Physical constraint and digital twinning fused nonlinear system reduced-order model generation method

Abstract

The invention relates to a nonlinear system reduced-order model generation method fusing physical constraint and digital twinning, and belongs to the technical field of digital twinning. The method comprises the steps of performing sparse sampling on high-dimensional dynamic response data, extracting a dominant mode of high-fidelity model data, and retaining a mode of a physical abrupt change region through physical field gradient constraint in the extraction process; the high-fidelity finite element model and the low-fidelity simplified model are combined, and a mixed order reduction framework based on a multi-fidelity agent model is constructed; fusing a data driving error and a physical mechanism residual error in data-physical joint driving model training and optimization based on a mixed order reduction framework, and updating a primary function of a dominant mode based on online stream data; and performing cross validation on the output of the high-fidelity finite element model and the reduced-order model, and improving the precision of the reduced-order model through an iterative optimization strategy. The intelligent order reduction problem of the model is realized, and the accuracy and rapidity of the order reduction model are ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital twins, and particularly relates to a method for generating a reduced-order model of a nonlinear system that integrates physical constraints and digital twins. Background Art

[0002] Currently, in the fields of large structures such as automobiles and engineering equipment, structural durability simulation based on finite element models faces many challenges. On the one hand, the model structures of these large structures are complex, containing a large number of components and their interaction relationships, which makes it extremely difficult and time-consuming to establish an accurate finite element model. On the other hand, the nonlinear characteristics of the structure, such as material nonlinearity, geometric nonlinearity, and contact nonlinearity, further increase the difficulty and complexity of the simulation.

[0003] For example, when simulating the durability of a suspension system during vehicle driving, it is necessary to consider the hyperelastic deformation of rubber bushings, the large displacements of metal components, and the complex contact relationships between components. These nonlinear factors are coupled with each other, resulting in a significant increase in the difficulty of solving the finite element equations.

[0004] Moreover, durability simulation usually requires a large number of cyclic load analyses, and the calculation process is cumbersome. The time-consuming for a single simulation is several hours or even several days, which seriously restricts the speed of design iteration. At the same time, high-degree-of-freedom finite element models have extremely high demands on computing power and storage resources. For the structural durability simulation of a typical large construction machinery, the degrees of freedom of its finite element model can reach hundreds of thousands to millions, requiring the support of a high-performance computer cluster and occupying a large amount of storage space to save intermediate results and calculation data.

[0005] In this case, traditional durability simulation methods are no longer able to meet the requirements of rapid product iteration and optimization in modern industry. Therefore, there is an urgent need for an efficient method for generating a reduced-order model of a nonlinear system that integrates physical constraints and digital twins to solve the problems of low computational efficiency and high resource consumption faced by existing structural durability simulation based on finite element models, so as to provide more powerful technical support for the structural durability design and optimization of large mechanical equipment.

[0006] Currently, the dynamic response prediction of large mechanical equipment (such as cranes, gas turbines, and aero engines) faces the dual challenges of high-dimensional nonlinear systems: 1. Computational efficiency bottleneck: The degrees of freedom of finite element (FEM) or CFD full-order models are as high as millions, and the time-consuming for a single simulation is several hours to several days, making it difficult to meet the millisecond-level real-time requirements of digital twins; 2. Physics-data contradiction: Pure physical models (such as Galerkin projection) rely on strict mathematical derivations. Although they can retain conservation laws, the computational complexity of strong nonlinear terms is still as high as; Pure data-driven models (such as POD + Gaussian processes) can achieve fast prediction, but they are divorced from the constraints of physical laws and are prone to non-physical solutions (such as negative pressure and vorticity distortion) in extrapolation scenarios; 3. Poor adaptability to dynamic conditions: In scenarios such as equipment damage and sudden load changes, traditional reduced-order models (ROMs) cannot be updated in real time due to offline training and fixed modal bases, resulting in the accumulation of prediction errors. Summary of the Invention

