Material design method and system driven by symbolic regression based on mechanistic knowledge base of sub-systems

Abstract

The application discloses a material design method and system based on a sub-system mechanism knowledge base driven symbolic regression, and the method comprises the following steps: constructing a mechanism knowledge base, the mechanism knowledge base comprises a plurality of sub-bases corresponding to different material systems respectively, and each sub-base stores a corresponding mechanism unit; obtaining a data set of an original material, selecting a target sub-base corresponding to a material system to which the original material belongs from the mechanism knowledge base, and screening an available mechanism set from the target sub-base; performing symbolic regression based on the available mechanism set to generate an initial population, and performing evolutionary iteration processing on the initial population to obtain a candidate individual set; evaluating each candidate individual in the candidate individual set based on a constraint condition in the target sub-base, and performing evolutionary iteration processing on the candidate individuals that pass the evaluation. In the application, the sub-system mechanism knowledge is structured and embedded into core links such as population initialization, evolutionary iteration and individual evaluation of symbolic regression, so that the probability of generating false expressions is reduced.

Description

Technical Field

[0001] This invention belongs to the field of materials design technology, specifically relating to a materials design method and system driven by a subsystem mechanism knowledge base for symbolic regression. Background Technology

[0002] In the research and development of energy materials, materials such as solid electrolytes and electrocatalysts aim to obtain interpretable analytical physical formulas from experimental / computational data to reveal the quantitative relationships between components, structures, processes, and properties. Symbolic regression is an important means to achieve this goal. Summary of the Invention

[0003] General symbolic regression tools typically take a dataset and a set of operators as input, search an expression tree using an evolutionary algorithm, and output candidate analytical expressions using prediction error and complexity as fitness. This type of method lacks a knowledge base specific to the material system; different materials share the same operator pool, resulting in a highly random search process. This can easily lead to expressions with good numerical fits that violate the physical laws of materials, and the extracted knowledge is difficult to accumulate and reuse.

[0004] Some approaches leverage large-scale materials models to extract features or operator suggestions from literature and use cue words to assist symbolic regression. However, literature knowledge often exists as unstructured text, making it difficult for algorithms to directly verify and utilize it. Furthermore, the mechanistic differences between various energy material systems are not structurally represented, and large-scale models may produce inaccurate content. Such methods typically only provide external cues and are unlikely to deeply participate in core processes such as population initialization, mutation, and evaluation.

[0005] Other approaches add general physical constraints to symbolic regression and apply them to fitness as penalty terms. However, this approach does not differentiate constraints based on systems such as oxides, sulfides, and electrocatalysts, nor does it consider the applicable boundaries of the mechanisms. Furthermore, its constraints primarily apply to the final evaluation, making it difficult to compress the solution space in the early stages of the search, and it lacks a continuously updated library of subsystem mechanism units.

[0006] Therefore, based on the above problems, it is necessary to provide a material design method and system driven by a subsystem mechanism knowledge base for symbolic regression.

[0007] The purpose of this invention is to provide a material design method and system driven by symbolic regression based on a subsystem mechanism knowledge base, which can solve the problem mentioned above where the lack of classification for many types of energy materials leads to large search volumes and the potential for false analytical expressions.

[0008] To achieve the above objectives, a specific embodiment of the present invention provides a material design method driven by symbolic regression based on a subsystem mechanism knowledge base, the method comprising:

[0009] A mechanism knowledge base is constructed, which includes multiple sub-bases corresponding to different material systems, and each sub-base stores a corresponding mechanism unit.

[0010] Obtain the dataset of the original materials, select the target sub-library corresponding to the material system to which the original materials belong from the mechanism knowledge base, and filter out the set of usable mechanisms from the target sub-library;

[0011] Symbolic regression is performed based on the available mechanism set to generate an initial population, and the initial population is subjected to evolutionary iteration to obtain a candidate individual set;

[0012] Each candidate individual in the candidate individual set is evaluated based on the constraints within the target sub-library, and the candidate individuals that pass the evaluation are subjected to evolutionary iteration processing.

[0013] In one or more embodiments of the present invention, the step of performing symbolic regression based on the available mechanism set to generate an initial population specifically includes:

[0014] The mathematical sub-fragments corresponding to the mechanism units in the available mechanism set are embedded in the expression subtree of the original material to generate the first type of individual;

[0015] The second type of individual is generated by randomly generating an expression tree;

[0016] The first type of individuals and the second type of individuals are combined to generate the initial population.

[0017] In one or more embodiments of the present invention, the step of performing evolutionary iteration processing on the initial population to obtain a candidate individual set specifically includes:

[0018] The partial expression subtrees of each individual in the initial population are replaced with mathematical sub-fragments corresponding to the mechanism units in the available mechanism set to generate mutated individuals; wherein, calling mechanism units from other sub-libraries outside the target sub-library is prohibited;

[0019] The mathematical sub-fragments corresponding to the mechanistic units of the current material system originating from the initial population in the parent individuals are transferred to the offspring individuals to generate crossover individuals;

[0020] The initial population, the mutated individuals, and the crossover individuals are combined to generate the candidate individual set.

[0021] In one or more embodiments of the present invention, the method further includes:

[0022] When the mutated individuals and / or the crossover individuals are generated during the evolutionary iteration, the mechanism embedding probability in the early stage of the iteration is greater than the mechanism embedding probability in the later stage of the iteration.

[0023] Wherein, the mechanism embedding probability is the probability of embedding the mathematical sub-fragment corresponding to the mechanism unit in the available mechanism set into the expression tree of the corresponding individual when generating the mutant individual and / or the crossover individual.

