Composite material indentation inversion method and system based on automatic dimensional analysis

Abstract

The application discloses a composite material indentation inversion method and system based on automatic dimensional analysis, and relates to the field of data processing.The application changes the learning goal of a neural network from an empirical function under a specific scale to a general physical law description function through automatic dimensional analysis.Because the form of the function is independent of physical units and the absolute size of a system, the trained model has strong extrapolation ability and can make more accurate predictions for new working conditions outside the training data range.The model without dimensionality reduction has a sharp decrease in accuracy after exceeding the training range.In addition, by encoding prior physical knowledge such as dimensional consistency into the feature construction process, the task that the neural network needs to learn is greatly simplified.The network no longer needs to understand physical laws from scratch, but only needs to learn the mapping relationship between dimensionless numbers which are physically meaningful.

Description

Technical Field

[0001] This invention belongs to the field of data processing, and more specifically, relates to a composite material indentation inversion method and system based on automatic dimensional analysis. Background Technology

[0002] Composite materials are widely used in aerospace, automotive industry and biomedical engineering, and determining the mechanical properties of individual constituent phases in a material is the foundation of material design and performance optimization. However, due to the multiphase heterogeneity of composite materials and the complexity of their microstructure, directly separating and testing the mechanical properties of a single component is extremely challenging. Nanoindentation technology, as an in-situ characterization method, provides a feasible way to invert material properties through indentation experimental data. Currently, using machine learning methods to invert material properties from experimental data has become an important research paradigm; however, existing technologies have the following significant drawbacks and limitations: Firstly, traditional pure data-driven methods, such as directly statistically normalizing the raw measurement data (e.g., StandardScaler or MinMaxScaler) and then inputting it into the neural network, heavily rely on the scale range of the training data for predictive performance. Once a new working condition exceeding the training range is encountered, the prediction accuracy drops sharply. These methods cannot establish scale invariance across different scales. For example, consider a simple pendulum period formula. If a neural network is only trained on data with a pendulum length of 1 to 2 meters, the model will exhibit catastrophic errors when faced with a new sample with a pendulum length of 10 meters. This is because the model learns empirical correlations at a specific scale, rather than universal physical laws. Secondly, pure data-driven models require massive amounts of training data to achieve acceptable accuracy, while high-precision material indentation experimental data are expensive to acquire, which severely limits the feasibility of data-driven methods in practical engineering. Secondly, the decision-making logic inside the black-box neural network model is disconnected from the underlying physical laws, resulting in poor model interpretability and difficulty in being understood and trusted by domain experts. In high-risk decision-making scenarios (such as aerospace structural design and medical implant selection), such prediction results lacking physical basis are difficult to gain professional recognition. Finally, in the indentation problem, different combinations of mechanical properties may produce similar load-displacement curves, resulting in non-unique inversion results, which traditional methods cannot effectively solve.

[0003] Dimensional analysis is a classical physics method based on the law of physical similarity, and its theoretical foundation is Buckingham's theorem. This theorem states that a dimensionless analysis involving... n A physical quantity, which can be derived from k A set of independent fundamental dimensions (such as mass) M ,length L,time T The physical equations described by can be equivalently expressed as a equation involving ( nk Equations for 10 independent dimensionless numbers (Π numbers); applying dimensional analysis to neural network modeling, that is, replacing the original dimensional variables in the input and output of the neural network with dimensionless Π numbers, can bring three core advantages: improved generalization ability, improved data efficiency, and improved training process; however, for complex physical problems, manually performing dimensional analysis and finding the optimal combination of Π numbers with the richest information and the lowest redundancy is an extremely challenging task that relies on expert experience, and currently there is a lack of automated and systematic solutions. Summary of the Invention

[0004] To address the problems in related technologies, this invention proposes a composite material indentation inversion method and system based on automatic dimensional analysis, in order to overcome the aforementioned technical problems existing in the existing related technologies.

[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: This invention relates to a composite material indentation inversion method based on automated dimensional analysis, comprising the following steps: S1. Obtain material indentation experimental data as input feature data and obtain corresponding real material property data as training label data; S2. Construct a heuristic evolutionary framework driven by a large language model to realize the transformation from dimensional physical quantities to dimensionless number combinations; provide the large language model with structured task descriptions and code templates to generate a set of candidate dimensionless schemes; S3. Evaluate and screen the schemes in the candidate dimensionless scheme set to obtain the optimal dimensionless scheme. S4. The input features and training label data in S1 are processed to be dimensionless using the optimal dimensionless transformation scheme, and then a fully connected neural network is trained based on the processed data. S5. Input the new indentation experimental data into the fully connected neural network trained in S4, output dimensionless material property prediction values, and convert them into dimensional actual physical parameters through inverse transformation.

