A formula closed-loop generation method based on coating engineering constraint and prediction credibility checking

Abstract

This invention discloses a closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification. The method includes: parsing natural language formulation requirement descriptions and mapping them to a preset coating performance index dictionary to generate structured performance target objects; retrieving benchmark formulations from a historical formulation database based on these objects; outputting and terminating the process if the hard performance targets are met; otherwise, constructing a candidate constraint set based on unmet performance targets; inputting the benchmark formulations and constraint set into a large language model to generate initial candidate formulations, and determining the candidate formulations after performing deterministic engineering constraint verification; using a machine learning model to obtain predicted values ​​of coating performance indicators, and performing mechanistic reliability verification by combining historical reference formulations and training data coverage to obtain prediction reliability levels and out-of-distribution labels; and determining compliance item by item. If all hard performance targets are met and the reliability level is not low, the final recommended formulation is output; otherwise, adjustment constraint information is generated and returned to the generation step to form a closed loop. This method improves the efficiency of chemical feasibility verification and performance prediction reliability of candidate formulations.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design of coating formulations, and in particular to a closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification. Background Technology

[0002] Coating formulation design is a core step in the coating research and development process, traditionally relying heavily on the domain experience of researchers and extensive trial-and-error experiments. With the gradual penetration of artificial intelligence technology into materials science, existing research has attempted to introduce optimization algorithms and machine learning methods into the design and screening process of coating formulations to improve R&D efficiency and reduce experimental costs. Currently, relevant technical solutions can be mainly categorized into three types: formulation search methods based on genetic algorithms or particle swarm optimization algorithms, performance evaluation and feedback optimization methods based on machine learning models, and formulation retrieval and matching methods based on rule engines.

[0003] Formulation search methods based on genetic algorithms or particle swarm optimization typically set the types and proportions of formulation components or related process parameters as variables to be optimized. They then iteratively search within a pre-defined range of variables and select candidate formulations based on performance evaluation results. While these methods achieve a degree of automated formulation optimization, their input is usually limited to structured formulation component data and performance parameters. They struggle to directly handle the coating types, substrate conditions, application methods, testing methods, and multiple performance objectives described by researchers in natural language. When formulation design also needs to meet multiple engineering constraints such as raw material identity, inventory status, upper and lower limits of each component, component proportions, reaction equivalence ratios, pigment volume concentration, volatile organic compound content, and raw material compatibility, this engineering knowledge must be pre-encoded as search boundaries, objective functions, or penalty terms. The constraint construction process is complex and prone to omissions.

[0004] Performance evaluation and feedback optimization methods based on machine learning models typically train models using historical formulation data, raw material data, performance test data, and usage environment data to establish a mapping relationship between formulation composition and coating performance. The model output is then used to screen or iteratively optimize candidate formulations. While this approach can compensate for some of the shortcomings of traditional trial-and-error methods, in practical applications, the predictive accuracy of machine learning models is significantly limited by the coverage of the training data. When candidate formulations contain raw materials not found in the training data, or when the formulation proportions significantly exceed the range of historical samples, the performance predictions given by the model may have large deviations. Existing methods usually only output performance scores or risk levels, lacking mechanisms to identify and indicate whether the prediction results exceed the coverage of the training data, and failing to grade the predictive reliability of each performance indicator, making it difficult for researchers to determine the reliability of the prediction results.

[0005] The rule-based recipe retrieval and matching method primarily establishes a raw material comparison table and performance index mapping rules, performing static matching and filtering in a historical recipe database to provide users with historical recipes similar to their target needs as a reference. This method is relatively simple to implement, but it can only retrieve existing recipes and cannot automatically generate new candidate recipes based on unmet performance targets, nor can it perform systematic engineering constraint verification on the recipes. When historical recipes fail to meet all objectives, this method cannot provide further recipe adjustment or optimization capabilities.

[0006] Overall, while existing technologies have formed an iterative optimization framework driven by performance evaluation, formulation adjustment, simulation verification, or experimental verification, they have not yet formed an integrated closed-loop solution covering natural language requirement parsing, historical benchmark formulation retrieval, engineering hard constraint verification, performance prediction, out-of-distribution identification, indicator-by-indicator compliance evaluation, and formulation adjustment feedback. Especially under conditions of sparse coating formulation data, inconsistent testing conditions, and candidate formulations easily violating physicochemical constraints, how to simultaneously ensure that the generated formulation meets chemical feasibility requirements such as reaction equivalence, component ratios, pigment volume concentration, volatile organic compound content, and compatibility, and identify unreliable predictions beyond the coverage of training data, remains a problem that existing technologies have not yet effectively solved. Summary of the Invention

[0007] The purpose of this invention is to provide a closed-loop formulation generation method based on coating engineering constraints and prediction credibility verification. By integrating natural language requirement parsing, historical benchmark formulation retrieval, large language model generation under engineering constraints, machine learning performance prediction, and mechanism credibility verification based on training data coverage in a closed loop, this method improves the efficiency of chemical feasibility verification of candidate formulations and the reliability of performance prediction results. It solves the problems in the prior art where natural language formulation requirements are difficult to structure, candidate formulations are prone to violating physical and chemical constraints, and unreliable predictions that exceed the coverage of training data cannot be identified.

[0008] To address the aforementioned technical problems, a first aspect of this invention provides a closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification, comprising the following steps: S1, Receive natural language formulation requirement description, perform semantic parsing on the natural language formulation requirement description, and map the parsing result to a preset coating performance index dictionary to generate a structured performance target object; S2, based on the structured performance target object, retrieve the benchmark recipe from the historical recipe library; when the known performance of the benchmark recipe meets the hard performance target, output the benchmark recipe and terminate the process; when the benchmark recipe does not meet at least one hard performance target, construct a candidate generation constraint set based on the benchmark recipe and the unmet performance, the candidate generation constraint set being a set of engineering constraint conditions used to restrict the generation and verification of candidate recipes; S3, during the initial execution, the baseline formulation and the candidate generation constraint set are input into the large language model, which generates an initial candidate formulation. In subsequent iterations, the intermediate candidate schemes and the adjustment constraint information are used as input to the large language model. The intermediate candidate schemes are candidate formulations that failed to meet all hard performance targets in the previous iteration and were marked as intermediate candidate schemes. The adjustment constraint information is constraint information generated based on the unmet coating performance indicators from the previous round, used to constrain the generation of the next round's initial candidate formulation. The large language model generates the next round's initial candidate formulation. Based on the candidate generation constraint set, a deterministic engineering constraint verification is performed on the initial candidate formulation, and the initial candidate formulation that passes the engineering constraint verification is determined as the candidate formulation. S4. Based on the machine learning model, obtain the predicted values ​​of several coating performance indicators corresponding to the candidate formulation; based on the historical reference formulation, the physical and chemical parameters of the candidate formulation and the training data coverage of the machine learning model, verify the mechanism credibility of the predicted values, determine whether the coating performance indicators exceed the training data coverage, and obtain the prediction reliability level and out-of-distribution label of the coating performance indicators. S5, based on the predicted value, the predicted reliability level, and the out-of-distribution marker, each of the coating performance indicators is assessed for compliance; when all hard performance targets of the candidate formulation are assessed as compliant and the predicted reliability level is not low, the final recommended formulation is output; otherwise, the candidate formulation is marked as an intermediate candidate scheme, and adjustment constraint information is generated based on the uncompliant coating performance indicators; the adjustment constraint information and the intermediate candidate scheme are returned to step S3 to constrain the generation of the next round of initial candidate formulations, forming a closed loop for formulation recommendation.

[0009] Furthermore, the mechanism credibility verification in step S4 includes the following sub-steps: S41, retrieve historical reference formulas from the historical formula database that meet preset similarity conditions with the candidate formula in terms of coating type, raw material composition, component ratio and test conditions, and obtain the similarity between the candidate formula and the historical reference formula; S42, based on the feature set corresponding to each coating performance index in the candidate formulation, the historical reference formulation, and the training data coverage of the machine learning model, determine whether each coating performance index satisfies at least one out-of-distribution condition. S43, Based on the number of triggers, the trigger amplitude, and the similarity of the out-of-distribution conditions, determine the prediction reliability level of each of the coating performance indicators; S44, Based on the predicted reliability level and the judgment result of the out-of-distribution conditions, generate the out-of-distribution label and mechanism description of the coating performance index.

[0010] Furthermore, the external distribution conditions include at least one of the following: The candidate formulation includes raw materials that are not present in the training samples of the machine learning model and are related to the current coating performance indicators, and the mass fraction of the raw materials is higher than a preset trace threshold. The proportion of any raw material in the candidate formulation that is related to the current coating performance index exceeds the lower or upper bound of the calibration of that raw material proportion in the training sample. The physicochemical parameters related to the current coating performance indicators in the candidate formulation are at least one of reaction equivalence ratio, pigment volume concentration, volatile organic compound content, pigment-to-binder ratio, and volume solids content, which are outside the calibration range of the corresponding parameters in the training samples. The test methods or test conditions used in the candidate formulations are not covered by the training data of the machine learning model for the current coating performance indicators; The candidate formulation exceeds the calibration range in the multivariate feature space of the current coating performance index. The multivariate feature space is a space composed of multiple features of the candidate formulation that are related to the current coating performance index.

[0011] Furthermore, the predicted reliability level includes a high reliability level, a medium reliability level, and a low reliability level; Determining the predictive reliability level for each of the coating performance indicators in step S43 includes: Step S431: When no out-of-distribution conditions are triggered, and the highest similarity between the candidate formulation and the historical reference formulation that meets the preset similarity conditions is not lower than the preset high reliability similarity threshold, the predicted reliability level of the coating performance index is determined to be a high reliability level. Step S432: When only one univariate out-of-distribution condition is triggered, and the out-of-distribution magnitude of the univariate out-of-distribution condition does not exceed the preset mild out-of-distribution threshold, and the highest similarity is not lower than the preset medium reliability similarity threshold, and no related raw material conditions not seen in the training samples, test conditions not covered, or multivariate significant out-of-distribution conditions are triggered, the prediction reliability level of the coating performance index is determined to be medium reliability level. Step S433: When any of the following situations are triggered, the predicted reliability level of the coating performance index is determined to be a low reliability level: the candidate formulation contains related raw materials not seen in the training samples with a mass fraction higher than a preset trace threshold, the test method or necessary test conditions are not covered, multiple out-of-distribution conditions are triggered simultaneously, any related feature exceeds a preset severe out-of-bounds threshold, the multivariate distance or the ensemble variance of the machine learning model exceeds a preset threshold, or the highest similarity is lower than a preset low reliability similarity threshold.

[0012] Furthermore, the mechanism credibility verification does not modify the predicted value output by the machine learning model by default; only when there is a residual correction model or numerical correction rule verified by independent historical data or control experiments, where the residual correction model is a model established using historical data or control experiments to correct the output bias of the machine learning model, and the numerical correction rule is a correction rule based on physicochemical rules or empirical formulas, will a correction value be output, and the basic predicted value, correction value, correction rule version, and applicable scope will be recorded simultaneously; when there is no correction model or rule, the predicted value output by the machine learning model is the final predicted value.

[0013] Further, the retrieval of the benchmark formulation in step S2 includes the following sub-steps: S21, based on the application type in the structured performance target object, perform coating type hard filtration in the historical formula library and retain historical formulas consistent with the application type; S22, construct a performance vector by combining the known performance of the filtered historical formula with the hard performance targets in the structured performance target object according to the same performance index order, and unify the direction of the three comparison relationships: larger values ​​are better, smaller values ​​are better, and target range. S23, For each historical formula, calculate its constraint violation distance relative to each hard performance target, and introduce performance priority weight, missing performance penalty and test condition inconsistency penalty, and sum them up to obtain the baseline constraint violation distance. S24. Sort the historical recipes with the highest number of violations of the benchmark constraint from smallest to largest according to the benchmark constraint violation distance, and select the preset number of historical recipes as the benchmark recipes.

[0014] Furthermore, calculating the constraint violation distance in step S23 also includes: S231, when the performance index is an ordered level index, each level is converted into adjacent ordinal values ​​according to the preset level order, and the normalized constraint violation distance is calculated based on the ordinal difference, and each level is not treated as an independent category that is unordered from each other. S232, when a historical formula lacks measured data corresponding to any hard performance target, a missing performance penalty is set for the historical formula to lower its ranking position. S233, when the test method or test conditions of the historical formula are inconsistent with the structured performance target object, a penalty for inconsistent test conditions is added to the historical formula.

[0015] Furthermore, the large language model is only used to generate initial candidate formulations and adjustment instructions. The engineering constraint verification is performed by preset verification rules. The large language model does not participate in the determination of the engineering constraint verification, nor does it directly modify the component ratio, predicted value, or performance determination result of the candidate formulation.

[0016] Furthermore, the step S5, which involves determining the compliance of each of the coating performance indicators, includes: S511, based on the target values ​​in the structured performance target object, for performance indicators where a larger value is better, it is determined that the target is met when the predicted value is not lower than the target value; for performance indicators where a smaller value is better, it is determined that the target is met when the predicted value is not higher than the target value; for performance indicators with target ranges, it is determined that the target is met when the predicted value is within the target range. S512, Generate a status code for each of the coating performance indicators based on the judgment result. The status code includes a compliant status, a warning status, and a non-compliant status. S513, the candidate formulations are sorted from smallest to largest according to the number of indicators in the non-compliant state. When the number of indicators in the non-compliant state is the same, they are sorted from smallest to largest according to the weighted normalized non-compliant magnitude. The weighted normalized non-compliant magnitude is obtained by multiplying the normalized difference of each non-compliant performance indicator relative to the corresponding target value by the priority weight of the performance indicator and then summing them. When the weighted normalized non-compliant magnitudes are the same, they are sorted from highest to lowest according to the prediction reliability level.

