Fluid analysis data processing method based on frequency domain expert mixing

Abstract

The invention provides a fluid analysis data processing method based on frequency domain expert mixing. In the fluid analysis process, firstly, input multi-channel physical field data for fluid is input into a frequency spectrum partitioning and transformation processing module, then scores are output through a sparse expert activation and reasoning execution module according to a gating network, and a plurality of high-frequency experts with the top scores are screened out to participate in calculation; the frequency band expert scheduling and task distribution module is provided with a low-frequency basic expert network and a plurality of high-frequency expert sub-networks; and then processing results of the low-frequency part and the high-frequency part of the signal are sent to a frequency domain synthesis and physical field recovery module, data which can be directly used for simulation and analysis of systems such as fluid mechanics and the like are output, and corresponding fluid mechanics method operation is carried out. Partition processing and dynamic modeling of high and low frequency characteristics are realized, the expression ability of the model to high-frequency signals is enhanced, and the problem of information loss caused by traditional FNO high-frequency truncation is solved.

Description

Technical Field

[0001] This disclosure relates to the field of computers, and more specifically, to a method for fluid analysis data processing based on frequency domain expert hybridization. Background Technology

[0002] Partial differential equations (PDEs) are important mathematical tools for describing physical phenomena in continuous media. They characterize the relationships between multivariable functions and their partial derivatives, describing dynamic processes in nature and engineering, and playing a central role in modeling in many fields, including fluid mechanics. For example, the Navier-Stokes equations describe the motion of fluids, the heat conduction equation describes the diffusion of temperature in space and time, and the wave equation describes the propagation behavior of sound and electromagnetic waves. However, solving PDEs is challenging, especially when the structures and spaces involved become more complex. Therefore, exploring accurate and efficient solutions has not only attracted widespread interest in the field of fluid mechanics research but is also crucial for promoting the development of practical applications.

[0003] In real-world applications, most PDEs (Problems-Based Equations) cannot be directly solved analytically, so traditional methods primarily rely on numerical computation. Common numerical solution methods include the Finite Difference Method (FDM), Finite Volume Method (FVM), Finite Element Method (FEM), and Spectral Method. These methods discretize the equations in space and time, transforming continuous equations into a system of algebraic equations for solution. However, as spatial dimensionality and resolution increase, the computational complexity of these methods rises sharply, resulting in extremely high computational costs in high-dimensional and high-resolution scenarios. Furthermore, numerical methods are highly dependent on mesh quality, often requiring the design of different discrete operator formats for different applications, significantly limiting their versatility in complex multiphysics problems.

[0004] In recent years, with the development of deep learning technology, neural network-based PDEs solution methods have gradually emerged. Early Physics-Informed Neural Networks (PINNs) directly embedded physical constraints into the loss function, thus fitting the data in a continuous space. Operator learning methods, on the other hand, learn the mapping relationships between function spaces to achieve PDEs solutions across distributions and boundary conditions. A representative example is the Fourier Neural Operator (FNO), which significantly improves solution efficiency by performing a Fast Fourier Transform (FFT) in the frequency domain to learn the spectral mapping relationship between input and output fields. FNO can directly perform convolution operations in the frequency space, effectively capturing the global features of low-frequency components and overcoming the constraints of traditional numerical calculation methods that rely on mesh partitioning. Therefore, it is widely used in fields such as fluid mechanics, weather forecasting, and materials mechanics.

[0005] However, FNO still has significant drawbacks. Its core design is based on a high-frequency truncation strategy, retaining only a fixed low-frequency window to control computational complexity. However, this fixed frequency window leads to severe loss of high-frequency signals, significantly reducing the model's accuracy and stability in high-resolution inputs and long-duration rolling prediction tasks. This is particularly pronounced in systems with significant high-frequency perturbations, such as fluid dynamics, where FNO is prone to error accumulation and energy decay after long-term evolution. Existing research attempts to mitigate the high-frequency loss problem, such as frequency spreading or post-training corrections (e.g., diffused frequency domain correction, numerical solver guidance, etc.). However, these methods generally suffer from high training costs, increased model complexity, or poor generalization, making it difficult to achieve efficient generalization on various types of PDE systems.