[0007] To solve the above problems existing in the prior art, the present invention provides a method for generating a reduced-order model of a nonlinear system that integrates physical constraints and digital twins; The object of the present invention can be achieved by the following technical solutions: S1: Collect high-dimensional dynamic response data through the sensor network of the digital twin system, perform sparse sampling on the high-dimensional dynamic response data to obtain high-fidelity model data, extract the dominant modes of the high-fidelity model data, and retain the modes in the physically abrupt regions through physical field gradient constraints during the extraction process; S2: Combine a high-fidelity finite element model and a low-fidelity simplified model to construct a hybrid reduced-order framework based on a multi-fidelity surrogate model, perform dense sampling in the physically abrupt regions, and perform numerical space preprocessing on the nonlinear terms; S3: Based on the hybrid reduced-order framework, fuse data-driven errors and physical mechanism residuals in the data-physics joint-driven model training and optimization, and update the basis functions of the dominant modes based on online flow data; S4: Cross-validate the outputs of the high-fidelity finite element model and the reduced-order model, including global error assessment and focused analysis of local physically abrupt regions, construct an adaptive error threshold feedback mechanism based on the error quantification results, and improve the accuracy of the reduced-order model through an iterative optimization strategy.

[0008] Specifically, the sparse sampling method is as follows: Construct a physical field gradient magnitude matrix, identify high-gradient regions, perform dense sampling on the high-gradient regions using a Gaussian random measurement matrix, and perform sparse sampling on the low-gradient regions using a Bernoulli random matrix; Set the sampling frequencies for the transient stage, transition stage, and steady state stage in the time dimension.

[0009] Specifically, the dominant modes of the high-fidelity model data are a set of low-dimensional basis functions that characterize the key dynamic characteristics of the system.

[0010] Specifically, the method for extracting the dominant mode includes: physical constraint modal decomposition, mutation region modal retention, multi-scale modal selection, and dynamic modal update. Among them, the physical constraint modal decomposition constructs a weighted inner product space by combining the proper orthogonal decomposition with a physical field gradient weighting function to ensure that the extracted modes satisfy both the data statistical characteristics and the physical field gradient constraints. The dynamic modal update detects the proportion of new modal energy in the online flow data and triggers an incremental update of the basis functions according to the proportion of the new modal energy.

[0011] Specifically, the high-fidelity finite element model is a physically accurate model constructed based on the full-order finite element discretization method, and the low-fidelity simplified model is a lightweight proxy model generated by projection reduction and data-physics joint driving.

[0012] Specifically, the hybrid reduction framework includes a multi-fidelity data fusion module, a physical constraint embedding module, a non-linear term preprocessing module, a dynamic resource allocation module, and a stride error feedback link. The multi-fidelity data fusion module adjusts the hybrid weight in real time according to the distribution difference between the high-fidelity finite element model and the low-fidelity simplified model, and constructs a smooth transition field by interpolation in the junction region. The physical constraint embedding module introduces a gradient sensitivity weight matrix into the traditional projection to reconstruct the projection equation, and adds a residual term to the training loss function of the low-fidelity simplified model. The non-linear term preprocessing module performs digital space preprocessing on the non-linear term using discrete empirical interpolation and convolutional autoencoders. The dynamic resource allocation module adjusts the proportion of computing resources of the high-fidelity finite element model and the low-fidelity simplified model in real time based on the error feedback mechanism, and triggers local recomputation of the high-fidelity finite element model in the mutation region.

[0013] Specifically, the method for digital space preprocessing is as follows: Decompose the non-linear term into a steady-state component and a transient pulsating component: , where F(u) is the non-linear term, then the transient pulsating component is expressed as ΔF(u), Fmean is the steady-state component, is the correlation coefficient of the spatial basis function and the time basis function, and m is the total number of basis functions in the transient pulsating part. Perform sparse sampling on the transient pulsating component to obtain the key feature points of the transient pulsating component, and encode and decode the key feature points through a convolutional autoencoder to achieve an efficient representation of the non-linear term in the low-dimensional space.

[0014] Specifically, the data-driven error is the statistical deviation between the low-fidelity simplified model and the high-fidelity finite element model in dynamic response prediction.

[0015] Specifically, the physical mechanism residual is the degree of deviation of the low-fidelity simplified model from the constraints of mass, momentum, energy, and physical field gradients.

[0016] Specifically, the method of the iterative optimization strategy includes: When the global error exceeds the preset threshold, locate the error source through residual dominant mode analysis, and update the dominant mode basis function based on the online flow data in S3 to supplement the missing high-order modes; When the gradient mutation in the local physical mutation region exceeds the preset threshold, strengthen the physical constraint in the hybrid reduced-order framework of S2, and increase the sampling density of the corresponding local physical mutation region through gradient sensitivity analysis.