[0017] Furthermore, step S5, which involves returning the adjustment constraint information and the intermediate candidate solution to step S3 to constrain the generation of the next round of initial candidate formulations, thus forming a closed loop for formulation recommendation, further includes: S521: In each round, candidate formulations that fail the engineering constraint verification are first eliminated. Then, they are sorted according to the number of non-compliant state indicators, the weighted normalized non-compliant range, and the predicted reliability level. A preset number of non-overlapping candidate formulations are selected to enter the next round of adjustment. S522, Generate candidate signatures based on the set of unique raw material identifiers, the ratio of main agent to curing agent, and the component ratio rounded to a preset precision, and remove duplicate formulas through the candidate signatures; S523, when all hard performance targets of the candidate formulation are met and the predicted reliability level is not low, the candidate formulation is output as the final recommended formulation; S524, the iteration is terminated when the maximum number of iterations is reached, the improvement of the optimal weighted normalization failure rate after a preset number of consecutive rounds is less than a preset threshold, or the candidate set no longer generates new candidate signatures; S525, formulations that still do not meet the final recommended conditions at the end are output as intermediate candidate schemes to be verified experimentally, and are not marked as final recommended formulations.

[0018] Accordingly, a second aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described formula closed-loop generation method based on coating engineering constraints and prediction confidence verification.

[0019] Accordingly, a third aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described formula closed-loop generation method based on coating engineering constraints and prediction reliability verification.

[0020] The above-described technical solutions of the embodiments of the present invention have the following beneficial technical effects: 1. By constructing a closed-loop formulation recommendation system consisting of historical benchmark formulation retrieval, constrained generation of a large language model, deterministic engineering constraint verification, and indicator-by-indicator compliance evaluation, and by converting unmet coating performance indicators into adjustment constraint information and feeding it back to the large language model in each iteration, the feasibility and compliance rate of candidate formulations under engineering constraints such as reaction equivalence, component ratio, pigment volume concentration, volatile organic compound content, and raw material compatibility are improved. This solves the problems in existing technologies where natural language formulation requirements are difficult to effectively connect with engineering constraints and candidate formulations are prone to violating physicochemical constraints, leading to invalid experiments. 2. By setting up an independent deterministic engineering constraint verification step after the large language model generates the initial candidate formulation, and clarifying that the large language model is only responsible for generating the initial candidate formulation and adjustment instructions, and does not participate in the determination of engineering constraint verification or directly modify the component ratio and predicted value, the controllability and consistency of the formulation generation process are improved, and the problem of difficulty in ensuring engineering feasibility and result traceability when a single generation model directly outputs the formulation in the existing technology is solved. 3. By utilizing historical reference formulations, candidate formulation physicochemical parameters, and the coverage of training data for machine learning models to verify the mechanistic credibility of performance prediction values, and by determining whether each coating performance index triggers out-of-distribution conditions, determining the prediction reliability level, and out-of-distribution marker, the credibility of performance prediction results is improved in scenarios with sparse data and inconsistent test conditions. This solves the problem in existing technologies where prediction results are still directly used as the basis for compliance judgment when candidate formulations exceed the coverage of training data, leading to misjudgments. Attached Figure Description

[0021] Figure 1 This is a framework diagram of the formula closed-loop generation method based on coating engineering constraints and prediction credibility verification provided in the embodiments of the present invention; Figure 2 This is a flowchart of the formula closed-loop generation method based on coating engineering constraints and prediction credibility verification provided in the embodiments of the present invention; Figure 3 This is a flowchart illustrating the natural language requirement parsing steps provided in an embodiment of the present invention; Figure 4 This is a flowchart illustrating the candidate generation constraint construction and candidate recipe generation steps provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of a multi-agent collaborative framework for basic performance prediction and mechanism credibility verification provided in an embodiment of the present invention; Figure 6 This is a flowchart illustrating the steps for comprehensive evaluation and recommendation results output of candidate formulations provided in this embodiment of the invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0023] like Figure 1As shown in the embodiments of the present invention, the method can be roughly divided into two stages. The first stage is the baseline formulation determination and candidate generation constraint construction stage. The user's input natural language requirements are converted into structured performance target objects through requirement parsing, and matching baseline formulations are retrieved from the historical formulation library. When the baseline formulation meets all hard performance targets, it is directly output and subsequent steps are stopped; otherwise, a candidate generation constraint set is constructed based on the unmet performance, the composition of the baseline formulation, and the raw material database. The second stage is the candidate generation and evaluation stage. The large language model generates initial candidate formulations under the candidate generation constraint set, performs deterministic engineering constraint verification on the candidate formulations, and only inputs the verified candidate formulations into the machine learning model for performance prediction. Based on the historical reference formulations, the physical parameters of the candidate formulations, and the coverage of the training data, the mechanism credibility verification is performed to obtain the predicted values, prediction reliability levels, and out-of-distribution labels of each coating performance index. Subsequently, the standard is determined item by item according to the preset evaluation rules, and the large language model generates a mechanism explanation and subsequent adjustment suggestions. Throughout the entire process, the large language model does not determine whether the engineering constraints are met, nor does it directly modify the predicted values ​​and performance judgment results, thus achieving a closed-loop linkage between the three stages of generation, constraint, and credibility.

[0024] Please refer to Figure 2 This invention provides a closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification, comprising the following steps: S1 receives the user's input of a natural language formulation requirement description, performs semantic parsing on the natural language formulation requirement description, and maps the parsing result to a preset coating performance index dictionary to generate a structured performance target object.

[0025] This requirement description is typically expressed by coating R&D personnel in everyday language, such as "Recommend an epoxy primer for carbon steel substrates, with a salt spray requirement of no less than 150 hours and a surface drying time of no more than 1 hour." Such descriptions include key information such as coating type and performance indicators, as well as auxiliary information such as testing conditions, application methods, and substrate type. However, different users have different wording habits and indicator writing styles, making it difficult to directly use as input for subsequent retrieval and generation steps. Semantic parsing is performed on the natural language formulation requirement description, that is, identifying entities related to formulation design and their interrelationships from unstructured text, and mapping the recognition results to a pre-defined dictionary of coating performance indicators. The pre-defined dictionary of coating performance indicators includes standardized indicator names such as adhesion, hardness, salt spray resistance, activation period, surface drying time, complete drying time, thickness coating, hiding power, gloss, impact resistance, bending test, acid resistance, alkali resistance, and artificial weathering resistance. After semantic parsing and mapping, structured performance target objects are generated. The structured performance target object includes at least the application type, coating performance indicators, comparison relationships, target value, preferred range, constraint level, performance priority, and resolution status. The application type includes epoxy primer, acrylic polyurethane topcoat, or other coating types. The constraint level identifies hard performance targets, the performance priority determines key performance characteristics from the hard performance targets, and the resolution status indicates whether the information for the corresponding performance indicator is complete. When the user input lacks a test method, target value, or necessary test conditions, the resolution status of the corresponding performance indicator is set to require clarification, preventing the direct conversion of ambiguous descriptions into definite values. Through this step, the formulation requirements, originally in natural language form, are transformed into a structured expression with unified fields and clear semantics, providing a reliable data foundation for subsequent benchmark formulation retrieval and candidate generation constraint construction.

[0026] like Figure 3As shown, in the specific execution process of requirement parsing, the system receives the user's input natural language formulation requirement description, performs semantic parsing of the requirement through a large language model, and maps the parsing results to a preset coating performance index dictionary to generate a structured performance target object. This structured performance target object includes application type, coating performance index, test method, test conditions, comparison relationship, target value, unit of measurement, preferred range, constraint level, performance priority, and parsing status. Test conditions may include information such as substrate type, substrate pretreatment method, film thickness, curing temperature, curing time, and test environment. When the user input lacks a test method, target value, or necessary test conditions, the parsing status of the corresponding performance index is set to require clarification, and a clarification question is output; before the missing information is supplemented, ambiguous performance descriptions are not directly converted into definite values. For target values ​​that clearly exceed the preset engineering range, an over-limit warning is output but the parsing process is not forcibly terminated. The structured performance target object output in this step serves as input for subsequent benchmark formulation retrieval and candidate constraint construction.

[0027] S2: Based on the structured performance target object, retrieve the baseline recipe from the historical recipe library. When the known performance of the baseline recipe meets the hard performance target, output the baseline recipe and terminate the process. When the baseline recipe does not meet at least one hard performance target, construct a candidate generation constraint set based on the baseline recipe and the unmet performance target. The candidate generation constraint set is a set of engineering constraints used to restrict the generation and verification of candidate recipes.

[0028] A baseline formulation refers to a historical formulation retrieved from the historical formulation library that matches the structured performance target. During the retrieval, a hard filter is first applied based on application type, retaining only historical formulations consistent with the target coating type. Then, the known performance of the historical formulation is compared with the hard performance targets. When the known performance of a baseline formulation meets all hard performance targets, the baseline formulation is directly output and the process terminates. This approach is suitable when a formulation that directly meets the current requirements already exists in the historical formulation library, avoiding unnecessary candidate generation and performance prediction calculations, reducing computational resource consumption, and shortening response time. When a baseline formulation fails to meet at least one hard performance target, a candidate generation constraint set is constructed based on the baseline formulation and the unmet coating performance indicators. The candidate generation constraint set is a set of engineering constraints used to limit the generation and verification of candidate formulations. Its construction process is based on the composition of the baseline formulation, adjusting the component adjustment space corresponding to the unmet performance, and combining the raw material attributes in the raw material database and the theoretical parameter range corresponding to the target coating type to form the constraints that must be followed in subsequent generation steps. The introduction of this candidate generation constraint set makes the formulation adjustment no longer an unconstrained free combination, but a controlled modification of the existing formulation within a limited range, which is conducive to maintaining the engineering rationality of the candidate formulation and its inheritance from the benchmark formulation.

[0029] In S3, during the initial execution, the baseline formulation and the candidate generation constraint set are input into the large language model, which generates the initial candidate formulation. In subsequent iterations, intermediate candidate formulations and adjustment constraint information are input to the large language model. Intermediate candidate formulations are those that failed to meet all hard performance targets in the previous iteration and were marked as intermediate candidates. Adjustment constraint information is generated based on the unmet coating performance indicators from the previous iteration, used to constrain the generation of the next round's initial candidate formulation. The large language model then generates the next round's initial candidate formulation. Based on the candidate generation constraint set, deterministic engineering constraint verification is performed on the initial candidate formulations. Initial candidate formulations that pass the engineering constraint verification are determined as candidate formulations.

[0030] The baseline formulation provides the large language model with complete composition and proportion information of the initial formulation. The candidate generation constraint set limits the range of components that the large language model can adjust, the adjustment range, and the engineering conditions that must be met during the generation process. Based on the above inputs, the large language model generates an initial candidate formulation containing the adjusted proportions of each component and adjustment instructions. In subsequent iterations, intermediate candidate schemes and adjustment constraint information are used as inputs to the large language model. Intermediate candidate schemes are candidate formulations that failed to meet all hard performance targets in the previous iteration and were marked as intermediate candidates. Adjustment constraint information is constraint information generated based on the unmet coating performance indicators from the previous round, used to constrain the generation of the initial candidate formulation for the next round. The large language model generates the next round of initial candidate formulations based on the intermediate candidate schemes and adjustment constraint information. After generating the initial candidate formulations, deterministic engineering constraint verification is performed on the initial candidate formulations based on the candidate generation constraint set. The engineering constraint verification uses preset verification rules to check whether the initial candidate formulation meets the constraints such as raw material identity, component proportions, and theoretical parameters. When the initial candidate formulation fails to meet at least one engineering constraint, the information on the constraint violation is fed back to the large language model for correction. If an initial candidate formulation fails to pass all engineering constraint checks within a preset number of corrections, it is discarded. Initial candidate formulations that pass all engineering constraint checks are designated as candidate formulations and proceed to subsequent performance prediction and reliability verification stages. Thus, a mutually constraining relationship is formed between the large language model's generation capability and deterministic engineering verification: the large language model is responsible for proposing adjustment schemes within the constraints, while the engineering verification stage verifies whether the schemes meet the predetermined materialization conditions, thereby avoiding engineering infeasibility issues caused by directly using the output of the generative model. In specific implementation, the large language model's generation temperature can be set to 0.2, the top-p parameter to 0.9, and one candidate formulation is generated for each adjustment strategy, resulting in three initial candidate formulations. When the output cannot be parsed into the preset data structure, lacks necessary fields, or contains duplicate ingredient identifiers, a format error message is fed back to the large language model for regeneration, allowing for two regenerations; outputs that still cannot be parsed after a preset number of regenerations are discarded.