[0006] Preferably, step S1 includes the following steps: S11. Obtain material indentation test data, which includes load-displacement curve data and surface morphology displacement data; extract the fitting parameters of the load-displacement curve as input features, extract the displacement of key points on the interface as auxiliary input features, and merge the input features and auxiliary input features to obtain comprehensive input features; Then, the real material property data corresponding to the material indentation experiment data is obtained as the model training label. The real material property data includes the elastic modulus and Poisson's ratio. The fitting parameters include the intercept of the quadratic fitting function. Linear coefficients and quadratic coefficient The surface topography displacement data includes indentation depth of... Time interface points lateral displacement and vertical displacement The input features described in S1 also include system geometry and load scale parameters.

[0007] Preferably, step S2 includes the following steps: S21. Construct a heuristic evolutionary framework EoH based on a large language model (the EoH framework solves the three core challenges of combinatorial explosion, knowledge integration, and global optimization in dimensional analysis problems through the deep integration of large language models and evolutionary algorithms, and realizes automated and optimized physical knowledge-driven feature engineering), which is used to automatically explore conversion algorithms from dimensional physical quantities to dimensionless number combinations; by providing the large language model with structured task descriptions and code templates, it is guided to generate candidate dimensionless schemes that meet the requirements of dimensional consistency, and a set of candidate dimensionless schemes is obtained; The framework employs an evolutionary cycle mechanism from generation to evaluation to selection.

[0008] Preferably, the heuristic evolutionary framework EoH described in S2 includes three core components: a generation operator, a fitness evaluation function, and a selection mechanism. Generate operators are used to provide the large language model with a structured task description that includes function signatures, return value formats, mathematical operation rules, physical constraints, and code structure, guiding it to generate Python function equations that meet the requirements of dimensional consistency. In the later stages of evolution, the large language model improves or merges the current best function to generate a new generation of candidate functions. The fitness evaluation function is used to first verify whether the generated dimensionless numbers are strictly dimensionless by scaling transformation. If they fail, they are directly eliminated. Then, it is applied to the subsequent neural network training process and returns the loss value on the validation set. The selection mechanism employs an elite retention strategy to directly replicate the best few individuals to the next generation, while simultaneously selecting individuals from the remaining individuals based on their fitness ratio to participate in the generation process of the next generation. The heuristic evolutionary framework EoH described in S2 uses five evolutionary operators: the initialization generator (I1), responsible for global exploration and covering the search space; the crossover operator (E1), responsible for global innovation and escaping local optima; the improved crossover operator (E2), responsible for balancing exploration and utilization and reusing the core idea; the modification operator (M1), responsible for structural improvement and balancing exploration and utilization; and the parameter modification operator (M2), responsible for parameter optimization and extracting remaining performance. It also employs a selection mechanism combining an elite retention strategy and fitness ratio selection. E1: I1 offers diversity, E1 offers innovation, E1 E2: E1 discovers new ideas, E2 improves existing ideas, E2 M1: E2 explores new structures, M1 improves existing structures, M1 M2: M1 is an improved structure, and M2 is an optimized parameter; The population management employs an elite retention strategy and roulette wheel selection. The elite retention strategy, implemented in the survival method, merges the current population with the next generation, sorts them in descending order of score, and retains the top pop_size best individuals. Roulette wheel selection chooses from individuals with non-negative infinite scores, with a selection probability... p = 1 / ( r + n ),in r Rank individuals n The number of valid individuals; Where pop_size represents the number of optimal individuals to retain, and the pop_size value is automatically adjusted using a tiered strategy; Population management also includes a duplicate function detection mechanism. If a duplicate function is detected, the score of the new function is set to negative infinity.

[0009] Preferably, the structured task description in S2 adopts a role-playing approach, setting the large language model as a top physicist and engineer who is proficient in dimensional analysis and experimental-data pipeline. In this way, the LLM can call on a specific professional knowledge base and guide the LLM to think in the way of experts.