[0017] The beneficial effects of the present invention are as follows: Through the method provided by the present invention, the computational efficiency and accuracy of the dynamic response prediction of large mechanical equipment can be significantly improved. Specifically, this method combines the advantages of physical constraints and digital twins, effectively solving the problems of high computational complexity of pure physical models and lack of physical law constraints in pure data-driven models. Through sparse sampling and dominant mode extraction, the present invention can efficiently obtain the key features of high-fidelity model data while retaining the modal information of physical mutation regions. Combining the hybrid reduced-order framework constructed by high-fidelity finite element models and low-fidelity simplified models further improves the adaptability of the model under complex dynamic conditions.

[0018] In the process of data-physics joint-driven model training and optimization, the data-driven error and physical mechanism residual are combined to achieve a comprehensive evaluation and accurate positioning of the model error. By updating the basis function of the dominant mode with online flow data and the iterative optimization strategy based on the error quantification results, the reduced-order model can continuously improve itself and gradually improve the prediction accuracy.

[0019] In addition, it also has good versatility and scalability, and is applicable to the dynamic response prediction problems of various large mechanical equipment. By flexibly adjusting the sampling strategy, dominant mode extraction method, and the specific implementation method of the hybrid reduced-order framework, the present invention can meet the specific requirements under different application scenarios, providing strong technical support for the development of digital twin technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] For the convenience of those skilled in the art to understand, the present invention will be further described below with reference to the accompanying drawings.

[0021] Figure 1 FIG. is a schematic flowchart of a method for generating a reduced-order model of a nonlinear system that combines physical constraints and digital twins according to the present invention; Figure 2 FIG. is a state time-series diagram of a method for generating a reduced-order model of a nonlinear system that combines physical constraints and digital twins according to the present invention. Detailed implementation manners

[0022] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following will, in conjunction with the accompanying drawings and preferred embodiments, elaborate in detail on the specific implementation manners, structures, features and their effects of the present invention as follows.

[0023] Please refer to Figure 1-2 , a method for generating a reduced-order model of a non-linear system that integrates physical constraints and digital twins, comprising: S1: Collect high-dimensional dynamic response data through the sensor network of the digital twin system, obtain high-fidelity model data after sparse sampling of the high-dimensional dynamic response data, extract the dominant modes of the high-fidelity model data, and retain the modes in the physically abrupt regions through physical field gradient constraints during the extraction process; S2: Combine the high-fidelity finite element model and the low-fidelity simplified model to construct a hybrid reduced-order framework based on a multi-fidelity surrogate model, perform dense sampling in the physically abrupt regions, and perform numerical space preprocessing on the non-linear terms; S3: Integrate the data-driven error and the physical mechanism residual in the data-physics joint-driven model training and optimization based on the hybrid reduced-order framework, and update the basis functions of the dominant modes based on the online flow data; S4: Cross-validate the outputs of the high-fidelity finite element model and the reduced-order model, including global error assessment and focused analysis of the local physically abrupt regions, construct an adaptive error threshold feedback mechanism based on the error quantification results, and improve the accuracy of the reduced-order model through an iterative optimization strategy.

[0024] Specifically, the sparse sampling method is as follows: Construct a physical field gradient amplitude matrix, identify the high-gradient regions, perform dense sampling on the high-gradient regions using a Gaussian random measurement matrix, and perform sparse sampling on the low-gradient regions using a Bernoulli random matrix; set the sampling frequencies in three stages of the transient stage, transition stage, and steady state stage in the time dimension.

[0025] In this embodiment, an adaptive sampling strategy driven by the physical field gradient is constructed, and the sampling density is set to full sampling (sampling density 100%), exponential distribution sampling (density 50%-80%), and Latin hypercube sampling (density ≤ 30%) according to the gradient change rate. In the time dimension, the sampling frequencies in three stages are set within the characteristic time constant, and in the space dimension, the sampling points are dynamically allocated based on the KL divergence.

[0026] Specifically, the dominant modes of the high-fidelity model data are a set of low-dimensional basis functions that characterize the key dynamic characteristics of the system.

