A data fusion model migration and parameter self-adaption method and system

Abstract

The embodiment of the specification provides a data fusion model migration and parameter self-adaption method and system, wherein the method comprises the following steps: obtaining an initial function model expression, analyzing the symbolic structure thereof, identifying all numerical constant nodes and generating a constant list; replacing the constant nodes with adjustable parameter nodes according to a mapping rule, constructing a parameterized function family expression, and outputting an executable numerical calculation interface; obtaining a training data set and an initial parameter vector, calculating a predicted value through an independent variable input interface, constructing a loss function based on the difference between the predicted value and a dependent variable, calling an optimization algorithm to iteratively update the parameters until convergence, and outputting optimal parameters; backfilling the optimal parameters to the parameterized expression or the numerical calculation interface, generating a solidified migration model, and outputting a performance evaluation report and optional visual results of a reference and a fine adjustment model.

Description

Technical Field

[0001] This document relates to the field of data fusion and model parameter identification technology, and in particular to a data fusion model migration and parameter adaptation method and system. Background Technology

[0002] In the fields of engineering modeling and data analysis, common prediction or computational models can be represented in the form of analytical functions. These models typically consist of variable terms, numerical constant terms, and conventional symbolic operations. Since the numerical constants in the model often come from empirical settings, historical fitting, or calibration results under specific scenarios, when the application scenario of the model changes (e.g., changes in data sources, measurement calibers, object states, or expansion of the operating range), the original constant values ​​may no longer be applicable, leading to a significant increase in prediction error.

[0003] In existing technologies, common adaptation methods include: manually rewriting the model and refitting, adding correction terms to the original model, replacing the analytical model with a black-box machine learning model, or manually adjusting a small number of parameters. However, the above methods generally suffer from the following problems: 1) Manual rewriting and parameter tuning are highly dependent on domain experience, which is inefficient and difficult to standardize; 2) While black-box substitution methods can fit the data, they may compromise the interpretability and traceability of the original model structure, making them difficult to audit; 3) The lack of a general process that can automatically complete "constant identification - parameter replacement - data fitting - parameter backfilling and solidification" makes the migration and reuse of analytical models in multi-source data fusion scenarios costly.

[0004] Therefore, there is an urgent need for a data fusion model fine-tuning method that can be automatically implemented, is interpretable, and is easy to solidify and deploy, in order to solve the problem of the difficulty of adapting existing analytical models across scenarios. Summary of the Invention

[0005] This specification provides one or more embodiments of a data fusion model migration and parameter adaptation method, including: S1. Obtain the initial function model expression, parse the symbolic structure of the expression, traverse and identify all numerical constant nodes in the expression, and generate a constant list; S2. Based on the established mapping rules between constants and parameters, replace the numerical constant nodes with adjustable parameter nodes, generate parameterized function family expressions, and output an executable numerical calculation function interface; S3. Obtain the training dataset and initial parameter vector, use the independent variables in the training dataset as input, calculate the predicted value through the executable numerical calculation function interface, construct the loss function based on the difference between the predicted value and the dependent variable in the training dataset, call the optimization algorithm to iteratively update the adjustable parameters until the convergence condition is met, and output the optimal parameters. S4. Fill the parameter values ​​from the optimal parameters back into the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface to generate the solidified migration model, and output the performance evaluation report of the baseline model and the fine-tuned model, as well as optional visualization results.

[0006] Furthermore, the specific steps of obtaining the initial function model expression and parsing the symbolic structure of the expression are as follows: Syntax parsing of an expression yields an abstract syntax tree or symbol tree; The obtained abstract syntax tree or symbol tree is standardized, including: removing spaces, unifying the exponentiation operator, normalizing the unary negative sign, and converting all numerical constants into double-precision floating-point numbers.

[0007] Furthermore, when traversing and identifying all numerical constant nodes in the expression, it is determined whether the node type is an integer constant or a floating-point constant, and variable name nodes and symbolic constant nodes are excluded. The value of each constant, its position path in the expression tree, and the number of times it appears are recorded.

[0008] Furthermore, the mapping rule between the constants and parameters is as follows: a strategy of replacing them one by one according to the number of occurrences, a new adjustable parameter is assigned each time a constant node appears, and the same value constant at different positions corresponds to different parameters.