[0031] like Figure 4As shown, during the candidate generation constraint construction and candidate formulation generation process, the candidate generation constraint set is constructed based on the benchmark formulation, the performance indicators of the substandard coatings, the raw material database, and the target coating type. These constraints include adjustment strategy constraints, raw material identity constraints, single-component adjustment range constraints, component ratio constraints, key raw material protection constraints, theoretical parameter constraints, and raw material compatibility constraints. Adjustment strategy constraints include primary strategy, conservative strategy, and balanced strategy. The primary strategy prioritizes adjusting components whose impact on substandard performance exceeds a preset weight threshold. The conservative strategy uses an adjustment range not exceeding a preset conservative threshold and prioritizes avoiding degradation of already compliant performance. The balanced strategy uses preset balance weight coefficients to perform weighted adjustments among multiple performance targets. Single-component adjustment range constraints can be set to ensure that the proportion change of each component in the candidate formulation relative to the benchmark formulation does not exceed ±2 to ±3 percentage points. Component ratio constraints require that the sum of the mass percentages of all components in the main agent and the sum of the mass percentages of all components in the curing agent are both 100%, with errors due to rounding not exceeding ±0.01 percentage points. Subsequently, the complete composition of the benchmark formulation, raw material properties, current theoretical parameters, user-targeted performance, performance indicators of unqualified coatings, adjustment strategies, and candidate generation constraint sets are input into the large language model. The large language model outputs initial candidate formulations and adjustment instructions according to a preset data structure. The adjustment instructions include raw material identification, pre-adjustment ratio, post-adjustment ratio, adjustment direction, corresponding target performance, and adjustment rationale. After the initial candidate formulation is generated, it undergoes raw material identification verification, single-component adjustment range verification, component ratio verification, key raw material lower limit verification, reaction equivalent comparison verification, pigment volume concentration verification, volatile organic compound content verification, and raw material compatibility verification according to preset verification rules. When an initial candidate formulation fails to meet at least one engineering constraint, the information on the constraint violation is fed back to the large language model for correction. Initial candidate formulations that still fail to meet engineering constraints after a preset number of corrections are discarded. Initial candidate formulations that pass all engineering constraint verifications are determined as candidate formulations.

[0032] S4. Based on the machine learning model, predictive values ​​of several coating performance indicators corresponding to the candidate formulation are obtained. Based on historical reference formulations, physicochemical parameters of candidate formulations, and the training data coverage of the machine learning model, the predictive values ​​are verified for mechanistic reliability to determine whether the coating performance indicators exceed the training data coverage, and the prediction reliability level and out-of-distribution label of the coating performance indicators are obtained.

[0033] Before using machine learning models to obtain predicted values, the models have already been trained and evaluated. Corresponding machine learning models are established for different coating types. XGBoost models can be used to implement these models. For continuous numerical coating performance indicators such as salt spray resistance, surface drying time, hard drying time, activation period, and thick coating properties, regression models are trained. For ordered grade coating performance indicators such as adhesion grade and hardness grade, each grade is mapped to an ordinal value according to a preset order, and ordinal regression or cumulative probability ordinal models are used for training. The model output is then projected to the closest preset valid grade. Historical samples are grouped according to basic formulation series, production or experimental batches, and collection time. Samples from the same basic formulation series or batch are not assigned to training, validation, and test sets across sets; the training, validation, and test sets can be divided at approximately 70%, 15%, and 15% respectively. The model admission threshold is pre-calibrated based on the error distribution on the validation set. The test set is used only for a one-time independent evaluation and does not participate in feature selection, parameter adjustment, or threshold modification. Models that fail the independent test set evaluation are not used to output formal predicted values ​​for candidate formulations. After training and evaluation, the machine learning model takes the component ratios of the candidate formulation and the physicochemical parameters calculated based on the candidate formulation as input, and outputs predicted values ​​for each coating performance index. Based on this, the predicted values ​​are verified for mechanistic reliability according to the historical reference formulations, the physicochemical parameters of the candidate formulations, and the training data coverage of the machine learning model. Historical reference formulations are those from the historical formulation library that meet preset similarity conditions with the candidate formulations in terms of coating type, raw material composition, component ratios, and testing conditions. The purpose of mechanistic reliability verification is to determine whether each coating performance index involved in the candidate formulation exceeds the training data coverage of the machine learning model. When the candidate formulation contains raw materials not present in the training samples, or the proportions of certain components exceed the calibration range of those components in the training samples, or the testing methods and conditions are not within the coverage of the training data, the machine learning model's predicted value for that performance index may have a significant deviation. Through mechanistic reliability verification, such situations exceeding the training data coverage can be identified item by item, and a prediction reliability level and out-of-distribution label can be obtained for each coating performance index. The prediction reliability level reflects the extent to which the predicted value of a performance metric can be trusted, while the out-of-distribution label explicitly indicates whether the performance metric is outside the coverage of the training data. Through this step, performance predictions are no longer presented as a single numerical value, but also carry prediction reliability information, providing a more sufficient basis for subsequent achievement determination and recommendation decisions.

[0034] S5: Based on the predicted values, prediction reliability level, and out-of-distribution markers, each coating performance indicator is assessed for compliance. When all hard performance targets of the candidate formulation are deemed compliant and the prediction reliability level is not low, the final recommended formulation is output. Otherwise, the candidate formulation is marked as an intermediate candidate solution, and adjustment constraint information is generated based on the unmet coating performance indicators. The adjustment constraint information and the intermediate candidate solutions are returned to step S3 to constrain the generation of the next round of initial candidate formulations, forming a closed loop for formulation recommendation.

[0035] The compliance determination is based on the target values ​​and preferred ranges in the structured performance target object, and corresponding judgment methods are adopted for performance indicators of different comparison relationship types. After item-by-item judgment, each coating performance indicator has a corresponding status identifier. When all hard performance targets of the candidate formulation are judged to be compliant and the prediction reliability level is not low, the candidate formulation is output as the final recommended formulation. The final recommended formulation includes complete component composition and ratio information, as well as various performance prediction results and reliability descriptions, for R&D personnel to refer to and use for subsequent small-scale tests and experimental verification. When the candidate formulation does not meet the above conditions, the candidate formulation is marked as an intermediate candidate scheme, and adjustment constraint information is generated based on the non-compliant coating performance indicators. The adjustment constraint information records which performance indicators have not yet been compliant, the degree of non-compliance, and the direction that should be prioritized for adjustment in the next round of generation. The adjustment constraint information and the intermediate candidate scheme are returned to step S3 to constrain the generation of the initial candidate formulation in the next round. Through the above feedback mechanism, each iteration makes constrained adjustments to the non-compliant indicators based on the results of the previous round, gradually narrowing the gap between the candidate formulation and the target performance, forming a closed loop of formulation recommendation. When a coating performance indicator has both a baseline predicted value and a correction value, subsequent compliance determination, candidate ranking, and iterative adjustment will only read one set of final prediction results with a clearly identified source. This final prediction result is either the baseline predicted value or the correction value, and its source identifier will be recorded simultaneously. In the candidate comprehensive evaluation stage, only one set of final prediction results will be read for each performance indicator; multiple prediction values ​​from different sources are not allowed to be used simultaneously for the same performance indicator in ranking or compliance determination.

[0036] Specifically, the mechanism credibility verification in step S4 includes the following sub-steps: S41. Search the historical formula database for historical reference formulas that meet the preset similarity conditions with the candidate formula in terms of coating type, raw material composition, component ratio and test conditions, and obtain the similarity between the candidate formula and the historical reference formula.

[0037] like Figure 5As shown, a dual-path parallel prediction and verification framework can be constructed during the implementation of basic performance prediction and mechanism credibility verification. The fast prediction path calls a pre-trained XGBoost model, inputting the component ratios of candidate formulations and physicochemical parameters such as reaction equivalence ratio, pigment volume concentration, volatile organic compound content, pigment-to-binder ratio, and volume solids content. It outputs predicted values ​​for each coating performance index, used for rapid screening of multiple candidate formulations. The mechanism enhancement path is implemented by multiple verification modules divided according to coating performance indicators, such as adhesion verification modules, hardness verification modules, salt spray resistance verification modules, and other performance verification modules. Each verification module only accesses the feature subset, training data coverage statistics, and historical reference formulations related to the corresponding coating performance index. Each verification module performs the following operations: retrieving historical reference formulations similar to the candidate formulations, obtaining the measured performance values ​​of the historical reference formulations and the similarity between the candidate formulation and the historical reference formulations; reading the predicted values ​​output by the XGBoost model; comparing the differences between the candidate formulation and the historical reference formulation in terms of component ratios and physicochemical parameters; and determining whether at least one out-of-distribution condition is met. When out-of-distribution conditions are met, only the corresponding coating performance index is marked as out-of-distribution, and the prediction reliability level is determined based on the number of triggering conditions, the magnitude of the exceedance, historical nearest neighbor similarity, and multivariate distance. Out-of-distribution determination and prediction reliability level are performed by a deterministic program that can be tested offline; the large language model does not participate in the level calculation. Mechanism credibility verification does not modify the predicted values ​​output by the machine learning model by default; it only outputs corrected values ​​when an independently validated residual correction model or numerical correction rule exists, and must simultaneously output the base predicted value, corrected value, correction rule version, out-of-distribution label, and prediction reliability level.

[0038] After candidate formulations have undergone engineering constraint verification and have established a defined component composition and proportions, it is necessary to search for existing formulations with similar overall characteristics from the historical formulation database as a reference for mechanism verification. During the search, the coating type must be consistent, the raw material composition should have a high degree of overlap, the differences in component proportions should be within a preset tolerance range, and the test conditions should be as similar as possible. For each retrieved historical reference formulation, its similarity to the candidate formulation is calculated. The similarity calculation comprehensively considers factors such as the degree of overlap in raw material composition, the similarity of component proportions, and the consistency of test conditions, resulting in a quantitative index that can be used for subsequent comparisons. This similarity is used both to screen historical reference formulations that meet the preset similarity conditions and to provide a basis for measuring the closeness between the candidate formulation and existing formulations in determining the subsequent reliability level. Historical reference formulations with high similarity to candidate formulations can provide more valuable measured performance data and component proportion comparison information.

[0039] S42, based on the feature set corresponding to each coating performance index in the candidate formulation, the historical reference formulation, and the training data coverage of the machine learning model, determine whether each coating performance index meets at least one out-of-distribution condition.

[0040] The feature set corresponding to each coating performance index refers to the feature set composed of the raw material ratio, physicochemical parameters, and test conditions related to that performance index. Item-by-item judgment means that different coating performance indices are verified independently, and the out-of-distribution label is not indiscriminately extended to other performance indices simply because one performance index triggers an out-of-distribution condition. The judgment of out-of-distribution conditions revolves around whether the candidate formulation exceeds the coverage of the machine learning model's training data. When a candidate formulation contains raw materials not present in the training samples but related to the current performance index, and the mass fraction of these raw materials is higher than a preset trace threshold, the performance index may be in an out-of-distribution state. Similarly, when the ratio of any raw material in the candidate formulation related to the current performance index is lower or higher than the calibration lower or upper boundary of that raw material ratio in the training samples, an out-of-distribution condition may also be triggered. If the physicochemical parameters in the candidate formulation related to the current performance index exceed the calibration range of the corresponding parameters in the training samples, or if the test methods or test conditions used in the candidate formulation are not within the coverage of the training data for that performance index, these are all out-of-distribution situations. Furthermore, when a candidate formulation exceeds the calibration range in the multivariate feature space of the current performance index, it is also considered to satisfy the out-of-distribution condition. The multivariate feature space is composed of multiple features related to the current performance metric in the candidate formulation. It can reflect the degree of deviation of the candidate formulation from the overall distribution of the training samples under the combined effect of multiple features. By judging each feature in turn, it is possible to comprehensively identify specific situations where the candidate formulation exceeds the coverage of the training data in each performance metric dimension.

[0041] S43, based on the number of triggers, the magnitude of triggers, and the similarity of out-of-distribution conditions, determines the predictive reliability level of each coating performance index.

[0042] The prediction reliability level characterizes the credibility of the predicted value output by the machine learning model for a performance indicator. The specific type and number of triggering conditions are the primary considerations when determining the prediction reliability level. Performance indicators that do not trigger any out-of-distribution conditions typically have high reliability, as their predicted values ​​fall within the training data coverage. If only one mild univariate out-of-distribution condition is triggered, and the out-of-distribution magnitude does not exceed a preset mild out-of-distribution threshold, and there are no unseen raw materials, uncovered test conditions, or significant multivariate out-of-distribution conditions, the predicted value of the performance indicator still has a certain degree of credibility. When a candidate formulation contains unseen raw materials with a mass fraction higher than a preset trace threshold, or the test method or necessary test conditions are not covered, or multiple out-of-distribution conditions are triggered simultaneously, or any relevant feature exceeds a preset severe out-of-distribution threshold, or the multivariate distance or the ensemble variance of the machine learning model exceeds a preset threshold, or the similarity between the candidate formulation and historical reference formulation is lower than a preset low-reliability similarity threshold, the prediction reliability level of the performance indicator is determined to be low. Similarity plays a crucial auxiliary role in reliability assessment: higher similarity indicates a closer similarity between the candidate formulation and existing formulations, generally leading to more reliable predictions from the machine learning model within that region; conversely, lower similarity suggests that even without significant univariate out-of-bounds errors, the candidate formulation is still more likely to deviate from the historical sample distribution, resulting in a corresponding decrease in the reliability of the predicted values. By using the aforementioned rules to determine the prediction reliability level of each performance indicator, dimensional reliability information is provided for subsequent compliance assessments.

[0043] S44, based on the prediction reliability level and the judgment results of out-of-distribution conditions, generates out-of-distribution labels and mechanism descriptions for coating performance indicators.

[0044] Out-of-distribution markers are used to identify whether the coating performance index is determined to be outside the coverage of the machine learning model's training data. The mechanism description explains the conditions under which the predicted value of the performance index was obtained, why it was assigned the current prediction reliability level, and the main differences between the candidate formulation and historical reference formulations in terms of component ratios, physicochemical parameters, and testing conditions. The mechanism description is derived from the measured performance information of historical reference formulations, the similarity between the candidate formulation and historical reference formulations, and the triggering conditions of various out-of-distribution conditions, without changing the predicted value output by the machine learning model. Through mechanism credibility verification, the performance prediction results are no longer presented in a single numerical form, but simultaneously carry the prediction reliability level, out-of-distribution markers, and corresponding mechanism descriptions, providing a credibility-based judgment for whether the candidate formulation should enter the recommended output or the next iteration.