[0010] Preferably, the structured task description in S2 includes the following hard rules: Rule 1: Every dimensionless number must be strictly dimensionless at the sign level; Rule 2: Only element-wise multiplication, division, and exponentiation of input variables are allowed; Rule 3: All numeric constants must be written in floating-point form; Rule 4: The use of any aggregate functions is prohibited; Rule 5: The use of the attribute to be predicted is prohibited in the construction of dimensionless inputs; Rule 6: Self-combination of output attributes is prohibited; Rule 7: No conditional branches or logic that may lead to an early return; Rule 8: The dimensionless input dimension should be less than or equal to the original dimensional input dimension; Rule 9: For parameters such as Poisson's ratio that are dimensionless, directly input the dimensionless number into the output without any transformation or combination.

[0011] Preferably, the response processing of the large language model in S2 includes: extracting the algorithm description from the response using regular expressions, pruning the function prefix in the response using SampleTrimmer, and converting the pruned code into a Function object; if the response parsing fails, the sample is skipped. The evaluation mechanism described in S2 employs a security evaluation approach and uses a performance analyzer to record the entire evaluation process.

[0012] Preferably, the formula for converting the dimensionless material property prediction value into a dimensional parameter through inverse transformation in S5 is consistent with the inverse operation of the transformation logic in generating the candidate dimensionless scheme set in S2; the inverse transformation includes applying the inverse transformation of the dimensionless prediction result to the output scaler, and then back-deriving the actual dimensional parameter value according to the original dimensionless number expression defined by the equation function. The equation function is used to convert dimensional physical quantities from material indentation experiments into dimensionless numbers in order to train a physics-guided neural network.

[0013] The composite material indentation inversion system based on automatic dimensional analysis includes a training data acquisition module, a scheme generation module, a scheme selection module, a network training module, and a parameter output module. The training data acquisition module is used to acquire input feature data and training label data; The scheme generation module is used to generate a set of candidate dimensionless schemes. The solution screening module is used to evaluate and screen solutions; The network training module is used to train fully connected neural networks; The parameter output module is used to output dimensionless predicted values ​​of material properties and perform parameter conversion.

[0014] The present invention has the following beneficial effects: 1. In this invention, automatic dimensional analysis transforms the learning objective of the neural network from an empirical function at a specific scale into a universal physical law description function. Because the form of the function is independent of physical units and the absolute size of the system, the trained model possesses powerful extrapolation capabilities, enabling more accurate predictions of new operating conditions beyond the training data range. For example, for the problem of a simple pendulum period, a model trained with dimensionality can accurately predict the period ranging from 1 meter to 100 meters in length, while the accuracy of an un-dimensionalized model drops sharply beyond the training range.

[0015] 2. In this invention, by encoding prior physical knowledge such as dimensional consistency into the feature construction process, the learning task of the neural network is greatly simplified. The network no longer needs to understand physical laws from scratch, but only needs to learn the mapping relationship between dimensionless numbers that are already physically meaningful. Experiments show that the performance of traditional methods using the complete dataset can be achieved using only 20% of the samples. This has important practical value in the field of materials science where experimental costs are high.

[0016] 3. In this invention, each dimensionless number corresponds to a clear physical meaning, and the input and output of the model are both dimensionless quantities with physical meaning, making the decision-making process transparent to domain experts; this interpretability improves the credibility and acceptability of the method in high-risk decision-making scenarios.

[0017] 4. In this invention, after dimensionless transformation, the values ​​of each dimensionless number are usually distributed within a relatively concentrated range with similar scales (e.g., 0.1 to 100), avoiding the huge order-of-magnitude differences that may exist between the original physical quantities (e.g., elastic modulus 100-1000 MPa and Poisson's ratio 0.3). This makes the gradient of the loss function more balanced, which is beneficial to the stability and fast convergence of the optimization algorithm. Experiments show that the model trained with dimensionless transformation converges within 20 training rounds, while the model without dimensionless transformation requires more than 40 rounds.

[0018] 5. This invention utilizes a heuristic evolutionary framework driven by a large language model to automate the exploration of dimensionality analysis schemes, overcoming the limitations of manual analysis methods, such as high dependence on expert experience, low efficiency, and difficulty in handling complex problems. The framework guides the large language model to generate candidate functions that meet strict dimensional constraints through carefully designed task descriptions and code templates, and then filters them through fitness evaluation based on neural network performance, ultimately automatically discovering the optimal dimensionless scheme.