[0009] Furthermore, the mapping rule between the constants and parameters is as follows: a strategy of deduplicating and sharing parameters based on constant values, assigning the same adjustable parameter to constant nodes with the same value, and different parameters to constants with different values.

[0010] Furthermore, when obtaining the initial parameter vector, the original values ​​of each constant in the constant list are used as the initial values ​​of the corresponding adjustable parameters, and arranged in parameter order to form the initial parameter vector.

[0011] Furthermore, the loss function is constructed based on the difference between the predicted value and the dependent variable in the training dataset as follows: Data preprocessing is performed on the training dataset, including removing missing or outlier samples, mapping the dimensions of independent variables from different sources to a unified structure, and performing normalization or standardization transformations on the independent and dependent variables. Using the sum of squared residuals as the basic loss term, when the training dataset contains multiple data sources, weights are assigned to each sample, and the weighted sum of squared residuals is used as the loss function.

[0012] Furthermore, the optimization algorithm is invoked to iteratively update the adjustable parameters until the convergence condition is met, and the optimal parameters are output, specifically including: Select the optimizer type, update the initial parameter values ​​according to the optimizer rules, set the upper and lower bounds of the parameters, perform pruning or projection operations on parameter values ​​that exceed the boundaries after each iteration update, and determine whether convergence is achieved based on the amount of loss reduction or parameter update. If the loss decreases less than the threshold, the parameter update amount is less than the threshold, or the iteration limit is reached, then the convergence condition is met, and the optimal parameters are obtained.

[0013] Further, the parameter values ​​from the optimal parameters are backfilled into the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface to generate the solidified transfer model, specifically including: The text of the parameterless symbolic expression obtained by backfilling the optimal parameters into the symbolic expression, and the executable function generated by embedding the optimal parameters into the executable numerical function interface without passing in parameters; The optimal parameters are stored in the model configuration file to obtain the solidified migration model.

[0014] This specification provides one or more embodiments of a data fusion model migration and parameter adaptation method, including: Model parsing module: used to obtain the initial function model expression, parse the symbolic structure of the expression, traverse and identify all numerical constant nodes in the expression, and generate a constant list; Parameter mapping module: It is used to replace the numerical constant nodes with adjustable parameter nodes according to the established mapping rules between constants and parameters, generate parameterized function family expressions, and output an executable numerical calculation function interface. Model update module: used to obtain training dataset and initial parameter vector, use the independent variables in the training dataset as input, calculate the predicted value through the executable numerical calculation function interface, construct the loss function based on the difference between the predicted value and the dependent variable in the training dataset, call the optimization algorithm to iteratively update the adjustable parameters until the convergence condition is met, and output the optimal parameters; Model transfer module: used to backfill the parameter values ​​in the optimal parameters into the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface, generate the solidified transfer model, and output the performance evaluation report of the baseline model and the fine-tuned model and optional visualization results.

[0015] By employing the embodiments of this invention, the present invention can automatically identify expression constants and transform them into a family of adjustable parameters without altering the original model structure, enabling rapid transfer and adaptation of analytical models across scenarios. Fine-tuning only applies to the constant terms of the original model, with clear correspondences, allowing for the traceability of the source and role of each parameter in the expression, facilitating auditing and reproducibility. Data-driven optimization is performed using training / validation datasets, and the optimal parameters are backfilled to generate a persistent transferable model, while simultaneously outputting performance reports and optional visualization results. This significantly reduces the cost of manual rewriting and parameter tuning, improves model reuse efficiency and engineering feasibility, and has significant application value.

[0016] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a data fusion model migration and parameter adaptation method provided for one or more embodiments of this specification; Figure 2 A schematic diagram illustrating the composition of a data fusion model migration and parameter adaptation system provided for one or more embodiments of this specification; Detailed Implementation To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0019] Method Implementation Examples According to embodiments of the present invention, a data fusion model migration and parameter adaptation method is provided. Figure 1A flowchart illustrating a data fusion model migration and parameter adaptation method provided in one or more embodiments of this specification is shown below. Figure 1 As shown, the data fusion model migration and parameter adaptation method according to an embodiment of the present invention specifically includes: S1. Obtain the initial function model expression, parse the symbolic structure of the expression, traverse and identify all numerical constant nodes in the expression, and generate a constant list.