[0045] The steps S41 to S44 described above constitute the complete process of mechanism credibility verification. By retrieving historical reference formulations from the historical formulation database that are similar to the candidate formulation in terms of coating type, raw material composition, component ratio, and testing conditions, and obtaining similarity scores, and then combining the feature sets corresponding to each coating performance index in the candidate formulation with the training data coverage of the machine learning model, out-of-distribution judgments are made item by item. Based on the triggering conditions of out-of-distribution conditions and similarity, the prediction reliability level of each performance index is determined, ultimately generating out-of-distribution labels and mechanism descriptions. This mechanism credibility verification process ensures that the performance prediction values ​​output by the machine learning model are no longer isolated values ​​directly participating in subsequent evaluations, but are associated with the training data coverage and historical reference formulation information. It can identify specific situations where the candidate formulation exceeds the training data coverage for each performance index and clarify the credibility of the corresponding prediction values, providing a basis for subsequent item-by-item compliance judgment, candidate ranking, and iterative adjustment, thereby reducing the risk of performance prediction misjudgments due to the candidate formulation exceeding the training data coverage.

[0046] Furthermore, the external distribution conditions include at least one of the following: Candidate formulations include raw materials that are not present in the training samples of the machine learning model and are related to the current coating performance indicators, and the mass fraction of the raw materials is higher than the preset trace threshold.

[0047] During the training phase of the machine learning model, the model learns the mapping relationship between raw materials and performance by studying the types and proportions of raw materials in historical samples. When a candidate formulation introduces a raw material that has never appeared in the training samples, and the mass fraction of this raw material is higher than a preset trace threshold, the machine learning model lacks a basis for learning about the chemical behavior of this raw material, its interaction with other components, and its impact on the current performance index. Its output prediction is essentially an extrapolation of an unknown combination of raw materials. The preset trace threshold is used to distinguish whether the raw material truly participates in the formation of the formulation's performance, avoiding misclassification of trace components with extremely low mass fractions and negligible impact on performance as out-of-distribution factors. When the mass fraction of the raw material exceeds the trace threshold, the model's prediction of the performance index is considered to be outside the effective coverage of the training data, and the performance index should be marked as out-of-distribution. For example, if the rust-preventive pigment used in the training samples is zinc phosphate, and the candidate formulation introduces modified aluminum phosphate that did not appear in the training samples, and its mass fraction reaches 2%, this situation constitutes an out-of-distribution condition related to salt spray resistance.

[0048] The proportion of any raw material in the candidate formulation that is related to the current coating performance index exceeds the lower or upper bound of the calibration of that raw material proportion in the training sample.

[0049] Even if all raw materials used in a candidate formulation appear in the training samples, the specific proportion of a particular raw material may still exceed the actual usage range of that raw material in historical samples. The proportion distribution of each raw material in the training samples reflects the reasonable usage range of that raw material in historical formulations. The lower and upper calibration boundaries are obtained by statistically analyzing the proportion of that raw material in the training samples. When the proportion of that raw material in the candidate formulation is lower than the lower calibration boundary or higher than the upper calibration boundary, the machine learning model lacks sufficient training samples within that proportion range to support its predictions, and the output performance predictions may deviate from reality. For example, if the usage range of a certain type of epoxy resin in historical training samples is 25% to 35%, and the usage of this resin in the candidate formulation reaches 42%, it exceeds the upper calibration boundary, constituting an out-of-distribution condition related to hardness or adhesion. Such out-of-distribution conditions are usually directly related to excessively large adjustments of single components.

[0050] The physicochemical parameters in the candidate formulation that are related to the current coating performance indicators, including at least one of reaction equivalence ratio, pigment volume concentration, volatile organic compound content, pigment-to-binder ratio, and volume solids content, are outside the calibration range of the corresponding parameters in the training samples.

[0051] These parameters are not directly input raw material proportions, but rather derived features calculated from the formulation composition using a standardized approach. During the training phase, the machine learning model uses these physicochemical parameters as one of its input features, and the performance mapping relationship learned by the model is based on the historical value range of these parameters. Even if the proportions of each raw material in the candidate formulation are within the training sample range, the physicochemical parameters calculated after combining multiple raw materials may still exceed the calibration range of the historical samples. For example, if the calibration range of the reaction equivalence ratio in the training samples is 0.90 to 1.10, and the reaction equivalence ratio calculated for the candidate formulation is 0.82, exceeding the lower boundary of the calibration, this situation constitutes an out-of-range condition related to adhesion or salt spray resistance. Such out-of-range physicochemical parameters reflect that the candidate formulation deviates from the distribution area of ​​the historical samples in terms of overall stoichiometry.

[0052] The testing methods or conditions used in the candidate formulations are not covered by the training data of the machine learning model for the current coating performance indicators.

[0053] Measured data on coating performance indicators are highly dependent on testing methods and conditions; performance values ​​obtained under different testing methods or conditions are not directly comparable. When training machine learning models, samples for each performance indicator correspond to specific testing methods and conditions. When a candidate formulation specifies a testing method or condition not present in the training samples during the performance prediction phase, the machine learning model's prediction for that performance indicator cannot guarantee accuracy. For example, adhesion testing methods include the cross-cut test, pull-off test, and circular test. If the training samples only contain measured adhesion data for the cross-cut test, but the candidate formulation requires the pull-off test to evaluate adhesion, then this test method is not covered by the training data. Similarly, if salt spray resistance tests in the training samples are all obtained under specific film thickness and curing time conditions, and the curing time in the candidate formulation's test conditions is significantly shorter than the curing time range covered by the training samples, then this constitutes an out-of-distribution condition. In such cases, even if the raw materials and proportions of the candidate formulation are similar to those in the training samples, the inconsistency in testing conditions can still lead to significant deviations between predicted and actual values.

[0054] The candidate formulation exceeds the calibration range in the multivariate feature space of the current coating performance index. The multivariate feature space is a space composed of multiple features of the candidate formulation that are related to the current coating performance index.

[0055] The fact that a single variable is not out of bounds does not necessarily mean that the candidate formulation is within the effective coverage of the training data as a whole. When multiple features deviate from the concentrated distribution area of ​​the training samples in a specific combination, even if each feature is within its own calibration range individually, the performance corresponding to this feature combination may still be in a sparse or blank area during model training. For example, the amount of epoxy resin and the pigment volume concentration in the candidate formulation may be within the training sample range, but their specific combination is rarely seen in the training samples. Multivariate distance calculation results show that the candidate formulation deviates far from the distribution center of the training samples in the multivariate feature space of this performance indicator, exceeding the preset calibration range. This kind of out-of-bounds at the multivariate level is usually more subtle than that of a single variable, so it needs to be identified through multivariate distance, distance based on neighborhood density, or ensemble variance of machine learning models. Setting such out-of-bounds conditions helps to capture training coverage blind spots that cannot be detected by univariate verification, improving the ability to identify the reliability of prediction results.

[0056] Furthermore, the predicted reliability levels include high reliability, medium reliability, and low reliability. Step S43, determining the predicted reliability level for each coating performance index, includes: S431, when no out-of-distribution conditions are triggered, and the highest similarity between the candidate formulation and the historical reference formulation that meets the preset similarity conditions is not lower than the preset high reliability similarity threshold, the predicted reliability level of the coating performance index is determined to be a high reliability level.

[0057] When all raw materials related to the current coating performance index in the candidate formulation appear in the training samples of the machine learning model, the proportions of each raw material are within the calibration range of the training samples, the physicochemical parameters do not exceed the historical calibration range, the test methods and test conditions are within the coverage range of the training data, and the candidate formulation does not exceed the calibration range in the multivariate feature space, it indicates that the candidate formulation is within the effective coverage area of ​​the training data in the current performance index dimension. Based on this, the highest similarity between the candidate formulation and historical reference formulations that meet the preset similarity conditions is further examined. This highest similarity reflects the degree of similarity between the candidate formulation and the closest historical reference formulation in terms of raw material composition, component proportions, and test conditions. When the highest similarity is not lower than the preset high reliability similarity threshold, it indicates that the candidate formulation is highly similar to historical formulations that are sufficiently supported by existing measured data, and the predictions of the machine learning model in this region have a relatively sufficient training sample as a basis. Therefore, in this performance index dimension, the predicted value output by the machine learning model is considered to have high credibility, and the prediction reliability level is determined to be high reliability. A high reliability level means that when using this predicted value for subsequent compliance determination, it can be directly used according to normal judgment rules without additional experimental verification prompts. However, it should be noted that a high reliability level does not mean that the predicted value is completely consistent with the actual value. It only means that the predicted value is within the credible range in both the training data coverage and similarity dimensions.

[0058] S432, when only one univariate out-of-distribution condition is triggered, and the out-of-distribution magnitude of the univariate out-of-distribution condition does not exceed the preset mild out-of-distribution threshold, and the highest similarity is not lower than the preset medium reliability similarity threshold, and no related raw material conditions not seen in the training samples, test conditions not covered, or multivariate significant out-of-distribution conditions are triggered, the prediction reliability level of the coating performance index is determined to be medium reliability level.

[0059] The medium reliability level is applicable when a candidate formulation exhibits only a slight deviation from the training data coverage for a certain performance indicator, but remains within an acceptable range overall. Specifically, the candidate formulation triggers only one univariate out-of-distribution condition for that performance indicator, and the out-of-distribution magnitude of this univariate out-of-distribution condition does not exceed a preset slight out-of-distribution threshold. The slight out-of-distribution threshold distinguishes between slight and significant deviations: when the out-of-distribution magnitude is small, although the candidate formulation slightly exceeds the calibration boundary of a certain raw material ratio or physicochemical parameter in the training samples, the deviation is limited, and the prediction of the machine learning model near this boundary can still be reasonably inferred using information from neighboring training samples. Simultaneously, the highest similarity between the candidate formulation and a historical reference formulation that meets the preset similarity condition is not lower than the preset medium reliability similarity threshold, indicating that although the candidate formulation has a single out-of-distribution condition, it still has a high degree of similarity to a certain historical reference formulation overall, and the measured data of that historical reference formulation can provide some support for the reasonableness of the predicted value. Furthermore, the medium reliability level also requires that no related raw material conditions not seen in the training samples, no covered test conditions, or no multivariate significant out-of-distribution conditions are triggered. When a candidate formulation contains raw materials, test methods, or test conditions not found in the training samples, or when these conditions are outside the training data coverage, or when they significantly exceed the limits in the multivariate feature space, a medium reliability level cannot be assigned solely based on the small magnitude of a single out-of-limit event. A medium reliability level indicates that the predicted value of this performance indicator can be used as a reference, but the out-of-limit situation should be taken into account in subsequent compliance determination and recommendation decisions, and supplementary experimental verification should be conducted if necessary.

[0060] S433, when any of the following conditions are triggered, the prediction reliability level of the coating performance index is determined to be low reliability level: the candidate formulation contains related raw materials not seen in the training samples with a mass fraction higher than the preset trace threshold, the test method or necessary test conditions are not covered, multiple out-of-distribution conditions are triggered at the same time, any related feature exceeds the preset severe out-of-bounds threshold, the multivariate distance or the ensemble variance of the machine learning model exceeds the preset threshold, or the highest similarity is lower than the preset low reliability similarity threshold.

[0061] The determination of a low reliability level covers several scenarios that may lead to severe distortion of predictions. The first scenario is when the candidate formulation contains related ingredients not found in the training samples, with a mass fraction exceeding a preset trace threshold. Ingredients not found in the training samples mean that the machine learning model has never learned the influence of this ingredient on the current performance index. Even if the proportion of this ingredient in the candidate formulation is low, as long as it exceeds the trace threshold, its contribution to performance cannot be reliably estimated through the model output. The second scenario is when the testing method or necessary testing conditions are not covered. Changes in testing methods or conditions can cause the same formulation to produce different measured results on the same performance index. When the training data does not contain testing methods or conditions corresponding to the candidate formulation, there may not be a stable correspondence between the model's predicted value and the actual test value. The third scenario is when multiple out-of-distribution conditions are triggered simultaneously. When multiple dimensions exceed their limits simultaneously, the factors exceeding the limits may overlap or interact, further amplifying the deviation outside the training data coverage, and significantly reducing the reliability of the model's predictions in that region. The fourth scenario is when any related feature exceeds a preset severe out-of-distribution threshold. The severe out-of-bounds threshold is used to indicate that the degree of out-of-bounds deviation has reached a significant level. For example, the proportion of a key raw material is much higher than the upper limit of the training sample, or a certain physicochemical parameter differs too much from the calibration range of the training sample. In this region, the model has almost no reference training samples, and the output prediction value has a high risk of extrapolation. The fifth situation is when the multivariate distance or the ensemble variance of the machine learning model exceeds a preset threshold. The multivariate distance is used to measure the degree to which the candidate formulation deviates from the distribution center of the training samples in the multivariate feature space, and the ensemble variance is used to measure the degree of divergence in the output prediction values ​​of multiple sub-models for the same performance index. When the multivariate distance or ensemble variance exceeds the preset threshold, it indicates that the candidate formulation is in a sparse region of the training samples or that the model itself has a large uncertainty in predicting the sample. The sixth situation is when the highest similarity between the candidate formulation and the historical reference formulation that meets the preset similarity conditions is lower than the preset low reliability similarity threshold. Even if no univariate out-of-bounds conditions are triggered, if the overall similarity between the candidate formulation and all historical reference formulations is low, it indicates that the candidate formulation differs significantly from the formulation supported by existing measured data in terms of raw material composition, component ratio, or testing conditions, and the model output lacks sufficient historical basis. When any of the above conditions are triggered, the predicted reliability level of the coating performance index will be determined to be low. A low reliability level means that the predicted value of the performance index cannot be used as a reliable basis for achieving the standard, and subsequent experimental verification of the performance index or further adjustments to the candidate formulation are required to bring it back to the range of training data coverage.