[0019] 6. This invention ensures the robustness and security of the method through technologies such as a security evaluation mechanism (independent process execution), a protected division mechanism (preventing division by zero errors), a timeout mechanism (preventing infinite loops), and Numba acceleration (improving computational efficiency), enabling it to run stably in practical engineering applications. Furthermore, it employs the AdamW optimizer in conjunction with a cosine annealing learning rate scheduler, combined with batch normalization regularization technology, to further enhance the training stability and convergence speed of the neural network. The weighted loss mechanism ensures balanced optimization of multiple output objectives, avoiding the problem of over-optimizing one objective while neglecting others.

[0020] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the EoH framework process of the present invention. Detailed Implementation

[0023] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0024] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0025] Example 1 Please see Figure 1 This embodiment describes a composite material indentation inversion method based on automatic dimensional analysis, including the following steps: S1. Obtain composite material indentation experimental data as input feature data and obtain corresponding real material property data as training label data; S1 includes the following steps: S11. Obtain composite material indentation test data, which includes load-displacement curve data and surface morphology displacement data; extract the fitting parameters of the load-displacement curve as input features, extract the displacement of key interface points as auxiliary input features, and merge the input features and auxiliary input features to obtain comprehensive input features; Then, the real material property data corresponding to the composite material indentation test data are obtained as model training labels. The real material property data includes the elastic modulus and Poisson's ratio of the fiber and the matrix. The fitting parameters include the intercept of the quadratic fitting function. Linear coefficients and quadratic coefficient The surface topography displacement data includes indentation depth of... fiber-matrix interface points lateral displacement and vertical displacement ; The input features described in S1 also include system geometry and load scale parameters, such as feature length. (Fiber radius) and maximum experimental load ; S2. Construct a heuristic evolutionary framework driven by a large language model to realize the transformation from dimensional physical quantities to dimensionless number combinations; provide the large language model with structured task descriptions and code templates to generate a set of candidate dimensionless schemes; S2 includes the following steps: S21. Construct a heuristic evolutionary framework EoH based on a large language model (the EoH framework solves the three core challenges of combinatorial explosion, knowledge integration, and global optimization in dimensional analysis problems through the deep integration of large language models and evolutionary algorithms, and realizes automated and optimized physical knowledge-driven feature engineering), which is used to automatically explore conversion algorithms from dimensional physical quantities to dimensionless number combinations; by providing the large language model with structured task descriptions and code templates, it guides it to generate candidate dimensionless schemes (i.e., Python function equation) that meet the requirements of dimensional consistency, and obtains a set of candidate dimensionless schemes; The framework employs an evolutionary cycle mechanism from generation to evaluation to selection; The heuristic evolutionary framework EoH described in S2 includes three core components: generation operator, fitness evaluation function, and selection mechanism. Generate operators are used to provide the large language model with a structured task description that includes function signatures, return value formats, mathematical operation rules, physical constraints, and code structure, guiding it to generate Python function equations that meet the requirements of dimensional consistency. In the later stages of evolution, the large language model improves or merges the current best function to generate a new generation of candidate functions. The fitness evaluation function is used to first verify whether the generated dimensionless numbers are strictly dimensionless by scaling transformation. If they fail, they are directly eliminated. Then, it is applied to the subsequent neural network training process and returns the loss value on the validation set. The selection mechanism employs an elite retention strategy to directly replicate the best few individuals to the next generation, while simultaneously selecting individuals from the remaining individuals based on their fitness ratio to participate in the generation process of the next generation. The evolutionary algorithm parameters in the EoH framework are set as follows: The population size of the evolutionary algorithm is automatically adjusted according to the maximum number of samples. When the maximum number of samples is greater than or equal to 10,000, the population size is 40; when the maximum number of samples is greater than or equal to 1,000 and less than 10,000, the population size is 20; when the maximum number of samples is greater than or equal to 200, the population size is 10; otherwise, the population size is 5. The maximum number of generations is set to 10; the maximum number of samples is set to 100 candidate functions for evaluation; the number of individuals selected is set to 2; and the initial sample size limit is set to the smaller of the maximum sample size and the double population size. The heuristic evolutionary framework EoH described in S2 uses five evolutionary operators: initialization generation operator (I1), crossover operator (E1), improved crossover operator (E2), modification operator (M1), and parameter modification operator (M2); and adopts a selection mechanism that combines elite retention strategy and fitness ratio selection (roulette wheel selection); Specifically, the initialization generator (I1) is responsible for global exploration, covering the search space; the crossover operator (E1) is responsible for global innovation, escaping local optima; the improved crossover operator (E2) is responsible for balancing exploration and utilization, reusing the core idea; the modification operator (M1) is responsible for structural improvement, balancing exploration and utilization; the parameter modification operator (M2) is responsible for parameter optimization, extracting remaining performance; and a selection mechanism combining an elite retention strategy and fitness ratio selection is adopted; I1 E1: I1 offers diversity, E1 offers innovation, E1 E2: E1 discovers new ideas, E2 improves existing ideas, E2 M1: E2 explores new structures, M1 improves existing structures, M1 M2: M1 improves the structure, M2 optimizes the parameters; if the initialization operator is missing and random code is used, it will lead to 99.9% of the code having syntax errors or dimensional errors; if the crossover operator is missing, innovation cannot be generated and knowledge cannot be accumulated; if the mutation operator is missing, premature convergence will occur, and it will be impossible to break through the bottleneck; if the selection operator is missing, there is no evolutionary direction, resulting in wasted resources; if the retention operator is missing, excellent individuals will be lost. in: The specific implementation scheme of the initialization generation operator is as follows: In the initialization phase, the initialization generation operator prompt word is used to send the task description and code template to the large language model, requiring the large language model to generate a brand-new dimensionless function; the prompt word requires the