[0024] In one or more embodiments of the present invention, the step of evaluating each candidate individual in the candidate individual set based on the constraints within the target sub-library specifically includes:

[0025] The hard constraints in the target sub-library are invoked to evaluate the candidate individuals, and candidate individuals that fail to meet any of the hard constraints are eliminated or penalized.

[0026] The candidate individuals that pass the hard constraint condition verification are evaluated based on the comprehensive fitness, and the candidate individuals that meet the preset requirements are selected; wherein, the comprehensive fitness includes at least one of the following: the prediction error of the candidate individual's expression, the complexity of the candidate individual's expression, the degree of conformity between the candidate individual and the prior rules of the target sub-library, and the degree of matching between the candidate individual and the negative samples in the target sub-library.

[0027] In one or more embodiments of the present invention, the step of filtering the set of available mechanisms from the target sub-library specifically includes:

[0028] Extract the operating condition feature vector of each sample from the dataset of the original material, wherein the operating condition feature vector includes at least one of temperature, chemical composition and crystal phase ratio;

[0029] Traverse each mechanism unit in the target sub-library and mark the failure mechanism unit based on the failure boundary conditions of each mechanism unit;

[0030] The mechanism units in the target sub-library that are not marked as failure mechanism units are retained to obtain the set of available mechanisms.

[0031] In one or more embodiments of the present invention, the method further includes:

[0032] The failure boundary conditions include the relationship between multiple feature functions of the operating condition feature vector and corresponding thresholds;

[0033] If the operating condition feature vector of any sample makes the failure boundary condition of any of the aforementioned mechanism units true, then the mechanism unit is marked as a failure mechanism unit.

[0034] In one or more embodiments of the present invention, after the selected candidate individuals that have passed the evaluation undergo repeated evolutionary iterations, the method further includes:

[0035] Generate candidate analytical expressions for all the candidate individuals after the iteration is completed;

[0036] Extract new mechanistic units from the candidate analytical expressions that have been validated through first-principles simulations and / or experimental datasets;

[0037] Identify the material system to which the new mechanism unit belongs, and write the new mechanism unit into the sub-library of the corresponding material system in the mechanism knowledge base.

[0038] In one or more embodiments of the present invention, writing the new mechanism unit into the sub-library of the material system corresponding to the mechanism knowledge base specifically includes:

[0039] The new mechanism unit is first stored in a temporary cache area, and a low confidence tag is assigned to the new mechanism unit. The temporary cache area is associated with each sub-base in the mechanism knowledge base.

[0040] Repeatedly verify the mechanism units in the temporary cache area, and migrate the mechanism units with improved confidence from the temporary cache area to the sub-library corresponding to their material system.

[0041] A specific embodiment of the present invention also provides a material design system driven by a subsystem mechanism knowledge base for symbolic regression, the system comprising:

[0042] A construction module is used to construct a mechanism knowledge base, which includes multiple sub-libraries corresponding to different material systems, and each sub-library stores a corresponding mechanism unit.

[0043] The filtering module is used to obtain the dataset of the original materials, select the target sub-library corresponding to the material system to which the original materials belong from the mechanism knowledge base, and filter out the set of usable mechanisms from the target sub-library;

[0044] The generation module is used to perform symbolic regression based on the available mechanism set to generate an initial population, and to perform evolutionary iteration processing on the initial population to obtain a candidate individual set;

[0045] The evaluation module is used to evaluate each candidate individual in the candidate individual set based on the constraints in the target sub-library, and the candidate individuals that pass the evaluation are subjected to evolutionary iteration processing.

[0046] Compared with existing technologies, the material design method driven by the subsystem mechanism knowledge base of this invention constructs a mechanism knowledge base containing multiple sub-libraries corresponding to different material systems, each storing mechanism units. After obtaining the original material dataset, a target sub-library corresponding to the material system to which the original material belongs is selected, and a set of available mechanisms is screened from the target sub-library. This allows the initial population generation and evolutionary iteration of symbolic regression to be driven by the subsystem mechanism knowledge. At the same time, candidate individuals are evaluated based on the constraints within the target sub-library, and only those candidates that pass the evaluation continue to evolve and iterate. This structurally embeds the subsystem mechanism knowledge into the core links of symbolic regression, such as population initialization, evolutionary iteration, and individual evaluation. It enables matching and calling mechanism units and constraints according to the material system, compresses the solution space and guides the search direction in the early stages of the search, improves the physical rationality and interpretability of candidate formulas, and reduces the probability of generating false expressions that have no physical meaning or violate material mechanisms. This is conducive to the continuous accumulation, reuse, and updating of material design knowledge according to the system. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is an application scenario diagram of the material design method driven by the subsystem mechanism knowledge base according to one embodiment of the present invention;

[0049] Figure 2 This is a flowchart of a material design method driven by a subsystem mechanism knowledge base for symbolic regression, as described in one embodiment of the present invention.

[0050] Figure 3 This is a schematic diagram of a material design system driven by symbolic regression based on a subsystem mechanism knowledge base, as shown in one embodiment of the present invention.

[0051] Figure 4 This is a hardware structure diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0052] To enable those skilled in the art to better understand the technical solutions in this disclosure, the technical solutions in the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this disclosure.

[0053] In energy materials research and development, materials such as solid electrolytes and electrocatalysts often require interpretable analytical physical formulas from experimental or computational data to reveal the quantitative relationships between composition, structure, processing, and performance. Symbolic regression is an important means to achieve this goal. However, existing symbolic regression-based material design methods suffer from at least the following technical problems:

[0054] (1) The physical mechanisms of different subsystems of energy materials are very different. Existing symbolic regression does not have a knowledge base for subsystems. All materials use the same set of operators and search rules, resulting in an explosion of search space and slow iteration convergence. For example, oxide solid electrolytes and sulfide solid electrolytes are completely different in ion transport mechanisms, defect chemistry, and grain boundary behavior. The reaction mechanism of electrocatalysts is also completely different from that of electrolytes.

