivative regularization term of the prediction result in the temperature direction, pressure direction, or temperature-pressure neighborhood direction. The prediction results generated by the target correction formula are subjected to partial derivative canonical constraint processing to obtain the target thermal property prediction results of the target material.

2. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The method obtains the target thermal property data results generated by the high-precision physical model of the target at at least some state points, as well as the target thermal property data results generated by the low-precision physical model at each temperature state point and pressure state point. State points for which low-precision physical model results have been obtained but high-precision physical model results for the target have not been obtained are marked as state points to be predicted.

3. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The target thermophysical properties include one or more of the following: Gibbs free energy, entropy, heat capacity, coefficient of thermal expansion, elastic constant, dielectric constant, and thermal conductivity.

4. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The low-precision physical model includes multiple types of models such as static calculation model, simple harmonic calculation model, quasi-harmonic calculation model, or few-factor temperature effect model; the target high-precision physical model includes multi-factor calculation model or full-factor calculation model, and the target high-precision physical model has higher calculation accuracy or more complete physical effects than the low-precision physical model.

5. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The target thermal properties are objectified as follows: When the target thermal property is in scalar form, the scalar thermal property is used as the object of symbolic regression modeling. When the target thermal property is in matrix or tensor form, the components of the matrix or tensor thermal property or the finite temperature-related physical quantities derived from the matrix or tensor thermal property are used as the objects of symbolic regression modeling.

6. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The candidate physical features include: the output value of the low-precision physical model; the difference, ratio or relative deviation between the output values ​​of different low-precision physical models; and the combined features between the output value of the low-precision physical model and the temperature, pressure, volume, energy difference, free energy difference or phase structure information of the state point.

7. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The method of generating candidate correction formulas using symbolic regression is as follows: Based on the candidate operator set, the upper limit of formula complexity, and the upper limit of the number of features, a symbolic regression method is used to search for an explicit mathematical expression between the target thermal properties generated by the low-precision physical model and the target thermal properties generated by the high-precision physical model, which serves as a candidate correction formula; the symbolic regression method includes one or more of SISSO, genetic programming symbolic regression, or sparse regression symbolic regression.

8. The method for calculating thermal properties based on partial derivative canonical constraints and multi-model symbolic regression fusion as described in claim 1, characterized in that, The candidate correction formulas are sorted and filtered using an evaluation function that includes prediction error, formula complexity, and partial derivative regularization term to obtain the target correction formula.

9. The method for calculating thermal properties based on partial derivative canonical constraint multi-model symbolic regression fusion according to claim 8, characterized in that, The partial derivative canonical term includes one or more of the following: temperature direction partial derivative canonical term, pressure direction partial derivative canonical term, or temperature-pressure neighborhood direction partial derivative canonical term. Organize adjacent state points according to temperature direction, pressure direction, or temperature-pressure neighborhood direction; construct partial derivative regularization terms based on the first-order difference, second-order difference, local partial derivative, or local rate of change of the predicted values ​​of adjacent state points. When the partial derivative regularization term exceeds the preset range of change, or when the overall change trend of the state point is inconsistent with that of the adjacent state points, the candidate correction formula is penalized, its ranking is reduced, or it is eliminated, and / or the prediction results of the candidate correction formula are marked as abnormal, locally smoothed, abnormally corrected, or missing information is filled.

10. A thermal property calculation system based on partial derivative canonical constraint multi-model symbolic regression fusion, characterized in that, The system executes the thermal property calculation method based on partial derivative canonical constraint multi-model symbolic regression fusion as described in any one of claims 1-9, including: The data acquisition unit is used to acquire the target thermal property data of the target material generated by different physical models at multiple temperature and pressure state points. A data processing unit is used to match the target thermal property data to form a model calibration dataset; The feature construction unit is used to objectify the target thermal properties and construct candidate physical features based on the output results of multiple low-precision physical models and their associated features. A scaling unit is used to transform the candidate physical features to a dimensionless symbolic regression feature space through a reference scale. The symbolic regression unit is used to generate candidate correction formulas based on candidate physical features in the dimensionless symbolic feature space and the target thermal property results of the high-precision physical model of the target using the symbolic regression method. The formula selection unit is used to determine the target correction formula based on the prediction error, formula complexity, and partial derivative canonical constraints. The partial derivative canonical constraint unit is used to perform partial derivative canonical constraint processing on the prediction results generated by the target correction formula based on the prediction results of adjacent state points. The result output unit is used to output the predicted results of the target thermal properties of the target material.

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