large language model to first describe the new algorithm and main steps in one sentence (the description must be enclosed in curly braces {}), and then implement the given Python function; The specific implementation scheme of the crossover operator is as follows: Select two individuals from the population, provide their algorithm descriptions and code to the large language model, and require the large language model to create a new algorithm that is completely different from the given algorithm (the algorithm represented by the two parent individuals selected from the population); the prompt word requires the large language model to first identify the general core idea of ​​the provided algorithm, then describe the new algorithm in one sentence based on the core idea, and finally implement the given Python function; The specific implementation scheme of the improved crossover operator is as follows: select 2 individuals from the population, require the large language model to identify the general core idea of ​​the provided algorithm, and create a new algorithm based on the core idea; prompt words require the large language model to first identify the general core idea of ​​the provided algorithm, describe the new algorithm based on the core idea, and finally implement the given Python function; The specific implementation scheme for modifying the operator is as follows: Select one individual from the population and provide its algorithm description and code to the large language model. The large language model is required to create a new algorithm that is different from the given algorithm but can be a modified version of the provided algorithm. The prompt word requires the large language model to first describe the new algorithm and its main steps, and then implement the given Python function. The specific implementation scheme of the parameter modification operator is as follows: Select one individual from the population, require the large language model to identify the main algorithm parameters, and assist in creating a new algorithm with different parameter settings; the prompt word requires the large language model to first describe the new algorithm and main steps, and then implement the given Python function; The population management employs an elite retention strategy and roulette wheel selection. The elite retention strategy is implemented in the survival method (the core mechanism in population management, implementing the "survival selection" stage in evolutionary algorithms. This method ensures that only individuals with the highest fitness are retained in each generation, thus driving the population towards a better solution). The population and the next generation are merged, sorted in descending order of score, and the top pop_size individuals are retained. pop_size is automatically adjusted based on the maximum sample size (max_sample_nums), using a tiered strategy: when the maximum sample size is ≥ 10000, pop_size is 40, accounting for 0.4%; when the maximum sample size is ≥ 1000, pop_size is 20, accounting for 2%; when the maximum sample size is ≥ 10000, pop_size is 20, accounting for 2%; and when the maximum sample size is ≥ 10000, pop_size is 20, accounting for 2%. When the maximum sample size is 200, `pop_size` is 10, representing 5% of the total sample size. When the maximum sample size is less than 200, `pop_size` is 5, representing 2.5% of the total sample size. The code uses heuristic settings based on empirical rules to ensure the "optimality" of `pop_size`. The roulette wheel selection process chooses individuals from a non-negative infinite fraction, with a selection probability... p = 1 / ( r + n ),in r Rank individuals (starting from 0). n The number of valid individuals; Population management also includes a duplicate function detection mechanism. If a duplicate function is detected (same string or same score), the score of the new function is set to negative infinity to ensure population diversity. Here, `pop_size` represents the number of optimal individuals to retain. The structured task description in S2 adopts a role-playing approach, setting the large language model as a top physicist and engineer proficient in dimensional analysis and experimental-data pipelines; the task description mandates the following function signature: def equation ( C 0, C 1, C 2, , , a , F , E f (Fiber elastic modulus). (Matrix stiffness) (Lateral deformation of fibers) (lateral deformation of the matrix) tuple[np.ndarray (multidimensional homogeneous array), np.ndarray]: The return value is a tuple of (piinputs (dimensionless input π number combinations), pioutputs (dimensionless output π number combinations)), where piinputs can only consist of observable experimental quantities, and each column of pioutputs corresponds to only one attribute to be predicted; where Ef represents the fiber elastic modulus. The structured task description described in S2 includes the following hard rules: Rule 1: Every dimensionless number must be strictly dimensionless at the sign level, i.e., mass. M ,length L ,time T All powers of 0; if rule 1 is missing, the evaluation will fail, leading to evolutionary collapse; Rule 2: Only element-wise multiplication, division, and exponentiation of input variables are allowed; the absence of rule 2 will lead to parsing difficulties. Rule 3: All numeric constants must be written in floating-point form; failure to comply with rule 3 will result in call failure. Rule 4: Do not use any aggregation functions (such as np.sum, np.mean, np.max, etc.); failure to use rule 4 will lead to overfitting. Rule 5: The use of the attribute to be predicted is prohibited in dimensionless input constructions. E f , , , If rule 5 is missing, training will be slow. Rule 6: Self-combination of output attributes is prohibited (e.g., ...) , (etc.); the absence of rule 6 would lead to dimensional errors; Rule 7: No conditional branches or logic that may lead to an early return; Rule 8: The dimensionless input dimension should be less than or equal to the original dimensional input dimension; failure to follow rule 8 will result in information leakage. Rule 9: For parameters such as Poisson's ratio that are inherently dimensionless, directly input the dimensionless number into the output without any transformation or combination; failure to include rule 9 will lead to accuracy issues. The response processing of the large language model in S2 includes: using regular expressions r '{. Extract the algorithm description (thought process) from the response, use SampleTrimmer to trim the function prefix in the response, and convert the trimmed code into a Function object; if response parsing fails, skip the sample; the evaluation mechanism described in S2 adopts a security evaluation method; specifically, SecureEvaluator supports a security evaluation mode (safeevaluate=True), which executes the generated code in an independent process to prevent malicious code from affecting the main process; it supports the Numba acceleration option (usenumbaaccelerate=True), using the @numba.jit (nopython=True) decorator to accelerate function execution; it supports the protected division option (useprotecteddiv=True), which will... a / b Replace with a protected division expression. a / ( b + delta )',in delta The default value is 1e-5 to prevent division by zero errors; it supports setting a random seed (randomseed), which is set in the first line of the function body using np.random.seed (the random number seed setting function) to ensure the reproducibility of experiments; it supports a timeout mechanism (timeoutseconds) to terminate the evaluation after the timeout. The S2 uses a performance analyzer to record all evaluation processes; EoHProfiler records the score, algorithm description, sampling time, and evaluation time of each evaluation function; it registers population information to a JSON file (pop{generation}.json); it records historical samples to a file (samples{start}~{end}.json); it records the best sample to a file (samples_best.json); and it supports multiple visualization tools such as TensorBoard and WandB.