[0055] (2) The materials have small sample sizes and the experimental noise is common. The algorithm is easy to output false analytical formulas with high mathematical fit, but which violate the laws of material physics. For example, the ionic conductivity formula for the generation activation energy of garnet LLZO is mathematically able to fit the dataset, but it completely violates the Arrhenius thermally activated transport physics.

[0056] (3) Existing methods have limitations in processing material mechanism knowledge. For example, knowledge is stored in papers and review texts, which are unstructured texts and cannot be directly read and called by symbolic regression programs. Some existing solutions only add a few general constraints to the final scoring, and the mechanism knowledge cannot penetrate into the population initialization and crossover mutation generation stages.

[0057] (4) There are a large number of “mechanism failure boundaries” in different material systems. A certain mechanism is valid in one type of material but completely fails in another type of material. Existing technology does not distinguish failure boundaries and may incorrectly call inapplicable physical mechanisms across material systems.

[0058] (5) Lack of a closed-loop sedimentation mechanism. After obtaining effective new mechanisms through symbolic regression mining, they cannot be classified, verified, and written back to the knowledge base according to the material system. Each round of mining tasks starts from scratch.

[0059] To address the aforementioned technical problems, this application provides a material design method driven by symbolic regression based on a subsystem mechanism knowledge base. The basic concept is as follows: A mechanism knowledge base is constructed, comprising multiple sub-bases corresponding to different material systems, each storing corresponding mechanism units; a dataset of the original material is obtained; a target sub-base corresponding to the material system to which the original material belongs is selected from the mechanism knowledge base, and a set of usable mechanisms is screened from the target sub-base; symbolic regression is performed based on the set of usable mechanisms to generate an initial population, and the initial population undergoes evolutionary iteration to obtain a set of candidate individuals; each candidate individual in the candidate individual set is evaluated based on constraints within the target sub-base, and the selected candidate individuals that pass the evaluation undergo evolutionary iteration.

[0060] Through the above concept, the subsystem mechanism knowledge no longer remains in the literature or external prompts, but enters the core links of symbolic regression such as population initialization, evolutionary iteration, and individual evaluation in the form of structured mechanism units and constraints. In this way, mechanism units and constraints are matched and called according to the material system, compressing the solution space and guiding the search direction in the early stage of the search, improving the physical rationality and interpretability of candidate formulas, reducing the probability of generating false expressions that have no physical meaning or violate the material mechanism, and facilitating the continuous accumulation, reuse, and updating of material design knowledge according to the system.

[0061] Reference Figure 1 In one implementation scenario example, the server and terminal are connected via a network, and the server, terminal, or both cooperate to run the material design method driven by symbolic regression based on the subsystem mechanism knowledge base provided in this application embodiment. For example, the server can construct the aforementioned mechanism knowledge base, and the terminal can obtain a dataset of original materials. After the terminal obtains the dataset of original materials, it can send it to the server, which then runs the material design method driven by symbolic regression based on the subsystem mechanism knowledge base provided in this application embodiment to perform various processes of symbolic regression, thereby outputting analytical expressions for individual materials that meet the requirements. Of course, the material design method shown above can also be implemented by the server or the terminal alone, and this application does not impose any restrictions on this.

[0062] In the above implementation environment, the terminal and the server communicate via a communication network. Optionally, the communication network can be a wired network or a wireless network, and it can be at least one of a local area network (LAN), a metropolitan area network (MAN), and a wide area network (WAN). The server can be a standalone physical server, a server cluster or a distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDN), and big data and artificial intelligence platforms. The server and terminal devices can be independent devices or integrated into the same system; there is no limitation here.

[0063] Based on the above description of the material design process driven by subsystem mechanism knowledge base symbolic regression, it can be seen that the material design method driven by subsystem mechanism knowledge base symbolic regression proposed in this application can be executed by any suitable computer device (terminal or server); or, the material design method driven by subsystem mechanism knowledge base symbolic regression can be executed by both a terminal and a server. For ease of explanation, the following description will use the execution of the material design method driven by subsystem mechanism knowledge base symbolic regression by a computer device as an example.

[0064] The following describes the material design method of subsystem mechanism knowledge base driven symbolic regression of this application with specific embodiments.

[0065] Please refer to Figure 2 The material design method driven by the subsystem mechanism knowledge base in one embodiment of the present invention includes:

[0066] S11. Construct a mechanism knowledge base, which includes multiple sub-bases corresponding to different material systems, each storing corresponding mechanism units. Specifically, the mechanism knowledge base is divided into independent sub-bases according to major material categories. In this embodiment, the mechanism knowledge base may include an oxide solid electrolyte sub-base, a sulfide solid electrolyte sub-base, and an electrocatalyst sub-base, each storing corresponding mechanism units. Each sub-base can store multiple mechanism units, whose fields include a mechanism physical description, optional mathematical sub-expression fragments, a set of mechanism derived descriptors, a set of hard physical constraints, a set of soft prior constraints, failure boundary conditions, a set of negative sample fragments, and a confidence label.

[0067] Taking the oxide solid electrolyte sub-library as an example, the Arrhenius thermally activated ion transport mechanism unit can be entered. Its physical description is that lithium ions in crystalline oxide solid electrolytes are transported by thermal activation over the migration barrier. The mathematical sub-fragment is the Arrhenius equation. The mechanism descriptor includes migration activation energy and temperature. Hard physical constraints include activation energy greater than zero, ionic conductivity greater than zero, and conductivity increasing monotonically with increasing temperature. Soft prior constraints include vacancy concentration and conductivity exhibiting a volcano-like change. Failure boundaries include near superionic phase transition, extremely low temperature quantum tunneling, and low-temperature polycrystalline samples dominated by grain boundary impedance. Negative samples include expression fragments with activation energy less than zero, with a high confidence level.