[0020] First, the initial function model expression E(x) input by the user is obtained. This expression must contain at least the set of independent variables x=(x1,x2,...,xn) (which can be scalars or vectors), several numerical constants (such as floating-point / integer constants like 0.5, 0.1, etc.), and regular symbolic operations and function calls, including addition, subtraction, multiplication, division, exponentiation, and nested functions (such as sin, cos, exp, etc.). In engineering implementation, the carrier of the E(x) expression can be a mathematical formula string, an abstract syntax tree (AST) object, or a symbolic expression object, which is uniformly converted into an internally processable structured form.

[0021] The input expression is parsed to generate an abstract syntax tree or symbol tree. Then, the resulting tree structure is standardized, including removing all whitespace characters, unifying exponentiation operators, normalizing unary negative signs, and representing all numerical constants with a unified type, such as converting them to double-precision floating-point numbers. This results in the output of a structured expression object T(E) that can be traversed and whose constant positions can be located.

[0022] Next, for the input structured expression object T(E), traverse all nodes of the standardized expression tree and determine whether each node is a numeric constant node. The criteria for determining a numeric constant node are: the node type belongs to integer constant or floating-point constant, and the node is neither a variable name node nor a symbolic constant node. For each identified numeric constant node, record the following information: the constant value c. i The path p of the constant in the expression tree i The output should include the constant's occurrence count and the number of times it appears. Finally, output a list of constants C = [c0, c1, ..., c...]. k-1 (Preserve original values), list of constant positions (P = [p0, p1,..., p...) k-1 This contains the aforementioned information for all identified numerical constants.

[0023] S2. Based on the established mapping rules between constants and parameters, replace the numerical constant nodes with adjustable parameter nodes, generate parameterized function family expressions, and output an executable numerical calculation function interface.

[0024] After obtaining the list of constants, for the input list of constants C and the list of positions P, an adjustable parameter (β) is assigned to each constant. j This invention establishes a mapping relationship between constants and parameters, supporting two equivalent mapping strategies, which users can choose according to their actual needs: The first strategy is to replace each occurrence sequentially: a new adjustable parameter is assigned each time a constant node appears, as shown below: ; Even if constants in different locations have the same value, they correspond to different parameters; The second strategy is to deduplicat and share parameters based on constant values: for constant nodes with the same value, the same adjustable parameter is assigned, as shown below: ; Different values ​​of constants correspond to different parameters.

[0025] Regardless of the strategy employed, a mapping dictionary will be established, recording the parameter symbol corresponding to each constant node. This mapping can be performed numerically or positionally, and an adjustable parameter list β = [β0, β1, ..., β...]. m-1 Simultaneously, the original values ​​of each constant in the constant list are used as the initial values ​​β of the corresponding adjustable parameters. (0) Arrange the parameters in order to form the initial parameter vector, i.e., β. j (0) = c, thus obtaining the parameter mapping dictionary M, such as {(p0)->β0, (p1)->β1} or {0.5->β0,0.1->β1}, and the parameter initial value vector β. (0) .

[0026] After mapping is complete, the expression tree is traversed. For each constant node in the expression tree, based on the structured expression object T(E) and the mapping dictionary (M), a substitution is performed according to the mapping (M): E(x) → F(x, β), replacing each numerical constant node with the corresponding adjustable parameter node. During the substitution process, the original expression's operational structure and function call relationships remain unchanged; only the constants are changed into parameter placeholders. This yields the parameterized symbolic expression, i.e., the function family model F(x, β), where x is the independent variable and β is the adjustable parameter vector.

[0027] To enable the parameterized model to be invoked by the numerical computation engine, an executable numerical computation function interface is further generated. This interface takes the parameterized symbolic expression F(x,β) and the parameter order β as input, and outputs a directly runnable numerical function (e.g., Python / NumPy), with explicit I / O constraints. The function receives two arrays: an array of independent variables x (shape equal to the number of samples × the dimension of the independent variables) and an array of parameters β (length equal to the number of parameters). It calculates the predicted value for each sample based on F(x,β). This returns the result, resulting in the executable function y = f(x, β). When generating the function, explicitly specify the dimension indices of the independent variables and the order of the parameters to ensure data alignment during call.

[0028] S3. Obtain the training dataset and initial parameter vector. Using the independent variables in the training dataset as input, calculate the predicted values ​​through the executable numerical calculation function interface. Construct a loss function based on the difference between the predicted values ​​and the dependent variables in the training dataset. Call the optimization algorithm to iteratively update the adjustable parameters until the convergence condition is met, and output the optimal parameters.