[0027] In this embodiment, the dominant mode of the high-fidelity model data refers to a set of low-dimensional basis functions that are extracted from sparse-sampled high-dimensional dynamic data through a mode decomposition method constrained by physical field gradients and can characterize the key dynamic characteristics of the system. Its core features include: Physical mechanism dominance: The mode needs to satisfy the conservation laws (mass and momentum conservation) and the gradient constraint conditions in the mutation regions (shock waves, vortex cores) to avoid physical distortion caused by pure data-driven methods. Multi-scale separation ability: Separate steady-state modes (low frequency), transient modes (high frequency), and intermittent modes through time-frequency decoupling technology to ensure that the mode basis functions can cover the full-frequency domain dynamic behavior. Compactness and completeness: On the premise of ensuring computational efficiency, the dominant mode needs to cover at least 95% of the system energy (POD energy truncation criterion), and the energy contribution rate of the residual mode does not exceed the preset threshold.

[0028] Specifically, the extraction method of the dominant mode includes: physical constraint mode decomposition, mutation region mode retention, multi-scale mode selection, and dynamic mode update; among them, the physical constraint mode decomposition uses proper orthogonal decomposition combined with a physical field gradient weighting function to construct a weighted inner product space to ensure that the extracted mode satisfies both the data statistical characteristics and the physical field gradient constraints; the dynamic mode update detects the proportion of new mode energy in the online flow data and triggers incremental basis function update according to the proportion of new mode energy.

[0029] In this embodiment, the weighted inner product space can be expressed as: , where represents the inner product of vectors u and v in the weighted inner product space, N represents the dimensions of vectors u and v, that is, the number of elements in the vector; represents the physical field value at the i-th position; represents the physical field gradient at the i-th position; tanh is the hyperbolic tangent function, which is used to map the modulus of the gradient to a specific range, and ui and vi respectively represent the components of vectors u and v at the i-th position.

[0030] The gradient weighting mechanism can increase the modal energy in the physical mutation region where the gradient value exceeds the threshold by 2-3 orders of magnitude by introducing the hyperbolic tangent weight function; Multi-scale coupling: Combine global energy truncation and local residual compensation to reduce the local error to less than 5% while retaining 95% of the energy; Dynamic update guarantee: The incremental POD algorithm reduces the computational complexity of mode update from O(N³) to O(kN²) (k is the number of new modes); Physical consistency: The construction of the weighted inner product space ensures that the extracted modes simultaneously satisfy the data statistical characteristics and the physical field gradient constraints.

[0031] Specifically, the high-fidelity finite element model is a physically accurate model constructed based on the full-order finite element discretization method, and the low-fidelity simplified model is a lightweight surrogate model generated by projection reduction and data-physics joint driving.

[0032] In this embodiment, the high-fidelity finite element model: uses anisotropic mesh encryption in physically discontinuous regions (vortex cores, crack propagation paths), verifies mesh convergence through the gradient recovery technique (ZZ Error Estimator), and for strongly nonlinear problems (such as large deformations of hyperelastic materials), uses Newton-Raphson iteration + line search and introduces a quasi-static time step adaptive algorithm to avoid divergence; embeds a flux correction term (Flux-Corrected Transport, FCT) in the finite element weak form to ensure strict conservation of mass and momentum in discontinuous regions; the low-fidelity simplified model is based on the dominant modal basis functions extracted by S1, and projects the full-order equation into a low-dimensional space: , where the nonlinear force term is sparsely sampled and reconstructed by DEIM, ɸ is the dominant modal basis function, and a is the coefficient vector in the low-dimensional space.

[0033] Specifically, the hybrid reduced-order framework includes a multi-fidelity data fusion module, a physical constraint embedding module, a nonlinear term preprocessing module, a dynamic resource allocation module, and a step error feedback link; The multi-fidelity data fusion module adjusts the hybrid weight in real time according to the distribution difference between the high-fidelity finite element model and the low-fidelity simplified model, and constructs a smooth transition field through interpolation in the junction region; The physical constraint embedding module introduces a gradient sensitivity weight matrix to reconstruct the projection equation in the traditional projection and adds a residual term to the training loss function of the low-fidelity simplified model; The nonlinear term preprocessing module uses discrete empirical interpolation and convolutional autoencoders to preprocess the nonlinear term in the digital space; The dynamic resource allocation module adjusts the computational resource ratio of the high-fidelity finite element model and the low-fidelity simplified model in real time based on the error feedback mechanism, and triggers local recomputation of the high-fidelity finite element model in discontinuous regions.