[0006] In summary, traditional FNO methods suffer from inherent limitations in high-frequency information modeling and cross-resolution generalization, leading to decreased accuracy and insufficient stability in complex fluid dynamics and multi-scale scenarios. Therefore, there is an urgent need for a PDEs solver capable of dynamic modeling in the frequency domain and progressive co-learning between high and low frequencies, maintaining computational efficiency while ensuring high-frequency detail capture and long-term prediction stability, thereby addressing the aforementioned problems.

[0007] While existing Fourier Neural Operators (FNOs) have high computational efficiency in solving partial differential equations, they still have significant shortcomings. Summary of the Invention

[0008] The purpose of this disclosure is to provide a fluid analysis data processing method based on frequency domain expert hybridization, which aims to solve the problems of existing methods using fixed frequency truncation, resulting in the loss of high-frequency information and the inability to accurately describe local changes and detailed features in complex systems such as fluid mechanics; fixed low-frequency windows limiting the generalization ability of models at different resolutions, which easily leads to error accumulation and unstable results during high-resolution input or long-term prediction; and improved methods for high-frequency problems having large computational overhead, complex structure, and difficulty in being universally applicable to multiple types of partial differential equations.

[0009] In general, a fluid analysis data processing method based on frequency domain expert hybrid is provided. In the fluid analysis process, the input multi-channel physical field data of the fluid is first input into the spectrum partitioning and transformation processing module, and the spectrum is extracted by fast Fourier transform. Low-frequency global information and high-frequency local information are divided according to the preset frequency range and output to the sparse expert activation and inference execution module. The sparse expert activation and inference execution module selects several high-frequency experts with the highest scores to participate in the calculation based on the scores output by the gating network, and freezes the remaining experts so that they do not participate in the inference process; by introducing a sparse regularization term for optimization, the system is guided to minimize the number of activated experts while maintaining prediction accuracy. The frequency band expert scheduling and task allocation module sets up a low-frequency basic expert network and multiple high-frequency expert sub-networks. The low-frequency part of the signal is processed by the basic expert network, while the high-frequency part is processed by the high-frequency expert sub-modules corresponding to multiple high-frequency experts selected by the selective activation sparse expert activation and inference execution module to process specific frequency band information. The high-frequency expert sub-network is constructed in the system training phase through the high-frequency expert initialization and weight inheritance module. It uses the traditional FNO pre-training parameters as a shared weight basis and introduces a low-rank bias structure to perform lightweight expansion to construct the high-frequency expert sub-network. The processing results of the low-frequency and high-frequency components of the signal are then sent to the frequency domain synthesis and physical field recovery module to reconstruct the spectrum results, perform zero-filling processing on the inactive frequency bands, and restore the data to the physical field form in the spatial domain through inverse fast Fourier transform. The output data can be directly used for the simulation and analysis of systems such as fluid mechanics, and corresponding fluid mechanics method calculations are performed.

[0010] In the spectrum partitioning and transformation processing module, the input physical field is represented as: ,in Indicates the number of channels. Indicates the number of points in a space or grid. First, the input is mapped to the frequency domain using a Fast Fourier Transform, resulting in the complex spectral distribution in the frequency domain: ; Subsequently, the system divides the entire frequency spectrum into a fixed window size. Divide the frequency axis so that it is evenly divided into sections. Each frequency band is defined as follows: Among them, the first The segment corresponds to the low-frequency fundamental region, and the remaining part is divided into the high-frequency enhancement region.

[0011] The sparse expert activation and inference execution module is constructed in such a way that all high-frequency experts participate in the optimization during the training phase. During the reasoning phase, only the gating system with the highest score is activated. One expert is selected, while the remaining experts remain frozen and do not participate in the calculation; the specific reasoning formula is as follows: in, This indicates the top gating score in the current frequency band. A set of experts; to prevent the gating mechanism from frequently activating too many experts and causing computational redundancy, a regularization term is introduced to constrain the expert activation probability during the optimization phase and promote sparse learning: Indicates that the gating network is in the first stage. Frequency band input The activation probability output on This represents the expected calculation of the expert activation probability across all frequency bands. The regularization term, through a frequency-band weighted summation of the gated output, implements a statistical constraint on the overall expert activation frequency, encouraging the model to develop sparse expert-use strategies during the optimization process.