[0029] After obtaining the parametric model and its numerical computation interface, the model fine-tuning phase begins. First, the training / fitting data dataset is acquired. This dataset can contain single-source or multi-source data, divided into a training set and a... Optional verification / test suite At the same time, obtain the initial parameter vector β (0) Before constructing the loss function, the training dataset undergoes data preprocessing. Preprocessing includes: removing missing or outlier samples to avoid invalid data interfering with optimization; mapping the dimensions of independent variables from different sources to a unified structure; optionally performing normalization or standardization transformations on independent and dependent variables to eliminate the influence of dimensions and prevent ill-conditioned gradients during optimization; and assigning weights to data from different sources. This achieves data fusion and weighting. After preprocessing, a cleaned training set is obtained. .

[0030] The loss function measures the difference between the model's predicted values ​​and the actual values. In this embodiment, the sum of squared residuals (SSR) is used as the basic loss term. Specifically, based on the input model F(·) and the sample... , parameter β, for each sample The independent variable is input into the numerical calculation function interface, and the predicted value is obtained using the current parameter value. Calculate the difference between the predicted value and the actual dependent variable. The residual vector is obtained. Then, the squared residuals of all samples are summed. When the training dataset contains multiple data sources, weights are assigned to each sample, and the weighted sum of squared residuals is used as the loss function.

[0031] Input residual vector Weight Regularization configuration, which by default uses the sum of squared residuals (SSR) as the loss function: ; Optional regularization terms can be added. The loss function after adding regularization terms is as follows: ; in This can be an L2, L1, or physical constraint penalty term, resulting in a computable loss function. .

[0032] After constructing the loss function, the optimization algorithm is called to iteratively update the adjustable parameters. Input loss function. initial value The system allows users to configure optimizer types, such as local optimization algorithms or a combination of global and local optimization. During iteration, the parameter vector is adjusted according to the selected optimizer's update rules, and parameter boundary pruning or projection operations are performed. Specifically, if the user sets upper and lower bounds for the parameters, if the parameter value exceeds the boundary after each update, it is pruned to the boundary or projected back into the feasible region. Convergence conditions are monitored: convergence is determined when the decrease in the loss function is less than a preset threshold, the parameter update amount is less than a preset threshold, or the number of iterations reaches a preset upper limit. The iteration then stops, and the current optimal parameter vector is output. If convergence is not achieved, the iteration continues.

[0033] S4. Fill the parameter values ​​from the optimal parameters back into the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface to generate the solidified migration model, and output the performance evaluation report of the baseline model and the fine-tuned model, as well as optional visualization results.

[0034] After obtaining the optimal parameter vector, it is used through parameterized expressions. Optimal parameters ,Will Backfill into the previously generated parameterized model. Backfilling methods include: generating parameterless symbolic expression text: substituting the optimal parameter values ​​into the parameterized symbolic expression, replacing all parameter nodes with specific numerical values, resulting in a final symbolic expression without any parameters; generating an executable function that requires no input parameters: embedding the optimal parameter values ​​into the numerical computation function interface, fixing the parameter values, and generating a function that only requires input variables to output predicted values; and backfilling the optimal parameter vector... Save as a model configuration file and output the solidified migration model. .

[0035] To verify the transfer effect, performance evaluation reports for the baseline model and the fine-tuned model are also output. The baseline model refers to the model using the original constants (initial parameters), and the fine-tuned model refers to the transfer model using the optimal parameters. Evaluation metrics include at least the coefficient of determination R² and root mean square error (RMSE), and can be expanded to include relative root mean square error RRMSE, percentage of prediction error (PRE), etc. The system calculates various metrics for the two models on the training set and an optional validation set, generating a comparison report. In addition, optional visualization results can be output, such as scatter plots comparing predicted and observed values, histograms of residual distribution, and loss reduction curves during the optimization process, to help users intuitively understand the model improvement effect.

[0036] The specific implementation method is as follows: Example 1: Function Familyization and Fine-tuning Based on Constant Parameterization Step S1: Obtain the initial model expression Let the initial function model expression be: ; Where (x1, x2) are input variables, and 0.5 and 0.1 are numerical constants in the expression.

[0037] Step S2: Constant Identification and Constant List Generation Parse the expression structure, traverse the nodes and identify numerical constants to obtain a list of constants: C = [0.5, 0.1].