[0062] Furthermore, the mechanism credibility verification does not modify the predicted values ​​output by the machine learning model by default. Corrected values ​​are only output when a residual correction model or numerical correction rule, validated independently with historical data or controlled experiments, exists. The residual correction model is a model established using historical data or controlled experiments to correct biases in the machine learning model's output, and the numerical correction rule is a correction rule based on physicochemical rules or empirical formulas. At this time, the base predicted value, the corrected value, the version of the correction rule, and its applicable scope are recorded simultaneously. If no correction model or rule exists, the predicted value output by the machine learning model is the final predicted value.

[0063] The mechanism credibility verification process defaults to not modifying the predicted values ​​output by the machine learning model. This approach uses the machine learning model's output as the basic numerical anchor for performance prediction. The mechanism credibility verification process only identifies out-of-distribution conditions, classifies reliability, and explains the mechanism based on this basic predicted value, without directly altering the numerical values ​​themselves. The purpose is to avoid disrupting the consistency of predicted values ​​by introducing adjustments that have not been independently verified, ensuring that subsequent compliance determination and candidate ranking are based on prediction results with clear sources. When a coating performance indicator in a candidate formulation is determined to have a high reliability level, the predicted value output by the machine learning model is used as the final predicted value for that performance indicator and directly enters the subsequent evaluation stage. When a performance indicator is marked as out-of-distribution or its predicted reliability level is reduced, the mechanism credibility verification process only expresses its judgment on the credibility of the predicted value by lowering the reliability level and outputting experimental verification prompts, without changing the predicted value itself. This default rule ensures that even if a candidate formulation triggers out-of-distribution conditions, the predicted values ​​read in subsequent evaluation stages are still the basic predicted values ​​initially given by the machine learning model, avoiding traceability difficulties caused by inconsistent modifications to the same indicator's predicted value in multiple stages.

[0064] Corrected values ​​are output only when a residual correction model or numerical correction rule validated independently using historical data or controlled experiments exists. A residual correction model is a model established using historical data or controlled experiments to correct the output bias of a machine learning model. A numerical correction rule is a correction rule based on physicochemical rules or empirical formulas. Both correction models and rules must be validated independently of the training data to avoid the risk of overfitting caused by self-correction using the training set's own errors. For example, for a certain coating performance index, historical data accumulates records of the deviation between the machine learning model's predicted values ​​and the measured values. A residual correction model established based on these deviation records can correct the basic predicted values ​​when a candidate formulation triggers specific out-of-distribution conditions. Similarly, a physicochemical rule can determine the direction of change in a performance index when the proportion of a specific raw material increases, but it cannot directly provide a reliable numerical magnitude. In this case, a corrected value can only be output after validation through controlled experiments and the formation of a repeatable numerical correction rule. This constraint avoids arbitrary adjustments to predicted values ​​based solely on qualitative experience.

[0065] When an independently validated residual correction model or numerical correction rule exists and is applied in practice, the basic predicted value, the corrected value, the version of the correction rule, and the scope of application must be recorded simultaneously with the output correction value. Recording the basic predicted value preserves the original output of the machine learning model, facilitating the traceability of the data source before correction. Recording the corrected value clarifies the numerical value actually used in subsequent evaluations. Recording the correction rule version distinguishes correction rules established at different times and under different conditions, preventing the results from becoming unreproducible due to rule updates. Recording the scope of application indicates the effective range of coating types, raw material systems, and performance indicators for the correction model or rule, preventing the application of correction rules to candidate formulations beyond their applicable scope. Through these simultaneous records, a correspondence is maintained between the basic predicted value and the corrected value, allowing subsequent evaluation stages to clearly identify whether the final prediction result read is the basic predicted value or the corrected value, as well as the source and applicable conditions of the corrected value.

[0066] When no residual correction model or numerical correction rule exists, the predicted value output by the machine learning model is the final predicted value. In this case, even if the mechanistic credibility check identifies an out-of-distribution state or assigns a low reliability level, the predicted value will not be modified. Instead, its use will be restricted in subsequent achievement determination and recommendation stages through out-of-distribution labeling and low reliability levels. This approach aligns with the aforementioned principle of not modifying predicted values ​​by default, ensuring the uniqueness of the source of performance prediction results throughout the entire method. The final predicted value serves as a unified numerical basis in subsequent achievement determinations, candidate ranking, and iterative adjustments, thus ensuring that each step of numerical comparison and judgment in the formula recommendation closed loop has a clear source and consistent semantics.

[0067] Specifically, the process of retrieving the baseline formulation in step S2 includes the following sub-steps: S21, based on the application type in the structured performance target object, perform hard filtration of the coating type in the historical formula library, and retain historical formulas consistent with the application type.

[0068] The application type is identified from the natural language description and written into the structured performance target object during the requirements analysis phase. This specifies the coating type of the target formulation, such as epoxy primer, acrylic polyurethane topcoat, or polyurethane waterproof coating. The historical formulation library may store formulations of multiple coating types simultaneously. Different types of coatings differ significantly in film-forming mechanisms, curing systems, pigment volume concentration ranges, and performance evaluation indicators. If coating type filtering is not performed during the retrieval phase, different types of formulations will be included in the comparison when calculating performance vectors and constraint violation distances, resulting in historical formulations that do not fundamentally match the target requirements being mixed into the ranking results. Hard filtering of coating types retains only historical formulations that are completely consistent with the target application type, eliminating invalid comparisons caused by different coating types from the source. After hard filtering, all historical formulations entering the subsequent similarity measurement and ranking stages belong to the same coating type, ensuring that subsequent comparisons based on performance vectors and constraint violation distances are based on the comparability of the same coating system.

[0069] S22, construct a performance vector by combining the known performance of the filtered historical formula with the hard performance targets in the structured performance target object according to the same performance index order, and unify the direction of the three comparison relationships: larger values ​​are better, smaller values ​​are better, and target range.

[0070] The construction of performance vectors requires that historical formulations and hard performance targets maintain consistency across the indicator dimensions to ensure a one-to-one correspondence between components in subsequent distance calculations. After constructing the performance vectors, the directions of three comparison relationships—larger values ​​are better, smaller values ​​are better, and target ranges—are unified. The evaluation directions for different coating performance indicators are not the same: for indicators such as adhesion grade, surface drying time, and complete drying time, smaller values ​​represent better performance, while for indicators such as salt spray resistance, activation period, and thick coating thickness, larger values ​​represent better performance. If distance calculations are directly mixed, the directional differences between the "larger values ​​are better" and "smaller values ​​are better" indicators will render the distance calculation results meaningless. The purpose of directional unification is to transform performance differences in different directions into a consistent measurement direction, allowing differences in each performance dimension to participate in subsequent constraint violation distance calculations in the same direction. The performance vectors with unified directions can more accurately reflect the comprehensive deviation of historical formulations relative to hard performance targets across various performance dimensions, providing a consistent and interpretable numerical basis for benchmark formulation ranking.

[0071] S23. For each historical formulation, calculate its constraint violation distance relative to each hard performance target, and introduce performance priority weights, missing performance penalties and test condition inconsistency penalties, and sum them up to obtain the baseline constraint violation distance.

[0072] The constraint violation distance measures the extent to which a historical recipe deviates from the user-defined hard performance targets. When a historical recipe's performance meets the hard performance target, the constraint violation distance for that performance dimension is zero; when a performance fails to meet the hard performance target, the distance component for that dimension is calculated based on the normalized difference between the predicted or measured value and the target value. Normalization eliminates the impact of differences in the dimensions of different performance indicators on the overall distance calculation. Performance priority weights differentiate the importance of different hard performance targets. Higher weight performance indicators have a greater impact on distance calculation, and the ranking results tend to prioritize historical recipes that perform better in that key performance area. The missing performance penalty is set for situations where historical recipes lack measured data for a specific hard performance target. When a historical recipe lacks measured data corresponding to a specific hard performance target, the constraint violation distance for that performance dimension cannot be directly calculated. Setting a missing performance penalty can lower the ranking position of the historical recipe, preventing recipes with incomplete performance data from being prioritized as benchmark recipes. The test condition inconsistency penalty is set when the test methods or test conditions of a historical recipe are inconsistent with the requirements in the structured performance target object. Different testing conditions can reduce the comparability of the same performance metric. Even if the measured value meets the target, a certain ranking penalty should be imposed on the historical formula to reflect the deviation of the data in the dimension of testing conditions. By weighted summing of the above components, the baseline constraint violation distance for each historical formula is obtained.

[0073] S24. Sort the historical recipes with the highest number of violations of the baseline constraint from smallest to largest, and select the historical recipes with the highest number of violations as the baseline recipes.

[0074] The smaller the baseline constraint violation distance, the closer the historical formula is to the user-defined hard performance target, and the more suitable it is as the starting point for generating subsequent candidate formulas. A preset number is used to control the scale of baseline formulas entering subsequent stages, avoiding an excessive number of baseline formulas that would increase the computational burden of large language model generation and engineering constraint verification. In practice, the preset number is usually set based on the size of the historical formula library, the complexity of the target performance, and the computational resource constraints of the iteration rounds; for example, it can be set to five. When multiple historical formulas have the same baseline constraint violation distance, the cosine similarity between the known performance vector and the target performance vector is used as a secondary sorting criterion. The baseline formulas obtained after sorting and selection will serve as the starting formulas input into the large language model during the first round of candidate generation. If any of the selected baseline formulas already meet all hard performance targets, it will be directly output in the subsequent fast-return judgment and will not enter the candidate generation and performance prediction stages. This sorting and selection method balances the degree of target performance achievement and the consistency of test conditions, ensuring that the baseline formulas have both a fundamental performance advantage and comparability with the target requirements in terms of test conditions.

[0075] Furthermore, calculating the constraint violation distance in step S23 also includes: S231, when the performance index is an ordered level index, each level is converted into adjacent ordinal values ​​according to the preset level order, and the normalized constraint violation distance is calculated based on the ordinal difference, and each level is not treated as an independent category that is unordered from each other.

[0076] In the coatings industry, some performance indicators are not expressed as continuous numerical values, but rather as a pre-defined sequence of grades. For example, hardness is set in multiple grades from low to high, and adhesion grades also have a low-to-high order. Although these indicators are represented by grade symbols, there is a clear sequential order between grades. The differences between adjacent grades are not entirely identical in an engineering sense, but at least there is a directionality. When calculating constraint violation distance, if each grade is treated as an independent category without order, and only the grade of the historical formulation is judged as equal to the target grade, the differences in distance between different grades cannot be reflected. For example, when the target hardness is a high grade, the distance calculation should be different if the hardness of the historical formulation is only one grade lower than the target and three grades lower than the target. However, the unordered category treatment will simply classify both as non-compliance, losing the information of grade difference. Therefore, each grade is converted into adjacent ordinal values ​​according to the pre-defined grade order, and then the normalized constraint violation distance is calculated based on the ordinal difference. The difference between adjacent ordinal values ​​reflects the relative distance between grades. The larger the ordinal difference, the farther the historical formulation deviates from the target in that performance indicator. For example, hardness can be assigned an increasing ordinal number in the order of 6B, 5B, 4B, 3B, 2B, B, HB, F, H, 2H, 3H up to 9H. In this way, the distance calculation for ordered rank indicators preserves the sequential information between ranks and provides a quantifiable basis for comparison of differences between ranks, avoiding the treatment of each rank as an independent, unordered category. This approach allows ordered rank indicators to participate in the ranking process alongside continuous numerical indicators within the same constraint violation distance framework, improving the rationality of the benchmark formulation screening results.

[0077] S232, when a historical formula lacks measured data corresponding to any hard performance target, a missing performance penalty is applied to the historical formula to lower its ranking position.

[0078] The historical formula database contains formula data from diverse sources. Some historical formulas may lack measured values ​​for certain performance indicators due to incomplete records, missing test items, or the absence of performance testing requirements during the data collection phase. When a historical formula lacks measured data corresponding to a specific hard performance target, the constraint violation distance on that performance dimension cannot be calculated. If this dimension is directly ignored in the distance calculation, formulas with missing performance data will gain an undue ranking advantage when compared with formulas with complete performance data within the same ranking framework. For example, one historical formula may have measured values ​​for salt spray resistance but fail to meet the standard, while another historical formula lacks measured data for salt spray resistance. If no penalty is applied to missing data, the latter will not generate a distance component on the salt spray resistance dimension, and its overall distance may actually be smaller than the former, but this does not actually prove that its salt spray resistance meets the target. Missing performance penalties reduce the ranking position of the historical formula by adding a penalty component to the overall constraint violation distance, making formulas with incomplete performance data less likely to be prioritized as benchmark formulas. The specific magnitude of this penalty can be set based on the number of missing indicators, the priority weight of the missing indicators in the hard performance targets, and the overall data completeness in the historical formula database. By setting a penalty for missing performance, the benchmark recipe search results are more inclined to select historical recipes with complete performance data that can provide sufficient reference for subsequent candidate generation.

[0079] S233, when the test method or test conditions of a historical formulation are inconsistent with the structured performance target, a penalty for inconsistent test conditions shall be added to the historical formulation.