[0034] Specifically, the method of preprocessing in the digital space is: Decompose the nonlinear term into a steady-state component and a transient pulsating component: , Among them, F(u) is the non - linear term, and the transient pulsation component is expressed as ΔF(u), where F mean is the steady - state component, is the spatial basis function and the time - basis function 's correlation coefficient, and m is the total number of basis functions in the transient pulsation part; Sparsely sample the transient pulsation component to obtain the key feature points of the transient pulsation component, and encode and decode the key feature points through a convolutional auto - encoder to achieve an efficient representation of the non - linear term in the low - dimensional space.

[0035] In this embodiment, the greedy DEIM algorithm is used to select interpolation points for the transient component: , where U is the basis function, interpolation points are preferentially selected in the physical mutation region, and a local DEIM (LDEIM) is used to construct a sub - region interpolation point library for the multi - condition system; a gradient sensitivity weight is introduced into the interpolation matrix; in the potential space mapping of the convolutional auto - encoder (CAE), the encoder is designed to map the non - linear term compressed by DEIM to the potential space: , The encoder uses convolutional layers to extract local non - linear features, and the pooling layer realizes dimensionality reduction; the decoder is reconstructed to recover the approximate value of the non - linear term from the potential space.

[0036] Specifically, the data - driven error is the statistical deviation between the low - fidelity simplified model and the high - fidelity finite - element model in dynamic response prediction.

[0037] Specifically, the physical mechanism residual is the degree of deviation of the low - fidelity simplified model from the constraints of mass, momentum, energy, and physical field gradients.

[0038] In this embodiment, the data - driven error mainly includes modal truncation error (energy loss of unmodeled modes caused by POD energy truncation), sensor noise interference (noise pollution in the data collected by the digital twin system), and off - condition extrapolation error (boundary conditions or parameter change domains not covered by the training data); the error quantification method evaluates the overall prediction accuracy through global L2 error: , where ϵ data is the data - driven error, representing the average relative error between the prediction results of the low - fidelity simplified model (ROM) and the results of the high - fidelity finite - element model (HFEM) within the time interval [0, T]; u ROM (t) represents the system state vector predicted by the low - fidelity simplified model at time t, and u HFEM(t) represents the system state vector calculated by the high-fidelity finite element model at time t, which is usually regarded as the "true" solution; represents the L2 norm, which is used to measure the magnitude of a vector.

[0039] and the probability distribution difference that focuses on the physical mutation region through the local KL divergence; , where D KL is the divergence, p ROM (x) and p HFEM (x) represent the probability density functions at point x respectively, and p ROM represents the probability distribution based on the low-fidelity simplified model, and p HFEM represents the probability distribution based on the high-fidelity finite element model.

[0040] The physical mechanism residual refers to the degree of deviation of the reduced-order model from the conservation laws (mass, momentum, energy) and the physical field gradient constraints, which needs to be forced to be satisfied through regularization constraints; Construct a multi-objective loss function to jointly optimize the data-driven error and the physical mechanism residual.

[0041] Specifically, the method of the iterative optimization strategy includes; When the global error exceeds the preset threshold, locate the error source through the residual dominant mode analysis, and update the dominant mode basis function based on the online flow data in S3 to supplement the missing high-order modes; When the gradient mutation in the local physical mutation region exceeds the preset threshold, strengthen the physical constraints in the hybrid reduced-order framework of S2, and increase the sampling density of the corresponding local physical mutation region through gradient sensitivity analysis.

[0042] As mentioned above, it is only a preferred embodiment of the present invention, and there is no any form of limitation to the present invention. Although the present invention has been disclosed as above with the preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments with equivalent changes within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for generating a reduced-order model of a nonlinear system that integrates physical constraints and digital twins, characterized in that, Including: S1: Collect high-dimensional dynamic response data through the sensor network of the digital twin system, perform sparse sampling on the high-dimensional dynamic response data to obtain high-fidelity model data, extract the dominant modes of the high-fidelity model data, and retain the modes of the physical mutation region through physical field gradient constraints during the extraction process; S2: Combine the high-fidelity finite element model and the low-fidelity simplified model to construct a hybrid reduced-order framework based on the multi-fidelity surrogate model, perform dense sampling in the physical mutation region, and perform numerical space preprocessing on the nonlinear terms; S3: Based on the hybrid reduced-order framework, fuse the data-driven error and the physical mechanism residual in the data-physics joint-driven model training and optimization, and update the basis functions of the dominant modes based on the online flow data; S4: Cross-validate the outputs of the high-fidelity finite element model and the reduced-order model, including global error assessment and focused analysis of the local physical mutation region, construct an adaptive error threshold feedback mechanism based on the error quantification results, and improve the accuracy of the reduced-order model through an iterative optimization strategy.