[0038] Step S3: Construct the mapping relationship between constants and parameters Assign adjustable parameters to each constant in the constant list to form a mapping relationship: 0.5→β0, 0.1→β1; Simultaneously, an adjustable parameter vector is formed: β=[β0, β1]; Step S4: Replace constants to generate a parameterized model (function familyization) By replacing the numerical constants in the original expression with adjustable parameters, we obtain the parameterized model: ; And generate an executable numerical function interface (y=f(x,β)).

[0039] Step S5: Prepare fine-tuning input and set initial parameters Obtain the training / fitting dataset: ; And using the original model constants as initial parameters: ; Step S6: Construct the loss function and perform optimization. The default objective function is the sum of squared residuals. ; With optional parameter boundaries and iteration limits, an optimization algorithm is used to iteratively update β to obtain the optimal parameters: β * =(0.48,0.12) Step S7: Backfill and solidify parameters and output migration model β * Backfilling into the parameterized expressions and / or numerical function interfaces yields the final, persistent model:

[0040] Step S8: Performance Evaluation Output Calculate the baseline parameter β respectively (0) With the optimal parameter β * It outputs a baseline and fine-tuning comparison report based on performance metrics (R², RMSE, etc.); and optionally outputs a prediction-observation comparison chart, residual distribution chart, and optimization process information.

[0041] Example 2: Weighted fine-tuning of multi-source data fusion (optional enhancement implementation) Based on Example 1, when the training data consists of multiple sources, a weight (w_i) is assigned to each source sample, and a weighted sum of squared residuals is used: ; By using weights to reflect the credibility or noise level of data from different sources, robust fine-tuning can be achieved under multi-source data fusion.

[0042] The beneficial effects of this invention are as follows: This invention can automatically identify expression constants and convert them into a family of adjustable parameters without changing the original model structure, enabling rapid transfer and adaptation of analytical models across scenarios. Fine-tuning only applies to the constant terms of the original model, with clear correspondences, allowing traceability of the source and role of each parameter in the expression, facilitating auditing and reproducibility. Data-driven optimization is performed using training / validation datasets, and the optimal parameters are backfilled to generate a persistent transferable model, while simultaneously outputting performance reports and optional visualizations. This significantly reduces the cost of manual rewriting and parameter tuning, improves model reuse efficiency and engineering feasibility, and has significant application value.

[0043] System Implementation Examples According to embodiments of the present invention, a data fusion model transfer and parameter adaptation system is provided. Figure 2A schematic diagram illustrating the composition of a data fusion model migration and parameter adaptation system provided in one or more embodiments of this specification, as shown below. Figure 2 As shown, the data fusion model migration and parameter adaptation system according to an embodiment of the present invention specifically includes: Model parsing module 20: used to obtain the initial function model expression, parse the symbol structure of the expression, traverse and identify all numerical constant nodes in the expression, and generate a constant list; Parameter mapping module 22: Used to replace the numerical constant node with the adjustable parameter node according to the established mapping rules between constants and parameters, generate parameterized function family expressions, and output an executable numerical calculation function interface; Model update module 24: used to obtain the training dataset and initial parameter vector, use the independent variables in the training dataset as input, calculate the predicted value through the executable numerical calculation function interface, construct the loss function based on the difference between the predicted value and the dependent variable in the training dataset, call the optimization algorithm to iteratively update the adjustable parameters until the convergence condition is met, and output the optimal parameters. Model transfer module 26: used to backfill the parameter values ​​in the optimal parameters to the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface, generate the solidified transfer model, and output the performance evaluation report of the baseline model and the fine-tuned model and optional visualization results.

[0044] The embodiments of the present invention are system embodiments corresponding to the above method embodiments. The specific operation of each module can be understood by referring to the description of the method embodiments, and will not be repeated here.

[0045] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data fusion model transfer and parameter adaptation method, characterized in that, include: S1. Obtain the initial function model expression, parse the symbolic structure of the expression, traverse and identify all numerical constant nodes in the expression, and generate a constant list; S2. Based on the established mapping rules between constants and parameters, replace the numerical constant nodes with adjustable parameter nodes, generate parameterized function family expressions, and output an executable numerical calculation function interface; S3. Obtain the training dataset and initial parameter vector, use the independent variables in the training dataset as input, calculate the predicted value through the executable numerical calculation function interface, construct the loss function based on the difference between the predicted value and the dependent variable in the training dataset, call the optimization algorithm to iteratively update the adjustable parameters until the convergence condition is met, and output the optimal parameters. S4. Fill the parameter values ​​from the optimal parameters back into the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface to generate the solidified migration model, and output the performance evaluation report of the baseline model and the fine-tuned model, as well as optional visualization results.