[0080] The measured values ​​of coating performance indicators are highly dependent on the specific conditions under which the test is performed, including the test method, substrate type, substrate pretreatment, film thickness, curing temperature, curing time, and test environment. The same performance indicator measured under different test conditions for the same formulation may show significant differences. When the test method or test conditions of a historical formulation in the historical formulation library are inconsistent with the requirements of the structured performance target, the basis for comparing the measured value of that historical formulation with the target value for that performance indicator is not solid. Even if the measured value superficially meets the target, it cannot be concluded that the formulation can reproduce the result under the user-required test conditions. The test condition inconsistency penalty reflects this reduced comparability by adding a penalty component to the overall constraint violation distance. This penalty is determined based on the type and degree of the test condition difference. For cases where the test methods are completely different or the key test conditions differ significantly, the penalty is increased accordingly; for cases where there are only slight differences in the test environment, the penalty is decreased accordingly. By introducing the test condition inconsistency penalty, the benchmark formulation retrieval no longer uses the degree of performance value compliance as the sole criterion for ranking, but also considers the comparability of performance data across the test condition dimension. The selected baseline formulations not only have a good foundation in terms of performance targets, but also have test conditions that are closer to the actual needs of users, thus providing a more reliable basis for subsequent candidate generation and performance prediction.

[0081] In addition, the large language model is only used to generate initial candidate formulations and adjustment instructions. Engineering constraint verification is performed by preset verification rules. The large language model does not participate in the determination of engineering constraint verification, nor does it directly modify the component ratios, predicted values, or performance determination results of candidate formulations.

[0082] The large language model is only used to generate initial candidate formulations and adjustment instructions. Its output is limited to formulation adjustment schemes and corresponding reasons for adjustment, and is not directly used as the final formulation or performance evaluation conclusion. This limitation is based on the probabilistic and non-deterministic nature of the large language model's output: given the same input conditions, the large language model may generate different expressions or adjustment schemes, and the generated component ratio values ​​do not inherently possess engineering-meaning precision and consistency. Therefore, the large language model is positioned as a constrained adjustment scheme proposer in the formulation generation process, rather than an executor of engineering judgment or numerical verification. After the initial candidate formulations are generated, engineering constraint verification is performed by preset verification rules. The preset verification rules verify each condition in the initial candidate formulation in a deterministic manner, including the identity of raw materials, the adjustment range of single components, the sum of component ratios, the lower limit of key raw materials, the reaction equivalence ratio, the pigment volume concentration, the volatile organic compound content, and the raw material compatibility. The verification result depends only on the correspondence between the specific values ​​of the candidate formulation and the preset rules, and does not change due to changes in the number of executions or the expression method. By separating the generation function of the large language model from the verification function of the preset verification rules, the uncertainty and untraceability caused by the direct entry of the output of the generated model into the engineering judgment are avoided.

[0083] The large language model does not participate in the engineering constraint verification, nor does it directly modify the component ratios, predicted values, or performance evaluation results of candidate formulations. When the engineering constraint verification finds that the initial candidate formulation violates at least one engineering constraint, the violation information is fed back to the large language model, which then modifies the corresponding component ratios or adjustment instructions in the next generation round. However, the modifications still need to be verified again by the preset verification rules. Predicted values ​​are output by the machine learning model, and performance evaluation results are generated by preset evaluation rules based on predicted values, prediction reliability levels, and out-of-distribution labels. The large language model does not directly modify either of these. This mechanism clarifies the data sources and responsibility boundaries between each stage of formulation generation, engineering verification, performance prediction, and compliance determination. It avoids direct intervention by a single generation model in formulation values ​​and evaluation conclusions, ensuring the repeatability and traceability of results in the entire formulation recommendation closed loop. It also facilitates the separate configuration and verification of each stage in actual implementation.

[0084] like Figure 6As shown, in the comprehensive evaluation and recommendation result output stage of candidate formulations, the input is the prediction result of the candidate formulation, including the predicted value, prediction reliability level, out-of-distribution label, and mechanism explanation. First, each coating performance index is judged item by item according to preset evaluation rules: for performance indices where a larger value is better, the predicted value is considered to meet the target if it is not lower than the target value; for performance indices where a smaller value is better, the predicted value is considered to meet the target if it is not higher than the target value; for performance indices with a target range, the predicted value is considered to meet the target if it is within the target range. Then, a status code for each coating performance index is generated based on the judgment results. The status codes include compliant, warning, and non-compliant states. A compliant state indicates that the final predicted value meets the corresponding hard target, is not marked as out-of-distribution, and has a prediction reliability level that is not low; a warning state indicates that the hard target is met but deviates from the preferred range, or is marked as out-of-distribution or has a low prediction reliability level; a non-compliant state indicates that the final predicted value does not meet the corresponding hard target. The overall ranking of candidate formulations is first based on the number of non-compliant indicators from smallest to largest. If the number of non-compliant indicators is the same, they are ranked from smallest to largest by the weighted normalized non-compliant magnitude. If the magnitudes are the same, they are ranked from highest to lowest by the prediction reliability level. The large language model generates an overall description and subsequent adjustment suggestions based on the target value, final predicted value, status code, main influencing factors, out-of-distribution markers, and prediction reliability level, but does not modify the final predicted value and status code generated by the preset evaluation rules. A candidate formulation is only output as the final recommended formulation when all hard performance indicators are compliant and the prediction reliability level of key performance indicators is not low. The iteration terminates when the improvement of the optimal weighted normalized non-compliant magnitude after reaching the maximum number of iterations or the preset number of consecutive rounds is less than a preset threshold, or when the candidate set no longer generates new candidate signatures. Formulations that still do not meet the final recommendation conditions at the time of termination are output as intermediate candidate schemes to be experimentally verified and are not marked as final recommended formulations.

[0085] In one specific implementation of this invention, step S5 involves determining the compliance of each coating performance indicator, including: S511, based on the target values ​​in the structured performance target object, for performance indicators where larger values ​​are better, the target is considered met when the predicted value is not lower than the target value. For performance indicators where smaller values ​​are better, the target is considered met when the predicted value is not higher than the target value. For performance indicators with target ranges, the target is considered met when the predicted value is within the target range.

[0086] Performance indicators with higher numerical values ​​are considered better, meaning that a higher value indicates better coating performance. Examples include salt spray resistance, activation time, and thick coating properties. For these indicators, the performance indicator is considered to meet the target if the predicted value of the candidate formulation is not lower than the target value. Performance indicators with lower numerical values ​​are considered better, meaning that a lower value indicates better coating performance. Examples include adhesion grade, surface drying time, and hard drying time. For these indicators, the performance indicator is considered to meet the target if the predicted value of the candidate formulation is not higher than the target value. Performance indicators with target ranges are those where the target is not a single threshold but a range defined by a lower and upper limit, such as gloss or volume solids. For these indicators, the performance indicator is considered to meet the target if the predicted value of the candidate formulation falls within the target range. The direct basis for determining compliance is the predicted value of the candidate formulation, not the measured value of the benchmark formulation or historical reference formulation. When the predicted value of a performance indicator meets the target value requirement, that performance indicator is considered to have met the mandatory performance target in this round of evaluation. During the judgment process, performance indicators of different comparison types adopt judgment logic consistent with their respective engineering significance, ensuring that the compliance of each performance indicator is measured according to rules consistent with its direction. This item-by-item compliance judgment provides a clear basis for subsequent status code generation and candidate ranking.

[0087] S512 generates a status code for each coating performance indicator based on the judgment result. The status codes include compliance status, warning status, and non-compliance status.

[0088] Status codes are standardized markers used to identify the outcome of a single performance indicator in the compliance determination process. There are three statuses: compliant, warning, and non-compliant. A compliant status indicates that the predicted value of the performance indicator meets the corresponding hard target, and the performance indicator is not marked as out of distribution, nor is its prediction reliability level low. A warning status indicates that although the predicted value of the performance indicator meets the corresponding hard target, there are other factors that require attention, such as the performance indicator being marked as out of distribution, its prediction reliability level being low, or the predicted value deviating from the optimal range while meeting the hard target. A warning status does not constitute evidence that the performance indicator has reliably met the target. A non-compliant status indicates that the predicted value of the performance indicator does not meet the corresponding hard target. The generation of status codes does not rely on the subjective judgment of the large language model, but is directly determined by preset judgment rules based on the combination of the predicted value, prediction reliability level, and out-of-distribution marker. By generating status codes for each performance indicator, the compliance status of candidate formulations can be represented in a structured manner. The weights and processing methods of different performance indicators in subsequent ranking and screening can be directly correlated with the status codes, avoiding the semantic ambiguity caused by mixed ranking based solely on numerical comparisons. The status codes also provide an indicator-by-indicator basis for adjusting the generation of constraint information in subsequent iterations.

[0089] S513: Candidate formulations are sorted from smallest to largest based on the number of indicators with non-compliance status. When the number of non-compliance status indicators is the same, they are sorted from smallest to largest based on the weighted normalized non-compliance magnitude. The weighted normalized non-compliance magnitude is obtained by summing the normalized difference between each non-compliance performance indicator and its corresponding target value, multiplied by the priority weight of that performance indicator. When the weighted normalized non-compliance magnitudes are the same, they are sorted from highest to lowest prediction reliability level.

[0090] First, the candidates are sorted from smallest to largest based on the number of indicators that are not in compliance. Fewer indicators indicate that the candidate formulation has met the hard targets across more performance indicators, resulting in a higher overall compliance rate. When multiple candidate formulations have the same number of indicators that are not in compliance, they are further sorted from smallest to largest based on their weighted normalized non-compliance magnitude. The weighted normalized non-compliance magnitude is obtained by summing the normalized difference between each non-compliant performance indicator and its corresponding target value, multiplied by the priority weight of that performance indicator. The calculation method for the normalized difference is consistent with the normalization process in the aforementioned baseline constraint violation distance, used to eliminate dimensional differences between different performance indicators. The priority weight is read from the structured performance target object, reflecting the importance of different performance indicators in the formulation requirements, with key performance indicators having a higher weight than ordinary performance indicators. A smaller weighted normalized non-compliance magnitude indicates a smaller overall deviation of the candidate formulation from the non-compliant indicators, and a closer proximity to meeting all hard targets. When the weighted normalized non-compliance magnitudes are also the same, they are sorted from highest to lowest based on their prediction reliability level. Candidate recipes with high predictive reliability are prioritized because their predicted performance values ​​fall within the reliable region of the training data, resulting in a relatively lower risk of deviation from predictions in subsequent experimental verification. Through this three-level ranking rule, candidate recipes are uniformly ranked in each iteration based on three dimensions: degree of achievement, deviation magnitude, and predictive reliability. This provides a definite basis for selecting the candidate set for the next round of adjustment. This ranking result is not directly generated by the large language model but is calculated by preset ranking rules based on the status codes of each performance indicator, the weighted normalized non-achievement magnitude, and the predictive reliability level, ensuring the repeatability and logical consistency of candidate selection across multiple iterations.

[0091] Furthermore, step S5 adjusts the constraint information and intermediate candidate solutions, returning them to step S3 to constrain the generation of the next round of initial candidate formulations, forming a closed loop for formulation recommendation. This also includes: S521: In each round, candidate formulations that fail the engineering constraint verification are first eliminated. Then, they are sorted according to the number of non-compliant state indicators, the weighted normalized non-compliant range, and the predicted reliability level. A preset number of non-overlapping candidate formulations are selected to enter the next round of adjustment.

[0092] Each iteration begins by eliminating candidate recipes that fail the engineering constraint verification. While the engineering constraint verification is performed after candidate recipes are generated, eliminating those that fail verification again before proceeding to the next round of selection ensures that all candidate recipes entering the sorting and selection phases meet basic engineering feasibility requirements. If a candidate recipe is discarded due to failing the engineering constraint verification, it will not be included in the sorting and selection process for this round. After elimination, the remaining candidate recipes are sorted according to the number of non-compliant indicators, the weighted normalized non-compliant magnitude, and the prediction reliability level. This sorting rule is consistent with the sorting rule described earlier in the item-by-item compliance determination: first, the number of non-compliant indicators is compared, with fewer indicators taking precedence; if the number is the same, the weighted normalized non-compliant magnitude is compared, with smaller magnitudes taking precedence; if the magnitudes are still the same, the prediction reliability level is compared, with higher levels taking precedence. After sorting, the top-ranked, pre-set number of non-overlapping candidate recipes are selected for the next round of adjustment. The pre-set number is predetermined based on computing resources, iteration efficiency, and the size of the recipe library, and is used to control the size of candidate recipes for the next round of large language model generation and machine learning prediction. The requirement of non-duplication is ensured through deduplication of subsequent candidate signatures. Through the above elimination, sorting and selection process, the candidate formulations that enter the next round in each iteration are all engineering feasible, have a relatively high degree of compliance and good prediction reliability, and the iteration direction gradually converges towards all hard performance targets.

[0093] S522 generates candidate signatures based on the unique identifier set of raw materials, the ratio of main agent to curing agent, and the component ratio rounded to a preset precision, and removes duplicate formulas through candidate signatures.

[0094] Candidate signatures are used to uniquely identify the compositional characteristics of a candidate formulation. The raw material unique identifier set reflects all raw materials included in the candidate formulation and their unique identifiers in the raw material database, providing fundamental information for distinguishing the raw material composition of the formulation. The ratio of the main agent to the curing agent reflects the proportion of the main agent and the curing agent in the two-component coating; this ratio directly affects the reaction equivalence ratio and the final film-forming performance of the mixed formulation. Component ratios are rounded to a preset precision before generating candidate signatures to eliminate pseudo-duplications caused by differences in numerical precision. For example, if two candidate formulations differ only in the fourth decimal place of their component ratios, they are considered identical after rounding to the preset precision and are thus considered duplicate formulations. Candidate signatures are generated by combining the above information; candidate formulations with the same candidate signature are identified as duplicate formulations. By deduplicating candidate signatures, it is ensured that the candidate formulation set entering the next round of adjustment does not contain duplicate schemes, avoiding repeated large language model generation and machine learning prediction for formulations with the same or essentially the same composition, thereby improving iteration efficiency and ensuring that the candidate set output in each round has compositional diversity. After deduplication, the actual number of candidate formulas entering the next round may be less than the preset number. The subsequent termination conditions also provide a corresponding exit mechanism for the case where no new candidate signatures are generated in the candidate set.