[0068] Taking the sulfide solid electrolyte sub-library as an example, it can be entered into PS4. 3- The tetrahedral framework connects the transport mechanism units, and its physical description is that the sulfide solid electrolyte relies on PS4. 3- The tetrahedral three-dimensional interconnected framework enables lithium-ion migration; framework fracture leads to a decrease in conductivity. The mechanism derives descriptors including PS4. 3- Tetrahedral proportions and skeleton connectivity, hard physics constraints including PS4 3- When the connectivity of a tetrahedral network decreases, the ionic conductivity decreases. The failure boundary includes material decomposition or highly fragmented amorphous sulfides, with a high confidence level.

[0069] Taking the electrocatalyst sub-library as an example, volcano-related mechanism units can be entered, the catalytic activity and intermediate adsorption energy show a volcano-shaped curve, and corresponding constraints, descriptors and failure boundaries can be set.

[0070] The above describes some of the mechanism units corresponding to the sub-libraries, which is not a limitation on the type and number of sub-libraries and their corresponding mechanism units in this application.

[0071] Therefore, the mechanism knowledge base provides a foundation for subsequent material system identification, retrieval, filtering of mechanism units that fall within the failure boundary, and storage of newly added mechanism units. As a result, the mechanisms of different energy material systems are isolated from each other, and domain knowledge is transformed from unstructured text into machine-readable, searchable, and verifiable structured records, providing a foundation for subsequent symbolic regression analysis throughout the entire process.

[0072] S12. Obtain the dataset of the original materials, select the target sub-library corresponding to the material system to which the original materials belong from the mechanism knowledge base, and filter the set of available mechanisms from the target sub-library. Specifically, the original materials can be identified by meta-tags to determine which type of energy material they belong to, such as oxide solid electrolytes, sulfide solid electrolytes, or electrocatalysts, thereby selecting the corresponding target sub-library.

[0073] The selection of usable mechanisms from the target sub-library specifically includes:

[0074] The working condition feature vector of each sample is extracted from the dataset of the original material. The working condition feature vector includes at least one of temperature, chemical composition, and crystal phase ratio. The working condition feature vector can be one, two, or all of the three factors, and this application does not impose any restrictions on this.

[0075] The mechanism units in the target sub-library are traversed, and failure mechanism units are marked based on their failure boundary conditions. For example, using disjunctive normal form, if the operating condition feature vector of any sample makes the failure boundary condition of any mechanism unit true, then that mechanism unit is marked as a failure mechanism unit. Specifically, the failure boundary is represented in disjunctive normal form: F_j(x)=∨_k(f_{jk}(x)>θ_{jk}), where f_{jk} is the feature function and θ_{jk} is the corresponding threshold.

[0076] Mechanism units that are not marked as failure mechanism units in the target sub-library are retained to obtain the set of usable mechanisms. If sample x satisfies F_j(x)=True, then the mechanism unit j is marked as "failed". Only mechanism units that do not trigger the failure boundary for all samples are retained and output to the downstream unit along with their hard constraints, soft priors, and negative samples.

[0077] For example, given an input garnet LLZO dataset with sample temperatures around 300K, far from the superion phase transition temperature, and where the difference between the sample temperature and the phase transition temperature exceeds a set threshold, the failure boundary of the Arrhenius thermally activated transport mechanism is not triggered, and the mechanism is retained. If a sample temperature is close to the phase transition region, the Arrhenius mechanism is filtered out. Thus, the set of available mechanisms not only matches the material system but also the sample operating conditions, avoiding the incorrect application of effective physical mechanisms from material A to material B, and preventing the incorrect invocation of mechanism units under failure conditions. This further narrows the symbolic regression search space and improves the physical effectiveness of candidate formulas.

[0078] S13. Perform symbolic regression based on the available mechanism set to generate an initial population, and perform evolutionary iteration processing on the initial population to obtain a candidate individual set.

[0079] In this embodiment, a hybrid strategy is used to generate the initial population by performing symbolic regression based on the set of available mechanisms. Specifically, this includes:

[0080] The mathematical sub-fragments corresponding to the mechanism units in the available mechanism set are embedded in the expression subtree of the original material to generate the first type of individuals; the expression tree is generated randomly to generate the second type of individuals; the first type of individuals and the second type of individuals are combined to generate the initial population.

[0081] The first type of individual directly reuses the mature physical priors of the material system, such as directly embedding descriptor nodes or sub-fragments such as the Arrhenius equation, vacancy concentration, and octahedral distortion in the garnet LLZO mission; the second type of individual retains the ability to generate expression trees in a traditional way, and is used to explore new mechanisms that have not yet been entered into the knowledge base.

[0082] In one optional embodiment, the ratio of the first type of individuals to the second type of individuals can be dynamically adjusted based on the confidence level of the mechanism for the current task in the mechanistic knowledge base. When the confidence level is high, the proportion of individuals embedded with the mechanism sub-fragments of the current system is increased; when the confidence level is low, the proportion of randomly explored individuals is increased. Thus, the initial population is neither completely randomly generated nor completely limited by existing knowledge, but rather achieves a balance between reusing mature physical priors and retaining the ability to explore new mechanisms. This causes the symbolic regression to shift in a direction consistent with the laws of materials physics from the search starting point, accelerating the convergence speed under small sample conditions.