[0026] S3. Evaluate and screen the schemes in the candidate dimensionless scheme set to obtain the optimal dimensionless scheme. S4. The input features and training label data in S1 are processed to be dimensionless using the optimal dimensionless transformation scheme, and then a fully connected neural network is trained based on the processed data. The fully connected neural network described in S4 employs a 4-layer structure, with 256, 128, 64, and 32 neurons per layer, respectively. The activation function is ReLU, the optimizer is AdamW, the learning rate is set to 0.01, the learning rate scheduler is cosine annealing, the minimum learning rate is 1e-4, the weight decay coefficient is 1e-4, the number of training epochs is 300, and the batch size is 32. The network input layer has 5 neurons, corresponding to 5 dimensionless input data points; the output layer has 4 neurons, corresponding to four dimensionless output data points. E f , , , The network uses a batch normalization layer for regularization. Specifically, in the training process described in S4, the ratio of the training set, validation set, and test set is 70%, 10%, and 20%, respectively; the loss function is the mean squared error (MSELoss), calculated using weighted loss with weights of [1.0, 1.0, 1.0, 1.0], corresponding to the four output targets ( E f , , , ); S5. Input the new indentation experimental data into the fully connected neural network trained in S4, output dimensionless material property prediction values, and convert them into dimensional actual physical parameters through inverse transformation. The formula for converting the dimensionless material property predictions in S5 into dimensional parameters through inverse transformation is consistent with the inverse operation of the transformation logic in S2 for generating the candidate dimensionless scheme set; the inverse transformation includes applying the inverse transformation of the dimensionless prediction results to the output scaler, and then applying the original dimensionless number expression defined by the equation function (e.g., ...). The process involves reverse-engineering the actual, dimensional parameter values; additionally, it includes a performance evaluation step: using the coefficients of determination. The model's prediction accuracy is evaluated by mean absolute error (MAE) and root mean square error (RMSE), the model's training efficiency is evaluated by the loss convergence curve, and the model's data efficiency is evaluated by the performance changes under different training sample numbers. The equation function is used to convert dimensional physical quantities from material indentation experiments into dimensionless numbers in order to train a physics-guided neural network. For example, such as Figure 1As shown, the process first takes "task description" and "algorithm template" as input, and then "delivers them to a large model for heuristic evolutionary algorithm evolution." The "large model" iteratively "generates the final algorithm for converting data from dimensional to dimensionless," and continuously optimizes it based on a feedback mechanism of "selecting an algorithm based on scores and continuing evolution." The "dimensional data" (q1, q2, q3, ..., qn) on the left enters the "delivered algorithm," and after completing the "dimensional -> dimensionless" conversion, it is divided into a "dimensional training set" and a "dimensional test set." The "dimensional training set" is used to "train the model" to obtain the "delivered model"; the "dimensional test set" enters the "model inference," generating "dimensional output," which is then "converted back to dimensional," and finally, the current algorithm's performance is quantified through "evaluation scores." If the input is: , , , , The corresponding output is: , , , If the input is: , , , , , The corresponding output is: , , , If the input is: , , , , , , The corresponding output is: , , , .