[0095] S523: When all hard performance targets of the candidate formulation are met and the predicted reliability level is not low, the candidate formulation will be output as the final recommended formulation.

[0096] All hard performance targets are met, meaning that in the item-by-item compliance assessment, all performance indicators marked as hard by the constraint level are judged to meet the targets, and there are no situations where the predicted values ​​do not meet the targets, as seen in the non-compliance and warning states. The prediction reliability level is not low, meaning that none of the performance indicators of the candidate formulation are judged to have a low reliability level due to incomplete training data coverage, insufficient similarity, or multiple out-of-distribution conditions. The condition of a not low prediction reliability level, together with the condition that all hard performance targets are met, constitutes a necessary condition for the final recommendation. Its purpose is to prevent a candidate formulation that, although the predicted value of a performance indicator meets the target, is actually unreliable due to a low prediction reliability level from being output as the final recommended formulation. When a candidate formulation meets both of the above conditions, it will not enter the next iteration but will be output as the final recommended formulation. The final recommended formulation includes complete component composition, the ratio of main agent to curing agent, predicted values ​​of each performance indicator, prediction reliability level, out-of-distribution markers, and corresponding mechanism explanations, for R&D personnel to refer to and use in subsequent small-scale, pilot-scale, and performance testing. The final recommended formula is the convergence result of the formula recommendation closed loop, and its output marks the end of the closed loop iteration process under the current requirements.

[0097] S524. When the maximum number of iterations is reached, the improvement of the optimal weighted normalization of the consecutive preset number of rounds is less than the preset threshold, or the candidate set no longer generates new candidate signatures, the iteration is terminated.

[0098] There are three conditions for iteration termination; the iteration terminates when any one of them is met. The first condition is reaching the maximum number of iterations. This maximum number of iterations is pre-set based on constraints on computational resources and response time. When the number of iterations reaches this limit, the iteration terminates regardless of whether the current candidate recipe meets the final recommendation criteria, to avoid infinitely consuming computational resources. The second condition is that the improvement in the optimal weighted normalized difference (ODD) margin for a consecutive preset number of iterations is less than a preset threshold. The optimal ODD margin refers to the smallest ODD margin among all candidate recipes that pass the engineering constraint verification in each iteration. When the improvement in the optimal ODD margin for several consecutive iterations is less than the preset threshold, it indicates that continuing the iteration will hardly yield meaningful improvement in the degree of compliance, and the iteration enters a diminishing returns phase; continuing will only repeatedly generate solutions similar to the current candidate recipe. The third condition is that the candidate set no longer generates new candidate signatures. When a candidate formula enters the next round of selection, and all candidate formulas have already appeared in previous rounds (meaning the candidate set no longer generates new composition schemes), it indicates that the generation process can no longer explore new formula spaces under existing constraints, and continued iteration will not generate new candidate schemes. The three termination conditions mentioned above control the iteration process from three dimensions: computational cost, convergence quality, and solution space diversity. This ensures that the closed-loop iteration can gradually approach the target within a certain number of rounds and exit promptly when there is no improvement or repetition.

[0099] S525, formulations that still do not meet the final recommended conditions at the end are output as intermediate candidate schemes to be verified experimentally, and are not marked as final recommended formulations.

[0100] After the iteration terminates, several candidate formulations may still remain in the candidate set. While some of their coating performance indicators have been deemed compliant, they do not yet simultaneously meet all the conditions required for final recommendation. For example, some indicators may still be non-compliant, or a certain performance indicator may be marked as having a low reliability level. Although these candidate formulations do not qualify for final recommendation, they can still serve as intermediate candidate solutions with engineering reference value because they have passed engineering constraint verification and performance prediction. Researchers can select some of these solutions for small-scale or panel experiments to supplement performance information that was not determined by the machine learning model and mechanism credibility verification using experimental data. Intermediate candidate solutions are explicitly marked as not meeting the final recommendation conditions when output, and are not assigned the final recommendation formulation label. For intermediate candidate solutions whose actual performance meets the target after experimental verification, they can be added to the historical formulation library or training sample set through data feedback, providing new data basis for subsequent formulation recommendations. Through the above processing, the closed-loop iteration retains practical value after termination; candidate formulations that do not meet the final recommendation conditions are transformed into experimental verification candidates, continuing to provide reference for formulation development.

[0101] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings and specific examples. These examples are for illustrative purposes only and should not be considered as limiting the scope of the invention.

[0102] Example 1: Recommended Epoxy Primer Formulation This embodiment demonstrates the complete process of the closed-loop generation method for formulation based on coating engineering constraints and prediction credibility verification in the scenario of epoxy primer formulation recommendation.

[0103] The user's natural language formula request description is: "Please recommend an epoxy primer formula with a cross-cut test score of no higher than 2, a hardness of no less than 2H, a salt spray resistance of no less than 150 hours, a dry time of no more than 20 hours, a surface drying time of no more than 1 hour, an activation period of no less than 3 hours, and a thickness of no less than 600 microns." Semantic parsing is performed on the above natural language formulation requirements description, and the parsing results are mapped to a preset coating performance index dictionary to generate structured performance target objects. The application type is epoxy primer. The target values ​​and comparison relationships of each coating performance index are as follows: adhesion is measured using the cross-cut test, with a target value not higher than level 2; hardness target value is not lower than 2H; salt spray resistance target value is not lower than 150 hours; hardness target value is not higher than 20 hours; surface drying time target value is not higher than 1 hour; activation period target value is not lower than 3 hours; and coating thickness target value is not lower than 600 micrometers. All of the above performance indicators are set as hard performance targets. For test conditions not explicitly given by the user, default test conditions are read from the epoxy primer configuration file, namely, the substrate is a sandblasted carbon steel plate with a surface treatment grade of Sa2.5, a dry film thickness of 80±10 micrometers, and the test panel is cured for 7 days in an environment with a temperature of 23±2 degrees Celsius and a relative humidity of 50±5%. After the default test conditions are confirmed by the user, the parsing status is set to explicit.

[0104] Based on the structured performance target objects mentioned above, a benchmark formulation was retrieved from the historical formulation library. First, hard filtering of coating type was performed on the historical epoxy primer formulations. Then, performance vectors were constructed according to the same performance indicators, and the comparison relationships were aligned. The benchmark constraint violation distance for each historical formulation was calculated, and the highest-ranked historical formulation was selected as the benchmark formulation. The known properties of the benchmark formulation were: adhesion grade 2, hardness H, salt spray resistance 120 hours, hard drying time 12 hours, surface drying time 0.5 hours, activation period 4 hours, and thickness coating 580 microns. After item-by-item verification, it was found that hardness, salt spray resistance, and thickness coating did not meet the hard performance targets. The benchmark formulation did not fully meet the standards and entered the candidate constraint construction stage.

[0105] When constructing the candidate generation constraint set, three adjustment strategies are set: a primary strategy, a conservative strategy, and a balanced strategy. The primary strategy prioritizes adjusting components whose impact on hardness, salt spray resistance, and thick coating properties exceeds a preset weight threshold. The conservative strategy uses adjustments whose magnitude does not exceed a preset conservative threshold and prioritizes avoiding degradation of already achieved performance. The balanced strategy uses preset balance weight coefficients to perform weighted adjustments among multiple performance targets. Engineering constraints include: the adjustment magnitude of a single raw material does not exceed 3 percentage points; the sum of the proportions of all components in the main agent is 100%; the sum of the proportions of all components in the curing agent is 100%; the resin proportion is not lower than a preset lower limit; and the reaction equivalence ratio, pigment volume concentration, and volatile organic compound content are within the preset range corresponding to the epoxy primer.

[0106] The baseline formulation and candidate generation constraint set are input into a large language model, which then generates initial candidate formulations under three adjustment strategies. The primary strategy generates initial candidate formulations whose main components include epoxy resin liquid, anti-settling agent, organobentonite, mixed xylene, titanium dioxide, carbon black, low oil absorption powder, polyamide wax, silane coupling agent, zinc phosphate, mica powder, and epoxy resin. The curing agent includes curing agent, polyamide resin, accelerator, mixed xylene, and n-butanol, with a main component to curing agent ratio of 9:1. Deterministic engineering constraint verification is performed on the initial candidate formulations. The initial candidate formulation had a reaction equivalence ratio of 0.98, within the permissible range of 0.90 to 1.10; a pigment volume concentration of 51.82%, within the permissible range of 45% to 55%; a volatile organic compound content of 345.32 g / L, not exceeding the limit of 420 g / L; a pigment-to-binder ratio of 1.55, within the permissible range of 1.20 to 1.80; and a volume solids content of 69%, within the permissible range of 65% to 75%. All verifications passed, and this initial candidate formulation was selected as a candidate formulation.

[0107] The performance prediction values ​​of the candidate formulation were obtained using a machine learning model. The prediction results were: adhesion level 2, hardness H, salt spray resistance 134.1 hours, dry time 8 hours, surface dry time 0.6 hours, activation period 4 hours, and coating thickness 625 micrometers. The predicted values ​​were then verified for mechanistic reliability. Taking adhesion as an example, the historical reference formulation with the highest similarity was retrieved from the historical formulation database. Its measured adhesion value was level 2. The similarity between the candidate formulation and this historical reference formulation met the preset similarity conditions and did not trigger any out-of-distribution conditions, indicating a high reliability level for the adhesion prediction. After the mechanistic reliability verification was completed, the prediction reliability level and out-of-distribution markers of each performance indicator were used as inputs for subsequent compliance determination.

[0108] The results of the item-by-item compliance assessment are as follows: Adhesion prediction value is level 2, meeting the target and generating a compliant state; Hardness prediction value H does not meet the target of not less than 2H, generating a non-compliant state; Salt spray resistance prediction value is 134.1 hours, not meeting the target of not less than 150 hours, generating a non-compliant state; Drying time prediction value is 8 hours, meeting the target of not more than 20 hours, but deviating from the preferred range, generating a warning state; Surface drying time prediction value is 0.6 hours, meeting the target and generating a compliant state; Activation period prediction value is 4 hours, meeting the target and generating a compliant state; Thickness prediction value is 625 micrometers, meeting the target of not less than 600 micrometers, generating a compliant state. Because this candidate formulation has two non-compliant indicators, hardness and salt spray resistance, it does not meet the final recommended conditions and is marked as an intermediate candidate. Based on the unmet hardness index, adjustment constraints are generated to increase the effective equivalent of the curing agent or the proportion of high-functionality epoxy resin. Based on the unmet salt spray resistance index, adjustment constraints are generated to increase the proportion of zinc phosphate or flake mica powder within the allowable range of single-component adjustment and pigment volume concentration. This intermediate candidate solution and adjustment constraints are returned to the candidate formulation generation step for the next iteration. When all hard performance targets of a candidate formulation are met and the predicted reliability level is not low, this candidate formulation is output as the final recommended formulation. Formulations that still do not meet the final recommended conditions when the iteration termination condition is reached are output as intermediate candidate solutions to be experimentally verified.

[0109] Example 2: Quick Return to Baseline Formulation This embodiment demonstrates the operation of the baseline formula fast return mechanism when a formula that meets all the hard performance targets already exists in the historical formula library.

[0110] The system receives a natural language description of the formulation requirements from the user, and generates a structured performance target object after semantic parsing and mapping. The application type is epoxy primer, and the target values ​​and comparison relationships of each performance indicator are completely consistent with a historical formulation. Based on the structured performance target object, a benchmark formulation is retrieved from the historical formulation library. The known performance of each benchmark formulation in the library is checked item by item. If all known performance characteristics of a given benchmark formulation meet all the hard performance targets in the structured performance target object, the benchmark formulation is directly output, and a prompt indicating that an existing formulation can cover the requirements is generated. The steps of candidate generation, engineering constraint verification, performance prediction, and mechanism credibility verification are skipped, and the process terminates. This benchmark formulation fast-return mechanism eliminates the need for subsequent calculations when an existing formulation can meet the requirements, reducing computational resource consumption and shortening response time.

[0111] Example 3: Clarification of Requirements for Acrylic Polyurethane Topcoat This embodiment demonstrates a clarification mechanism in the requirements parsing stage when necessary information is missing from the natural language recipe requirement description entered by the user.

[0112] The system receives a user's input in natural language describing a formulation requirement as: "Recommend an acrylic polyurethane topcoat with high temperature resistance and good adhesion." Semantic recognition is performed on this requirement, identifying the application type as acrylic polyurethane topcoat and the two performance requirements: "high temperature resistance" and "good adhesion." When matching these performance requirements against a pre-defined dictionary of coating performance indicators, it is determined that "high temperature resistance" lacks information such as test temperature and duration, while "good adhesion" lacks information such as substrate type, test method, and target grade or target value. At this point, the corresponding performance indicator's resolution status is set to require clarification. Clarification questions are generated, requiring the user to supplement the test temperature, duration or temperature cycling conditions, permissible changes in appearance and performance, and test method for "high temperature resistance"; and requiring the user to supplement the substrate type, substrate pretreatment method, adhesion test method, and target grade or target value for "good adhesion." Before the user supplements this information, "high temperature resistance" is not directly converted to an artificial weathering resistance index, nor is "good adhesion" directly converted to a cross-cut adhesion level 1. After the user completes the information, the system calls the corresponding performance index configuration and raw material attribute configuration for the acrylic polyurethane topcoat according to the application type, updates the parsing status to clear, and continues to execute the steps of benchmark formula retrieval, candidate generation constraint construction, candidate formula generation, engineering constraint verification, performance prediction, mechanism credibility verification, and item-by-item compliance judgment to generate candidate formulas for acrylic polyurethane topcoat and corresponding performance evaluation results.