[0083] The process of iteratively processing the initial population to obtain a set of candidate individuals specifically includes:

[0084] The partial expression subtrees of each individual in the initial population are replaced with mathematical sub-fragments corresponding to mechanism units in the available mechanism set to generate mutated individuals; whereby calling mechanism units from other sub-libraries outside the target sub-library is prohibited; mathematical sub-fragments corresponding to mechanism units of the current material system originating from the initial population in the parent individuals are migrated to the child individuals to generate crossover individuals; the initial population, mutated individuals, and crossover individuals are combined to generate a candidate individual set. In this embodiment, mutation and crossover operations are performed on both the first and second types of individuals.

[0085] For example, when generating variant individuals and / or crossover individuals through evolutionary iteration, sulfide PS4 will not be used. 3- If the tetrahedral mechanism is incorrectly embedded in an individual oxide solid electrolyte, the mechanism will not be invoked when the sample falls into the failure boundary of a certain mechanism.

[0086] In one optional embodiment, when generating mutated and / or crossover individuals through evolutionary iteration, the mechanism embedding probability in the early stage of iteration is greater than that in the later stage. The mechanism embedding probability is the probability of embedding the mathematical sub-fragment corresponding to the mechanistic unit in the available mechanism set into the expression tree of the corresponding individual when generating mutated and / or crossover individuals. Therefore, by fully utilizing the prior knowledge of the existing system's mechanisms in the early stage of iteration and enhancing the search for novel mechanisms in the later stage, it prevents cross-system misuse of mechanisms and improves population diversity and global search capabilities.

[0087] S14. Evaluate each candidate individual in the candidate individual set based on the constraints within the target sub-library, and perform evolutionary iteration processing on the candidate individuals that pass the evaluation. Specifically, a two-level evaluation is performed on all candidate individuals in each generation. All candidate individuals include the first and second types of individuals in the initial population, as well as the new generation of individuals generated through crossover and mutation operations, i.e., the current generation of the complete population.

[0088] The two-tiered assessment is as follows:

[0089] In the first-level evaluation, hard constraints from the target sub-library are invoked to evaluate candidate individuals, eliminating or penalizing those that fail any of the hard constraints. For example, the activation energy calculated by the LLZO garnet candidate formula is less than zero, triggering hard constraints in the oxide sub-library and directly eliminating the individual. In an optional embodiment, instead of directly deleting individuals, a large penalty loss is imposed, relying on subsequent selection operations for natural elimination, to accommodate energy material systems with partially ambiguous constraint boundaries or exceptions.

[0090] In the second-level evaluation, the candidate individuals that pass the hard constraint condition verification are evaluated based on the comprehensive fitness, and the candidate individuals that meet the preset requirements are selected. The comprehensive fitness includes at least one of the following: the prediction error of the candidate individual's expression, the complexity of the candidate individual's expression, the degree of conformity between the candidate individual and the prior rules of the target sub-library, and the degree of matching between the candidate individual and the negative samples in the target sub-library.

[0091] Specifically, the overall fitness can be composed of the base fitness plus a soft prior reward and a negative sample penalty. The base fitness can be composed of the prediction loss and the expression complexity. The prediction loss is used to quantify the goodness of fit of the formula to the data, and the expression complexity can be obtained by statistically analyzing the total number of nodes and the maximum depth of the candidate expression tree and then weighting them to avoid overfitting.

[0092] Based on the basic fitness, soft prior rewards and negative sample penalties are superimposed. Soft prior rewards are given to candidate individuals that conform to statistical trends in the materials field (such as volcano-like relationships, the relationship between vacancy concentration and conductivity). Negative sample penalties are imposed on candidate individuals that hit negative samples.

[0093] Negative samples can come from expression fragments with confirmed physical errors in the literature, high-frequency subtree structures eliminated by hard constraints in previous generations of evolution, and formula fragments that violate the laws of materials physics and are annotated by domain experts. The matching method can be to perform subtree traversal on the candidate expression tree, and if there is a subtree that is structurally isomorphic to the negative sample fragment, it is considered a match and a penalty is applied.

[0094] The overall fitness can be represented as a combination of prediction loss, complexity penalty, soft prior reward, and negative sample penalty. A tournament selection process can be performed based on the overall fitness, randomly selecting several individuals from the current population, comparing their overall fitness, and choosing the individual with the best fitness for the next generation. This process is repeated until the size of the next generation population reaches a preset value. After the update iterations are complete, a candidate analytical formula for the Pareto front can be output.

[0095] Thus, different energy materials use their own exclusive hard constraints and soft priors, which can filter out false analytical formulas that have good mathematical fitting effects but do not conform to the physics of such materials, and maintain population diversity.

[0096] Please refer to Figure 1 In one optional embodiment, after repeated evolutionary iterations are performed on the selected candidate individuals that have passed the evaluation, a subsystem mechanism backflow update can be performed, specifically including:

[0097] S15: Generate candidate analytical expressions for all candidate individuals after the iteration ends, extract new mechanistic units from the candidate analytical expressions that have been verified to be valid through first-principles simulation and / or experimental datasets, identify the material system to which the new mechanistic units belong, and write the new mechanistic units into the sub-library of the corresponding material system in the mechanism knowledge base.

[0098] The criteria for validating a new mechanism unit may include: the prediction error of the sub-expression corresponding to the new mechanism unit on an independent validation dataset is lower than a preset threshold; the sub-expression does not violate the existing hard physical constraints of the material system; and the sub-expression does not have logical redundancy with existing mechanism units in the sub-library, for example, the structural similarity is lower than a preset threshold. If the above conditions are met, the expression is deemed valid and allowed to be added to the library.