2. The method according to claim 1, characterized in that, The specific steps of obtaining the initial function model expression and parsing the symbolic structure of the expression are as follows: Syntax parsing of an expression yields an abstract syntax tree or symbol tree; The obtained abstract syntax tree or symbol tree is standardized, including: removing spaces, unifying the exponentiation operator, normalizing the unary negative sign, and converting all numerical constants to double-precision floating-point number type.

3. The method according to claim 1, characterized in that, When traversing and identifying all numerical constant nodes in the expression, it is determined whether the node type is an integer constant or a floating-point constant, and variable name nodes and symbolic constant nodes are excluded. The value of each constant, its position path in the expression tree, and the number of times it appears are recorded.

4. The method according to claim 1, characterized in that, The mapping rule between constants and parameters is as follows: a strategy of replacing them one by one according to the number of times they appear. Each time a constant node appears, a new adjustable parameter is assigned. The same value constant at different positions corresponds to different parameters.

5. The method according to claim 1, characterized in that, The mapping rule between constants and parameters is as follows: a strategy of deduplicating and sharing parameters based on constant values ​​is adopted, and the same adjustable parameter is assigned to constant nodes with the same value, while constants with different values ​​correspond to different parameters.

6. The method according to claim 1, characterized in that, When obtaining the initial parameter vector, the original values ​​of each constant in the constant list are used as the initial values ​​of the corresponding adjustable parameters, and arranged in parameter order to form the initial parameter vector.

7. The method according to claim 1, characterized in that, The loss function is constructed based on the difference between the predicted value and the dependent variable in the training dataset as follows: Data preprocessing is performed on the training dataset, including removing missing or outlier samples, mapping the dimensions of independent variables from different sources to a unified structure, and performing normalization or standardization transformations on the independent and dependent variables. Using the sum of squared residuals as the basic loss term, when the training dataset contains multiple data sources, weights are assigned to each sample, and the weighted sum of squared residuals is used as the loss function.

8. The method according to claim 1, characterized in that, The optimization algorithm iteratively updates the adjustable parameters until the convergence condition is met, and the optimal parameters are output, including: Select the optimizer type, update the initial parameter values ​​according to the optimizer rules, set the upper and lower bounds of the parameters, perform pruning or projection operations on parameter values ​​that exceed the boundaries after each iteration update, and determine whether convergence is achieved based on the amount of loss reduction or parameter update. If the loss decreases less than the threshold, the parameter update amount is less than the threshold, or the iteration limit is reached, then the convergence condition is met, and the optimal parameters are obtained.

9. The method according to claim 1, characterized in that, The process of backfilling the parameter values ​​from the optimal parameters into the adjustable parameter nodes of the parameterized function family expression and / or the numerical calculation function interface to generate the solidified transfer model specifically includes: The text of the parameterless symbolic expression obtained by backfilling the optimal parameters into the symbolic expression, and the executable function generated by embedding the optimal parameters into the executable numerical function interface without passing in parameters; The optimal parameters are stored in the model configuration file to obtain the solidified migration model.

10. A data fusion model transfer and parameter adaptation system, characterized in that, include: Model parsing module: used to obtain the initial function model expression, parse the symbolic structure of the expression, traverse and identify all numerical constant nodes in the expression, and generate a constant list; Parameter mapping module: Used to replace the numerical constant nodes with adjustable parameter nodes according to the established mapping rules between constants and parameters, generate parameterized function family expressions, and output an executable numerical calculation function interface; Model update module: used to obtain training dataset and initial parameter vector, use the independent variables in the training dataset as input, calculate the predicted value through the executable numerical calculation function interface, construct the loss function based on the difference between the predicted value and the dependent variable in the training dataset, call the optimization algorithm to iteratively update the adjustable parameters until the convergence condition is met, and output the optimal parameters; Model transfer module: used to backfill the parameter values ​​in the optimal parameters into the adjustable parameter nodes in the parameterized function family expression and / or the numerical calculation function interface, generate the solidified transfer model, and output the performance evaluation report of the baseline model and the fine-tuned model and optional visualization results.

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