[0113] Example 4: Distribution Out-of-Distribution Labeling and Mechanism Credibility Verification This embodiment demonstrates the process of determining the out-of-distribution label and prediction reliability level when the proportion of a certain raw material in a candidate formulation exceeds the calibration range of the training samples.

[0114] The user input, expressed in natural language, describes a formulation requirement as: "Recommend an acrylic polyurethane topcoat formulation with a gloss level not exceeding 40 GU." After semantic parsing and mapping, a structured performance target object is generated, where gloss level is the target performance indicator, with a target value not exceeding 40 GU, and lower values ​​are considered better. After completing the benchmark formulation retrieval and candidate generation constraint construction, the benchmark formulation and candidate generation constraint set are input into a large language model to generate initial candidate formulations. The initial candidate formulation uses 10% matting agent, while the benchmark formulation uses 7%, with a single adjustment increment of 3 percentage points, not exceeding the single-component adjustment increment constraint. After passing engineering constraint verification, this initial candidate formulation is confirmed as a candidate formulation.

[0115] Gloss prediction values ​​were obtained using a machine learning model. The matting agent content in the historical training samples ranged from 2% to 8%, while the content in the candidate formulation was 10%, exceeding the upper boundary of the training sample calibration by 8%, a 25% exceedance. The amount of matting agent related to gloss in the candidate formulation exceeded the upper boundary of the training sample calibration, satisfying the out-of-distribution condition. The historical reference formulation with the highest similarity to the candidate formulation had a matting agent content of 7%, a measured gloss of 68 GU, and a similarity of 0.86 between the candidate formulation and this historical reference formulation. The basic predicted gloss value output by the machine learning model was 55 GU. Because the matting agent content exceeded the upper boundary of the training sample calibration, and the exceedance exceeded the preset severe out-of-distribution threshold, the prediction reliability level of this gloss performance indicator was determined to be low reliability, and an out-of-distribution label was generated. The mechanism description records the fact that the matting agent content exceeded the calibration range of the training samples and the difference in matting agent content with the closest historical reference formulation.

[0116] In this embodiment, no residual correction model or numerical correction rule for the relationship between matting agent dosage and gloss has been established and verified by independent historical data or control experiments. Therefore, no correction value is output, and the 55 GU output by the machine learning model is used as the final predicted value for gloss. In the item-by-item compliance judgment, the final predicted value of gloss, 55 GU, does not meet the target of not exceeding 40 GU, resulting in a non-compliance status, and the candidate formulation enters the next round of adjustment. This embodiment illustrates that when the proportion of a certain component in the candidate formulation exceeds the coverage range of the training data, the mechanism credibility check can identify this out-of-distribution state and indicate that the predicted value cannot be directly used as the basis for compliance by reducing the prediction reliability level and outputting an out-of-distribution label.

[0117] Accordingly, a second aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described formula closed-loop generation method based on coating engineering constraints and prediction confidence verification.

[0118] Accordingly, a third aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described formula closed-loop generation method based on coating engineering constraints and prediction reliability verification.

[0119] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0120] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0121] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0122] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification, characterized in that, Includes the following steps: S1, Receive natural language formulation requirement description, perform semantic parsing on the natural language formulation requirement description, and map the parsing result to a preset coating performance index dictionary to generate a structured performance target object; S2, based on the structured performance target object, retrieve the benchmark formula from the historical formula library; When the known performance of the baseline formulation meets the hard performance target, the baseline formulation is output and the process terminates; When the baseline formulation fails to meet at least one hard performance target, a candidate generation constraint set is constructed based on the baseline formulation and the unmet performance. The candidate generation constraint set is a set of engineering constraints used to restrict the generation and verification of candidate formulations. S3, during the first execution, the baseline recipe and the candidate generation constraint set are input into the large language model, and the large language model generates the initial candidate recipe; In subsequent iterations, intermediate candidate solutions and adjustment constraint information are used as inputs to the large language model. The intermediate candidate solutions are candidate formulations that failed to meet all hard performance targets in the previous iteration and were marked as intermediate candidate solutions. The adjustment constraint information is constraint information generated based on the unmet coating performance indicators in the previous round to constrain the generation of the initial candidate formulation in the next round. The large language model generates the initial candidate formulation for the next round. Based on the candidate generation constraint set, deterministic engineering constraint verification is performed on the initial candidate formulation, and the initial candidate formulation that passes the engineering constraint verification is determined as the candidate formulation. S4. Based on the machine learning model, obtain the predicted values ​​of several coating performance indicators corresponding to the candidate formulation; Based on historical reference formulations, candidate formulation physicochemical parameters, and the training data coverage of the machine learning model, the predicted values ​​are verified for mechanistic credibility to determine whether the coating performance indicators exceed the training data coverage and to obtain the prediction reliability level and out-of-distribution label of the coating performance indicators. S5. Based on the predicted value, the predicted reliability level, and the out-of-distribution marker, each of the coating performance indicators is assessed for compliance. When all hard performance targets of the candidate formulation are assessed as compliant and the predicted reliability level is not low, the final recommended formulation is output. Otherwise, the candidate formulation is marked as an intermediate candidate solution, and adjustment constraint information is generated based on the unmet coating performance indicators; The adjustment constraint information and the intermediate candidate solutions are returned to step S3 to constrain the generation of the next round of initial candidate formulations, forming a closed loop for formulation recommendation.

2. The method for generating closed-loop formulations based on coating engineering constraints and prediction reliability verification according to claim 1, characterized in that, The mechanism credibility verification in step S4 includes the following sub-steps: S41, retrieve historical reference formulas from the historical formula database that meet preset similarity conditions with the candidate formula in terms of coating type, raw material composition, component ratio and test conditions, and obtain the similarity between the candidate formula and the historical reference formula; S42, based on the feature set corresponding to each coating performance index in the candidate formulation, the historical reference formulation, and the training data coverage of the machine learning model, determine whether each coating performance index satisfies at least one out-of-distribution condition. S43, Based on the number of triggers, the trigger amplitude, and the similarity of the out-of-distribution conditions, determine the prediction reliability level of each of the coating performance indicators; S44, Based on the predicted reliability level and the judgment result of the out-of-distribution conditions, generate the out-of-distribution label and mechanism description of the coating performance index.

3. The closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification according to claim 2, characterized in that, The external distribution conditions include at least one of the following: The candidate formulation includes raw materials that are not present in the training samples of the machine learning model and are related to the current coating performance indicators, and the mass fraction of the raw materials is higher than a preset trace threshold. The proportion of any raw material in the candidate formulation that is related to the current coating performance index exceeds the lower or upper bound of the calibration of that raw material proportion in the training sample. The physicochemical parameters related to the current coating performance indicators in the candidate formulation are at least one of reaction equivalence ratio, pigment volume concentration, volatile organic compound content, pigment-to-binder ratio, and volume solids content, which are outside the calibration range of the corresponding parameters in the training samples. The test methods or test conditions used in the candidate formulations are not covered by the training data of the machine learning model for the current coating performance indicators; The candidate formulation exceeds the calibration range in the multivariate feature space of the current coating performance index. The multivariate feature space is a space composed of multiple features of the candidate formulation that are related to the current coating performance index.

4. The formula closed-loop generation method based on coating engineering constraints and prediction credibility verification according to claim 3, characterized in that, The predicted reliability levels include high reliability, medium reliability, and low reliability. Determining the predictive reliability level for each of the coating performance indicators in step S43 includes: Step S431: When no out-of-distribution conditions are triggered, and the highest similarity between the candidate formulation and the historical reference formulation that meets the preset similarity conditions is not lower than the preset high reliability similarity threshold, the predicted reliability level of the coating performance index is determined to be a high reliability level. Step S432: When only one univariate out-of-distribution condition is triggered, and the out-of-distribution magnitude of the univariate out-of-distribution condition does not exceed the preset mild out-of-distribution threshold, and the highest similarity is not lower than the preset medium reliability similarity threshold, and no related raw material conditions not seen in the training samples, test conditions not covered, or multivariate significant out-of-distribution conditions are triggered, the prediction reliability level of the coating performance index is determined to be medium reliability level. Step S433: When any of the following situations are triggered, the predicted reliability level of the coating performance index is determined to be a low reliability level: the candidate formulation contains related raw materials not seen in the training samples with a mass fraction higher than a preset trace threshold, the test method or necessary test conditions are not covered, multiple out-of-distribution conditions are triggered simultaneously, any related feature exceeds a preset severe out-of-bounds threshold, the multivariate distance or the ensemble variance of the machine learning model exceeds a preset threshold, or the highest similarity is lower than a preset low reliability similarity threshold.

5. The method for generating closed-loop formulations based on coating engineering constraints and prediction reliability verification according to claim 4, characterized in that, The mechanism credibility verification does not modify the predicted value output by the machine learning model by default. Only when there is a residual correction model or numerical correction rule verified by independent historical data or control experiments, where the residual correction model is a model established using historical data or control experiments to correct the output bias of the machine learning model, and the numerical correction rule is a correction rule based on physicochemical rules or empirical formulas, will a correction value be output, and the basic predicted value, correction value, correction rule version, and applicable scope will be recorded simultaneously. When the correction model or rule does not exist, the predicted value output by the machine learning model is the final predicted value.

6. The method for generating closed-loop formulations based on coating engineering constraints and prediction reliability verification according to claim 1, characterized in that, The retrieval of the benchmark formulation in step S2 includes the following sub-steps: S21, based on the application type in the structured performance target object, perform coating type hard filtration in the historical formula library and retain historical formulas consistent with the application type; S22, construct a performance vector by combining the known performance of the filtered historical formula with the hard performance targets in the structured performance target object according to the same performance index order, and unify the direction of the three comparison relationships: larger values ​​are better, smaller values ​​are better, and target range. S23, For each historical formula, calculate its constraint violation distance relative to each hard performance target, and introduce performance priority weight, missing performance penalty and test condition inconsistency penalty, and sum them up to obtain the baseline constraint violation distance. S24. Sort the historical recipes with the highest number of violations of the benchmark constraint from smallest to largest according to the benchmark constraint violation distance, and select the preset number of historical recipes as the benchmark recipes.

7. The method for generating closed-loop formulations based on coating engineering constraints and prediction reliability verification according to claim 6, characterized in that, Step S23, calculating the constraint violation distance, also includes: S231, when the performance index is an ordered level index, each level is converted into adjacent ordinal values ​​according to the preset level order, and the normalized constraint violation distance is calculated based on the ordinal difference, and each level is not treated as an independent category that is unordered from each other. S232, when a historical formula lacks measured data corresponding to any hard performance target, a missing performance penalty is set for the historical formula to lower its ranking position. S233, when the test method or test conditions of the historical formula are inconsistent with the structured performance target object, a penalty for inconsistent test conditions is added to the historical formula.

8. The method for generating closed-loop formulations based on coating engineering constraints and prediction reliability verification according to claim 1, characterized in that, The large language model is only used to generate initial candidate formulations and adjustment instructions. The engineering constraint verification is performed by preset verification rules. The large language model does not participate in the determination of the engineering constraint verification, nor does it directly modify the component ratio, predicted value, or performance determination result of the candidate formulation.

9. The closed-loop formulation generation method based on coating engineering constraints and prediction reliability verification according to claim 1, characterized in that, Step S5, which involves determining the compliance of each of the coating performance indicators, includes: S511, based on the target values ​​in the structured performance target object, for performance indicators where a larger value is better, it is determined that the target is met when the predicted value is not lower than the target value; for performance indicators where a smaller value is better, it is determined that the target is met when the predicted value is not higher than the target value; for performance indicators with target ranges, it is determined that the target is met when the predicted value is within the target range. S512, Generate a status code for each of the coating performance indicators based on the judgment result. The status code includes a compliant status, a warning status, and a non-compliant status. S513, the candidate formulations are sorted from smallest to largest according to the number of indicators in the non-compliant state. When the number of indicators in the non-compliant state is the same, they are sorted from smallest to largest according to the weighted normalized non-compliant magnitude. The weighted normalized non-compliant magnitude is obtained by multiplying the normalized difference of each non-compliant performance indicator relative to the corresponding target value by the priority weight of the performance indicator and then summing them. When the weighted normalized non-compliant magnitudes are the same, they are sorted from highest to lowest according to the prediction reliability level.

10. The method for generating closed-loop formulations based on coating engineering constraints and prediction reliability verification according to claim 1, characterized in that, Step S5, which involves returning the adjusted constraint information and the intermediate candidate solutions to step S3 to constrain the generation of the next round of initial candidate formulations, thus forming a closed loop for formulation recommendation, further includes: S521: In each round, candidate formulations that fail the engineering constraint verification are first eliminated. Then, they are sorted according to the number of non-compliant state indicators, the weighted normalized non-compliant range, and the predicted reliability level. A preset number of non-overlapping candidate formulations are selected to enter the next round of adjustment. S522, Generate candidate signatures based on the set of unique raw material identifiers, the ratio of main agent to curing agent, and the component ratio rounded to a preset precision, and remove duplicate formulas through the candidate signatures; S523, when all hard performance targets of the candidate formulation are met and the predicted reliability level is not low, the candidate formulation is output as the final recommended formulation; S524, the iteration is terminated when the maximum number of iterations is reached, the improvement of the optimal weighted normalization failure rate after a preset number of consecutive rounds is less than a preset threshold, or the candidate set no longer generates new candidate signatures; S525, formulations that still do not meet the final recommended conditions at the end are output as intermediate candidate schemes to be verified experimentally, and are not marked as final recommended formulations.

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