[0099] In one optional embodiment, when writing a new mechanism unit into the sub-library of the material system corresponding to the mechanism knowledge base, the new mechanism unit can first be stored in a temporary cache area and a low confidence mark can be assigned to the mechanism unit, wherein the temporary cache area is associated with each sub-library in the mechanism knowledge base; the mechanism units in the temporary cache area are repeatedly verified, and the mechanism units with improved confidence are migrated from the temporary cache area to the sub-library corresponding to their material system.

[0100] For example, a new semi-empirical mechanism for distortion and barrier was discovered in sulfide LGPS, verified, and then written into the sulfide solid electrolyte sub-library. This achieves a closed-loop iteration of data mining, new mechanism discovery, and categorization, reducing the risk of erroneous mechanisms contaminating the knowledge base and ensuring that subsequent mining tasks within the same system can continuously benefit from this approach.

[0101] Compared with existing technologies, this application does not merely add a few general constraints in the final scoring stage, but fully integrates mechanism knowledge into the entire symbolic regression process through a subsystem energy material mechanism knowledge base, material system identification and retrieval, failure boundary filtering, mechanism-guided population initialization, evolutionary iterative intervention with failure boundary verification, subsystem two-layer candidate evaluation, and subsystem mechanism backflow update.

[0102] Existing general symbolic regression tools do not distinguish the differences in physical mechanisms among oxides, sulfides, and electrocatalysts. They only use a globally fixed operator pool for random search, which easily produces spurious physical formulas and lacks mechanism sedimentation and closure. The knowledge of large-scale model-assisted schemes is unstructured text, which cannot distinguish the differences in mechanisms among different energy material systems. There are no structured fields for hard constraints, soft priors, and failure boundaries. Furthermore, large-scale models are prone to illusions, only providing external hints. Schemes that simply add global physical constraints are universally applicable, do not consider mechanism failure boundaries, and only affect the final score. They cannot compress the search space during the population generation stage, nor do they have a subsystem mechanism unit library that can be incrementally updated.

[0103] This application selects target sub-libraries and filters available mechanism sets, embeds mechanism sub-fragments of the system in the initialization stage, prohibits cross-system calls to mechanisms and dynamically adjusts the embedding probability in the evolution stage, performs hard physical constraint verification in the evaluation stage and then superimposes soft priors and negative samples to correct fitness, and classifies and stores them in the library according to material system in the reflow stage.

[0104] Therefore, compressing the solution space and guiding the search direction in the early stages of the search improves the physical rationality and interpretability of candidate formulas, reduces the probability of generating false expressions that have no physical meaning or violate material mechanisms, and is conducive to the continuous accumulation, reuse and updating of material design knowledge according to the system.

[0105] Please refer to Figure 3 In one embodiment of the present invention, a material design system driven by a subsystem mechanism knowledge base for symbolic regression is also provided. The system includes a construction module 21, a screening module 22, a generation module 23, an evaluation module 24, and a backflow update module 25.

[0106] The construction module 21 is used to construct a mechanism knowledge base, which includes multiple sub-bases corresponding to different material systems, and each sub-base stores the corresponding mechanism units; the filtering module 22 is used to obtain the dataset of the original material, select the target sub-base corresponding to the material system to which the original material belongs from the mechanism knowledge base, and filter out the set of available mechanisms from the target sub-base; the generation module 23 is used to perform symbolic regression based on the set of available mechanisms to generate an initial population, and perform evolutionary iteration processing on the initial population to obtain a set of candidate individuals; the evaluation module 24 is used to evaluate each candidate individual in the set of candidate individuals based on the constraints in the target sub-base, and the candidate individuals selected that pass the evaluation are subjected to evolutionary iteration processing.

[0107] In one optional embodiment, the generation module 23 is used to embed mathematical sub-fragments corresponding to mechanistic units in the available mechanism set into the expression subtree of the original material to generate a first type of individual; to generate a second type of individual by randomly generating an expression tree; and to combine the first type of individual and the second type of individual to generate an initial population.

[0108] In one optional embodiment, the generation module 23 is used to replace the partial expression subtrees of each individual in the initial population with mathematical sub-fractions corresponding to the mechanism units in the available mechanism set to generate mutated individuals; wherein, calling mechanism units from other sub-libraries outside the target sub-library is prohibited; the mathematical sub-fractions corresponding to the mechanism units of the current material system originating from the initial population in the parent individuals are migrated to the offspring individuals to generate crossover individuals; and the initial population, mutated individuals, and crossover individuals are combined to generate a candidate individual set.

[0109] In one optional embodiment, the generation module 23 is configured to, during the evolutionary iteration to generate mutated individuals and / or crossover individuals, have a higher mechanism embedding probability in the early stage of the iteration than in the later stage of the iteration; wherein, the mechanism embedding probability is the probability of embedding the mathematical sub-fragment corresponding to the mechanism unit in the available mechanism set into the expression tree of the corresponding individual when generating mutated individuals and / or crossover individuals.

[0110] In one optional embodiment, the evaluation module 24 is used to evaluate candidate individuals by invoking hard constraints in the target sub-library and to eliminate or penalize candidate individuals that fail to meet any of the hard constraints; to evaluate candidate individuals that pass the hard constraint validation based on the comprehensive fitness and to select candidate individuals that meet the preset requirements; wherein, the comprehensive fitness includes at least one of the following: the prediction error of the candidate individual's expression, the complexity of the candidate individual's expression, the degree of conformity between the candidate individual and the prior rules of the domain in the target sub-library, and the degree of matching between the candidate individual and the negative samples in the target sub-library.