2. The method according to claim 1, wherein The sparse sampling method is: Construct a physical field gradient amplitude matrix, identify the high-gradient region, perform dense sampling on the high-gradient region using a Gaussian random measurement matrix, and perform sparse sampling on the low-gradient region using a Bernoulli random matrix; Set the sampling frequencies for the transient phase, transition phase, and steady state phase in the time dimension.

3. The method according to claim 1, characterized in that, The dominant modes of the high-fidelity model data are a set of low-dimensional basis functions that characterize the key dynamic characteristics of the system.

4. The method according to claim 1, characterized in that, The extraction method of the dominant modes includes: physical constraint modal decomposition, modal retention in the mutation region, multi-scale modal selection, and dynamic modal update; among them, the physical constraint modal decomposition constructs a weighted inner product space by combining the proper orthogonal decomposition with a physical field gradient weighting function to ensure that the extracted modes satisfy both the data statistical characteristics and the physical field gradient constraints; the dynamic modal update detects the proportion of new modal energy through online flow data and triggers incremental basis function updates according to the proportion of new modal energy.

5. The method according to claim 1, wherein The high-fidelity finite element model is a physically accurate model constructed based on the full-order finite element discretization method, and the low-fidelity simplified model is a lightweight surrogate model generated through projection reduction and data-physics joint drive.

6. The method according to claim 1, wherein The hybrid reduced-order framework includes a multi-fidelity data fusion module, a physical constraint embedding module, a nonlinear term preprocessing module, a dynamic resource allocation module, and a stride error feedback link; The multi-fidelity data fusion module adjusts the hybrid weight in real time according to the distribution difference between the high-fidelity finite element model and the low-fidelity simplified model, and constructs a smooth transition field through interpolation in the junction region; The physical constraint embedding module introduces a gradient sensitivity weight matrix into the traditional projection to reconstruct the projection equation, and adds a residual term to the training loss function of the low-fidelity simplified model; The nonlinear term preprocessing module performs numerical space preprocessing on the nonlinear terms using discrete empirical interpolation and convolutional autoencoders; The dynamic resource allocation module adjusts the computational resource ratio of the high-fidelity finite element model and the low-fidelity simplified model in real time based on the error feedback mechanism, and triggers local recomputation of the high-fidelity finite element model in the mutation region.

7. The method according to claim 6, wherein The method of numerical space preprocessing is: Decompose the nonlinear term into a steady-state component and a transient pulsation component: ， Among them, F(u) is the non-linear term, and the transient pulsation component is expressed as ΔF(u), where F mean is the steady-state component, is the spatial basis function and the time basis function correlation coefficient, and m is the total number of basis functions in the transient pulsation part; Sparsely sample the transient pulsation component to obtain the key feature points of the transient pulsation component, and encode and decode the key feature points through a convolutional autoencoder to achieve an efficient representation of the nonlinear term in a low-dimensional space.

8. The method according to claim 1, wherein The data-driven error is the statistical deviation between the low-fidelity simplified model and the high-fidelity finite element model in dynamic response prediction.

9. The method according to claim 1, wherein The physical mechanism residual is the degree of deviation of the low-fidelity simplified model from the constraints of mass, momentum, energy, and physical field gradients.

10. The method according to claim 1, wherein The method of the iterative optimization strategy includes: When the global error exceeds the preset threshold, locate the error source through residual dominant mode analysis, and update the dominant mode basis function based on the online flow data in S3 to supplement the missing high-order modes; When the gradient mutation in the local physical mutation region exceeds the preset threshold, strengthen the physical constraints in the hybrid reduced-order framework of S2, and increase the sampling density of the corresponding local physical mutation region through gradient sensitivity analysis.

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