[0027] Example 2 This embodiment discloses a composite material indentation inversion system based on automatic dimensional analysis. The system can implement the methods of the above embodiments, including a training data acquisition module, a scheme generation module, a scheme selection module, a network training module, and a parameter output module. The training data acquisition module is used to acquire input feature data and training label data; The scheme generation module is used to generate a set of candidate dimensionless schemes. The solution screening module is used to evaluate and screen solutions; The network training module is used to train fully connected neural networks; The parameter output module is used to output dimensionless predicted values ​​of material properties and perform parameter conversion.

[0028] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0029] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily essential to the present invention.

Claims

1. A composite material indentation inversion method based on automatic dimensional analysis, characterized in that, Includes the following steps: S1. Obtain material indentation experimental data as input feature data and obtain corresponding real material property data as training label data; S2. Construct a heuristic evolutionary framework driven by a large language model to realize the transformation from dimensional physical quantities to dimensionless combinations of numbers. Provide the large language model with structured task descriptions and code templates to generate a set of candidate dimensionless schemes; Specifically, it includes: S21. Construct a heuristic evolutionary framework EoH driven by a large language model to automatically explore conversion algorithms from dimensional physical quantities to dimensionless number combinations; by providing the large language model with structured task descriptions and code templates, guide it to generate candidate dimensionless schemes that meet the requirements of dimensional consistency, and obtain a set of candidate dimensionless schemes. The framework employs an evolutionary cycle mechanism from generation to evaluation to selection; The heuristic evolutionary framework EoH described in S2 includes three core components: generation operator, fitness evaluation function, and selection mechanism. Generate operators are used to provide the large language model with a structured task description that includes function signatures, return value formats, mathematical operation rules, physical constraints, and code structure, guiding it to generate Python function equations that meet the requirements of dimensional consistency. In the later stages of evolution, the large language model improves or merges the current best function to generate a new generation of candidate functions. The fitness evaluation function is used to first verify whether the generated dimensionless numbers are strictly dimensionless by scaling transformation. If they fail, they are directly eliminated. Then, it is applied to the subsequent neural network training process and returns the loss value on the validation set. The selection mechanism is used to directly replicate the best few individuals to the next generation using an elite retention strategy, while selecting individuals from the remaining individuals in a fitness-proportional manner to participate in the generation process of the next generation. The heuristic evolutionary framework EoH described in S2 uses five evolutionary operators: initialization generation operator, crossover operator, improved crossover operator, modification operator, and parameter modification operator. It also employs a selection mechanism that combines elite retention strategy and fitness ratio selection. The initialization generator is responsible for global exploration and covers the search space; The crossover operator is used to handle global innovation and escape local optima. An improved crossover operator is used to balance exploration and utilization, reusing the core idea; Modify the operator to be responsible for structural improvement and to balance exploration and exploitation; Parameter modification operators are responsible for parameter optimization to maximize the use of remaining performance; Population management employs an elite retention strategy and roulette wheel selection. The elite retention strategy, implemented in the survival method, merges the current population with the next generation, sorts them in descending order of score, and retains the top pop_size best individuals. Roulette wheel selection chooses from individuals with non-negative infinite scores, with a selection probability... p = 1 / ( r + n ),in r Rank individuals n The number of valid individuals; Where pop_size represents the number of optimal individuals to retain, and the pop_size value is automatically adjusted using a tiered strategy; Population management also includes a duplicate function detection mechanism. If a duplicate function is detected, the score of the new function is set to negative infinity. S3. Evaluate and screen the schemes in the candidate dimensionless scheme set to obtain the optimal dimensionless scheme. S4. The input features and training label data in S1 are processed to be dimensionless using the optimal dimensionless transformation scheme, and then a fully connected neural network is trained based on the processed data. S5. Input the new indentation experimental data into the fully connected neural network trained in S4, output dimensionless material property prediction values, and convert them into dimensional actual physical parameters through inverse transformation.