[0111] In one optional embodiment, the screening module 22 is used to extract the operating condition feature vector of each sample from the dataset of the original material. The operating condition feature vector includes at least one of temperature, chemical composition and crystal phase ratio; traverse each mechanism unit in the target sub-library, and mark the failure mechanism unit based on the failure boundary conditions of each mechanism unit; retain the mechanism units in the target sub-library that are not marked as failure mechanism units to obtain the set of available mechanisms.

[0112] In one optional embodiment, the failure boundary condition includes the relationship between multiple characteristic functions of the operating condition feature vector and the corresponding threshold; if the operating condition feature vector of any sample makes the failure boundary condition of any mechanism unit true, then the mechanism unit is marked as a failure mechanism unit.

[0113] In one optional embodiment, the backflow update module 25 is used to generate candidate analytical expressions for all candidate individuals after the iteration ends; extract new mechanistic units from the candidate analytical expressions that have been verified to be valid through first-principles simulation and / or experimental datasets; identify the material system to which the new mechanistic unit belongs; and write the new mechanistic unit into the sub-library of the corresponding material system in the mechanism knowledge base.

[0114] In one optional embodiment, the backflow update module 25 is used to first store the new mechanism unit in a temporary cache area and assign a low confidence mark to the mechanism unit, wherein the temporary cache area is associated with each sub-library in the mechanism knowledge base; repeatedly verify the mechanism units in the temporary cache area, and migrate the mechanism units with improved confidence from the temporary cache area to the sub-library corresponding to their material system.

[0115] Therefore, each module of the material design system driven by the subsystem mechanism knowledge base of this application can execute the corresponding steps in the above method, thereby realizing the core links such as population initialization, evolutionary iteration and individual evaluation of subsystem mechanism knowledge structured embedding symbolic regression at the system level.

[0116] As per the above reference Figures 1 to 2 This specification describes a material design method driven by a subsystem mechanism knowledge base using symbolic regression, based on embodiments of the present specification. The details mentioned in the above description of the method embodiments also apply to the material design system driven by a subsystem mechanism knowledge base using symbolic regression, as described in the embodiments of the present specification. The above-described material design system driven by a subsystem mechanism knowledge base using symbolic regression can be implemented in hardware, software, or a combination of both.

[0117] Reference Figure 4 In one embodiment of the present invention, an electronic device is also provided. The electronic device may include at least one processor 31, a memory 32 (e.g., non-volatile memory 32), a RAM 33, and a communication interface 34, and the at least one processor 31, memory 32, RAM 33, and communication interface 34 are connected together via a bus. At least one processor 31 executes at least one computer-readable instruction stored or encoded in the memory 32.

[0118] It should be understood that the computer-executable instructions stored in memory 32, when executed, cause at least one processor 31 to perform the above-described combinations in the various embodiments of this specification. Figures 1 to 2 The description includes various operations and functions.

[0119] In the embodiments of this specification, electronic devices may include, but are not limited to: personal computers, server computers, workstations, desktop computers, laptop computers, notebook computers, mobile electronic devices, smartphones, tablet computers, cellular phones, personal digital assistants (PDAs), handheld devices, messaging devices, wearable electronic devices, consumer electronic devices, etc.

[0120] In one embodiment of the present invention, a program product, such as a machine-readable medium, is also provided. The machine-readable medium may have instructions (i.e., the elements implemented in software as described above), which, when executed by a machine, cause the machine to perform the above-described combinations of the various embodiments of this specification. Figures 1 to 2 The various operations and functions described. Specifically, a system or apparatus equipped with a readable storage medium storing software program code that implements the functions of any of the embodiments described above, and enabling the computer or processor of the system or apparatus to read and execute the instructions stored in the readable storage medium.

[0121] In this case, the program code read from the readable medium itself can perform the functions of any of the above embodiments, and therefore the machine-readable code and the readable storage medium storing the machine-readable code constitute a part of this specification.

[0122] Examples of readable storage media include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD-RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer or the cloud via a communication network.

[0123] Those skilled in the art will understand that the various embodiments disclosed above can be modified and varied without departing from the spirit of the invention. Therefore, the scope of protection of this specification should be defined by the appended claims.

[0124] It should be noted that not all steps and units in the above process and system structure diagrams are mandatory; some steps or units can be omitted according to actual needs. The execution order of each step is not fixed and can be determined as needed. The device structure described in the above embodiments can be a physical structure or a logical structure. That is, some units may be implemented by the same physical client, or some units may be implemented by multiple physical clients, or they may be jointly implemented by certain components in multiple independent devices.

[0125] In the above embodiments, the hardware units or modules can be implemented mechanically or electrically. For example, a hardware unit, module, or processor may include permanent dedicated circuitry or logic (such as a dedicated processor, FPGA, or ASIC) to perform the corresponding operation. The hardware unit or processor may also include programmable logic or circuitry (such as a general-purpose processor or other programmable processor), which can be temporarily configured by software to perform the corresponding operation. The specific implementation method (mechanical, dedicated permanent circuitry, or temporarily configured circuitry) can be determined based on cost and time considerations.

[0126] The specific embodiments described above with reference to the accompanying drawings are exemplary embodiments, but do not represent all embodiments that can be implemented or fall within the scope of the claims. The term "exemplary" as used throughout this specification means "serving as an example, instance, or illustration" and does not imply that it is "preferred" or "advantageous" compared to other embodiments. Specific details are included to provide an understanding of the described techniques. However, these techniques can be practiced without these specific details. In some instances, well-known structures and apparatuses are shown in block diagram form to avoid obscuring the concepts of the described embodiments.

[0127] The foregoing description of this disclosure is provided to enable any person skilled in the art to implement or use this disclosure. Various modifications to this disclosure will be apparent to those skilled in the art, and the general principles applicable herein can be applied to other variations without departing from the scope of this disclosure. Therefore, this disclosure is not limited to the examples and designs described herein, but is consistent with the widest scope of the principles and novel features disclosed herein.