[0012] The frequency band expert scheduling and task allocation module includes a basic low-frequency expert. And several expert subnetworks for processing high-frequency regions. For the input spectrum block The participation experts for this frequency band are determined through a learnable gating network. The core calculation formula for this process is: , in, For the Sigmoid function, For the gating parameter vector, The temperature coefficient is used to adjust the smoothness of the gating distribution; the gating network consists of an input normalization layer, a feature extraction layer, and an output activation layer, with the input spectral block... The gated response value is obtained by combining linear transformation and nonlinear function, and then the gated probability is calculated by temperature scaling and the Sigmoid function. During the training phase, the gated network and expert subnetwork jointly optimize the system, dynamically adjusting parameters through backpropagation to ensure that the gated outputs of different frequency bands reflect their importance in the overall spectrum, thus forming an adaptive expert selection mechanism. The output of each frequency band is generated according to the following rules: .

[0013] The high-frequency expert initialization and weight inheritance module adopts a low-rank parameter loop strategy, which reuses the weights of low-frequency basic experts to achieve efficient initialization of high-frequency experts. Specifically, the weight of each high-frequency expert is composed of a shared base weight. and low-rank update weights composition: in, and It is a low-rank matrix. Represents rank constraint. This is the scaling factor.

[0014] The frequency domain synthesis and physical field reconstruction module outputs the spectral fragments of each frequency band obtained after processing by the high and low frequency expert module. The complete spectral tensor is formed by splicing the components along the frequency dimension. ; For inactive or uncomputed frequency bands, a zero-filling operation is performed, followed by an inverse fast Fourier transform to convert the frequency domain signal back to the spatial domain, yielding the final output: This output This represents the physical field prediction result of the system at a given time, and its shape is consistent with the original input.

[0015] The technical effects to be achieved by the embodiments of the present invention are as follows: 1. Improve the modeling capability of high-frequency information and solve the problem of high-frequency feature loss caused by FNO fixed frequency truncation. By introducing a sparse expert structure in the frequency space, the partitioning and dynamic modeling of high and low frequency features are realized, which effectively enhances the model's ability to express high-frequency signals and solves the problem of information loss caused by traditional FNO high-frequency truncation. 2. Establish a progressive collaborative learning mechanism of "low-frequency pre-training - high-frequency fine-tuning" to achieve collaborative solution of high and low frequency information and efficient parameter update. By learning the global structure in the low-frequency stage and then making fine corrections in the high-frequency stage, collaborative modeling of high and low frequency features is achieved, which improves the convergence speed and stability of the model. 3. By introducing a sparse expert activation strategy, only the optimal high-frequency expert subnetwork is activated to participate in the computation during the inference phase, which greatly reduces redundant computation and achieves the goal of significantly improving inference efficiency while maintaining prediction accuracy, thus demonstrating good feasibility for industrial deployment. Attached Figure Description

[0016] The above and other objects and features of this disclosure will become clearer from the following description taken in conjunction with the accompanying drawings.

[0017] Figure 1 This is an architectural diagram illustrating a fluid analysis data processing method based on frequency domain expert hybridization according to an embodiment of the present disclosure. Detailed Implementation

[0018] The following detailed embodiments are provided to aid the reader in gaining a comprehensive understanding of the methods, apparatus, and / or systems described herein. However, various changes, modifications, and equivalents of the methods, apparatus, and / or systems described herein will become apparent upon understanding this disclosure. For example, the order of operations described herein is merely illustrative and is not limited to those orders set forth herein, but may be changed as will become clear upon understanding this disclosure, except for operations that must occur in a specific order. Furthermore, for clarity and conciseness, descriptions of features known in the art may be omitted.

[0019] The features described herein may be implemented in different forms and should not be construed as limited to the examples described herein. Rather, the examples described herein are provided only to illustrate some of the many feasible ways of implementing the methods, apparatus, and / or systems described herein, which will become clear upon understanding the disclosure of this application.

[0020] As used herein, the term “and / or” includes any one of the associated listed items and any combination of any two or more.

[0021] Although terms such as “first,” “second,” and “third” may be used herein to describe various components, assemblies, regions, layers, or parts, these components, assemblies, regions, layers, or parts should not be limited by these terms. Rather, these terms are used only to distinguish one component, assembly, region, layer, or part from another. Thus, without departing from the teaching of the examples described herein, the first component, first assembly, first region, first layer, or first part referred to as the first component, first assembly, first region, first layer, or first part may also be referred to as the second component, second assembly, second region, second layer, or second part.