2. The composite material indentation inversion method based on automatic dimensional analysis according to claim 1, characterized in that, S1 includes the following steps: S11. Obtain material indentation test data, which includes load-displacement curve data and surface morphology displacement data; extract the fitting parameters of the load-displacement curve as input features, extract the displacement of key points on the interface as auxiliary input features, and merge the input features and auxiliary input features to obtain comprehensive input features; Then, the real material property data corresponding to the material indentation experiment data is obtained as the model training label. The real material property data includes the elastic modulus and Poisson's ratio. The fitting parameters include the intercept of the quadratic fitting function. Linear coefficients and quadratic coefficient The surface topography displacement data includes indentation depth of... Time interface points lateral displacement and vertical displacement The input features described in S1 also include system geometry and load scale parameters.

3. The composite material indentation inversion method based on automatic dimensional analysis according to claim 1, characterized in that: The structured task description described in S2 adopts a role-playing approach, setting the large language model as top physicists and engineers.

4. The composite material indentation inversion method based on automatic dimensional analysis according to claim 1, characterized in that, The structured task description described in S2 includes the following hard rules: Rule 1: Every dimensionless number must be strictly dimensionless at the sign level; Rule 2: Only element-wise multiplication, division, and exponentiation of input variables are allowed; Rule 3: All numeric constants must be written in floating-point form; Rule 4: The use of any aggregate functions is prohibited; Rule 5: The use of the attribute to be predicted is prohibited in the construction of dimensionless inputs; Rule 6: Self-combination of output attributes is prohibited; Rule 7: No conditional branches or logic that may lead to an early return; Rule 8: The dimensionless input dimension should be less than or equal to the original dimensional input dimension; Rule 9: For parameters where Poisson's ratio is dimensionless, directly input the dimensionless number into the output without any transformation or combination.

5. The composite material indentation inversion method based on automatic dimensional analysis according to claim 1, characterized in that, The response processing of the large language model in S2 includes: extracting the algorithm description from the response using regular expressions, pruning the function prefix in the response using SampleTrimmer, and converting the pruned code into a Function object; if the response parsing fails, the sample is skipped. The assessment mechanism described in S2 adopts a security assessment approach.

6. The composite material indentation inversion method based on automatic dimensional analysis according to claim 1, characterized in that: In S2, a performance analyzer is used to record all evaluation processes.

7. The composite material indentation inversion method based on automatic dimensional analysis according to claim 1, characterized in that: The formula for converting the dimensionless material property prediction value into dimensional parameters through inverse transformation in S5 is consistent with the inverse operation of the transformation logic in S2 for generating a set of candidate dimensionless schemes. The inverse transformation includes applying the inverse transformation of the dimensionless prediction result to the output scaler, and then back-deriving the actual dimensional parameter value based on the original dimensionless number expression defined by the equation function. The equation function is used to convert dimensional physical quantities from material indentation experiments into dimensionless numbers in order to train a physics-guided neural network.

8. A system for implementing the composite material indentation inversion method based on automatic dimensional analysis as described in any one of claims 1-7, characterized in that: It includes a training data acquisition module, a scheme generation module, a scheme selection module, a network training module, and a parameter output module; The training data acquisition module is used to acquire input feature data and training label data; The scheme generation module is used to generate a set of candidate dimensionless schemes. The solution screening module is used to evaluate and screen solutions; The network training module is used to train fully connected neural networks; The parameter output module is used to output dimensionless predicted values ​​of material properties and perform parameter conversion.

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