Claims

1. A material design method driven by a subsystem mechanism knowledge base using symbolic regression, characterized in that, The method includes: A mechanism knowledge base is constructed, which includes multiple sub-bases corresponding to different material systems, and each sub-base stores a corresponding mechanism unit. Obtain the dataset of the original materials, select the target sub-library corresponding to the material system to which the original materials belong from the mechanism knowledge base, and filter out the set of usable mechanisms from the target sub-library; Symbolic regression is performed based on the available mechanism set to generate an initial population, and the initial population is subjected to evolutionary iteration to obtain a candidate individual set; Each candidate individual in the candidate individual set is evaluated based on the constraints within the target sub-library, and the candidate individuals that pass the evaluation are subjected to evolutionary iteration processing.

2. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 1, characterized in that, The step of generating an initial population by performing symbolic regression based on the set of available mechanisms specifically includes: The mathematical sub-fragments corresponding to the mechanism units in the available mechanism set are embedded in the expression subtree of the original material to generate the first type of individual; The second type of individual is generated by randomly generating an expression tree; The first type of individuals and the second type of individuals are combined to generate the initial population.

3. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 1, characterized in that, The step of performing evolutionary iteration processing on the initial population to obtain a candidate individual set specifically includes: The partial expression subtrees of each individual in the initial population are replaced with mathematical sub-fragments corresponding to the mechanism units in the available mechanism set to generate mutated individuals; wherein, calling mechanism units from other sub-libraries outside the target sub-library is prohibited; The mathematical sub-fragments corresponding to the mechanistic units of the current material system originating from the initial population in the parent individuals are transferred to the offspring individuals to generate crossover individuals; The initial population, the mutated individuals, and the crossover individuals are combined to generate the candidate individual set.

4. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 3, characterized in that, The method further includes: When the mutated individuals and / or the crossover individuals are generated during the evolutionary iteration, the mechanism embedding probability in the early stage of the iteration is greater than the mechanism embedding probability in the later stage of the iteration. Wherein, the mechanism embedding probability is the probability of embedding the mathematical sub-fragment corresponding to the mechanism unit in the available mechanism set into the expression tree of the corresponding individual when generating the mutant individual and / or the crossover individual.

5. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 1, characterized in that, The evaluation of each candidate individual in the candidate individual set based on the constraints within the target sub-library specifically includes: The hard constraints in the target sub-library are invoked to evaluate the candidate individuals, and candidate individuals that fail to meet any of the hard constraints are eliminated or penalized. The candidate individuals that pass the hard constraint condition verification are evaluated based on the comprehensive fitness, and the candidate individuals that meet the preset requirements are selected; wherein, the comprehensive fitness includes at least one of the following: the prediction error of the candidate individual's expression, the complexity of the candidate individual's expression, the degree of conformity between the candidate individual and the prior rules of the target sub-library, and the degree of matching between the candidate individual and the negative samples in the target sub-library.

6. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 1, characterized in that, The step of selecting the set of available mechanisms from the target sub-library specifically includes: Extract the operating condition feature vector of each sample from the dataset of the original material, wherein the operating condition feature vector includes at least one of temperature, chemical composition and crystal phase ratio; Traverse each mechanism unit in the target sub-library and mark the failure mechanism unit based on the failure boundary conditions of each mechanism unit; The mechanism units in the target sub-library that are not marked as failure mechanism units are retained to obtain the set of available mechanisms.

7. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 6, characterized in that, The method further includes: The failure boundary conditions include the relationship between multiple feature functions of the operating condition feature vector and corresponding thresholds; If the operating condition feature vector of any sample makes the failure boundary condition of any of the aforementioned mechanism units true, then the mechanism unit is marked as a failure mechanism unit.

8. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 1, characterized in that, After repeated evolutionary iterations, the selected candidate individuals that have passed the evaluation are further included in the following process: Generate candidate analytical expressions for all the candidate individuals after the iteration is completed; Extract new mechanistic units from the candidate analytical expressions that have been validated through first-principles simulations and / or experimental datasets; Identify the material system to which the new mechanism unit belongs, and write the new mechanism unit into the sub-library of the corresponding material system in the mechanism knowledge base.

9. The material design method driven by symbolic regression based on the subsystem mechanism knowledge base according to claim 8, characterized in that, The step of writing the new mechanism unit into the sub-library of the corresponding material system in the mechanism knowledge base specifically includes: The new mechanism unit is first stored in a temporary cache area, and a low confidence tag is assigned to the new mechanism unit. The temporary cache area is associated with each sub-base in the mechanism knowledge base. Repeatedly verify the mechanism units in the temporary cache area, and migrate the mechanism units with improved confidence from the temporary cache area to the sub-library corresponding to their material system.

10. A material design system driven by a subsystem mechanism knowledge base and symbolic regression, characterized in that, The system includes: A construction module is used to construct a mechanism knowledge base, which includes multiple sub-libraries corresponding to different material systems, and each sub-library stores a corresponding mechanism unit. The filtering module is used to obtain the dataset of the original materials, select the target sub-library corresponding to the material system to which the original materials belong from the mechanism knowledge base, and filter out the set of usable mechanisms from the target sub-library; The generation module is used to perform symbolic regression based on the available mechanism set to generate an initial population, and to perform evolutionary iteration processing on the initial population to obtain a candidate individual set; The evaluation module is used to evaluate each candidate individual in the candidate individual set based on the constraints in the target sub-library, and the candidate individuals that pass the evaluation are subjected to evolutionary iteration processing.

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