[0022] In the specification, when an element (such as a layer, region, or substrate) is described as being "on" another element, "connected to," or "bonded to" another element, the element may be directly "on" another element, directly "connected to," or "bonded to" the other element, or one or more other elements may be present in between. Conversely, when an element is described as being "directly on" another element, "directly connected to," or "directly bonded to" another element, no other elements may be present in between.

[0023] The terminology used herein is for the purpose of describing various examples only and is not intended to limit disclosure. Unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. The terms “comprising,” “including,” and “having” indicate the presence of the described features, quantities, operations, components, elements, and / or combinations thereof, but do not preclude the presence or addition of one or more other features, quantities, operations, components, elements, and / or combinations thereof.

[0024] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains upon understanding this disclosure. Unless expressly defined herein, terms (such as those defined in a general dictionary) shall be interpreted as having a meaning consistent with their meaning in the context of the relevant field and in this disclosure, and shall not be interpreted in an idealized or overly formalistic manner.

[0025] Furthermore, in the description of the examples, detailed descriptions of well-known related structures or functions will be omitted when it is believed that such detailed descriptions would lead to a vague interpretation of this disclosure.

[0026] Figure 1 This is a schematic diagram illustrating a fluid analysis data processing method based on frequency domain expert hybridization according to an embodiment of the present disclosure.

[0027] System overall design module: To achieve the aforementioned objective, this invention proposes a fluid analysis data processing method based on frequency domain expert hybridization. This device introduces a sparse expert mechanism in the frequency domain, employing dynamic selection and parameter iteration strategies to achieve progressive collaborative modeling of high and low frequency information, thereby improving solution accuracy and stability while maintaining computational efficiency.

[0028] This device mainly consists of the following five functional modules: spectrum partitioning and transformation processing module, frequency band expert scheduling and task allocation module, high-frequency expert initialization and weight inheritance module, sparse expert activation and inference execution module, and frequency domain synthesis and physical field recovery module. Its overall architecture is as follows: Figure 1 As shown: Module 1: Spectrum Partitioning and Transformation Processing Module. This module transforms the input multi-channel physical field data from the spatiotemporal domain to the frequency domain. It extracts the spectrum from the original input using Fast Fourier Transform (FFT) and divides the data into a low-frequency base region and a high-frequency enhancement region according to a preset frequency range. This provides standardized frequency domain input for subsequent expert scheduling and frequency band modeling, ensuring data format consistency and continuous processing.

[0029] Module 2, Sparse Expert Activation and Inference Execution Module: Based on the scores output by the gating network, only the top K high-frequency experts are selected for computation, while the remaining experts are frozen and do not participate in the inference process. By introducing a sparse regularization term for optimization, the system is guided to minimize the number of activated experts while maintaining prediction accuracy, effectively controlling model computational overhead and improving inference efficiency.

[0030] Module Three-Band Expert Scheduling and Task Allocation: The system has a built-in low-frequency basic expert network and multiple high-frequency expert sub-networks. The low-frequency part is processed uniformly by the basic network, while the high-frequency part is decided by this module by calling the gating mechanism. It selectively activates several high-frequency expert sub-modules to process specific frequency band information. Through its good adaptability and dynamism, it realizes intelligent matching of frequency bands and experts according to the characteristics of input data.

[0031] Module 4: High-Frequency Expert Initialization and Weight Inheritance Module: During the system training phase, the traditional FNO pre-trained parameters are used as the shared weight base. A low-rank bias structure is introduced to extend it in a lightweight manner, quickly constructing multiple high-frequency expert sub-networks. While ensuring the model's expressive power, the parameter scale and training cost are significantly reduced, improving the overall structural efficiency and generalization performance of the system.

[0032] Module 5, Frequency Domain Synthesis and Physical Field Reconstruction Module, enables the reconstruction of spectral results, zero-filling of inactive frequency bands, and the restoration of data to the spatial domain physical field form via Inverse Fast Fourier Transform (iFFT). As the system's output unit, it ensures that the final prediction results meet application requirements in terms of spatial continuity, numerical stability, and physical consistency, and can be directly used for the simulation and analysis of systems such as fluid mechanics.

[0033] Spectrum partitioning and transformation processing module: This module converts the input multi-channel physics data from its original spatiotemporal domain representation to its frequency domain representation, enabling subsequent modules to perform efficient operator learning and expert modeling in the frequency domain. The input physics representation is as follows: , in Indicates the number of channels. This represents the number of points in the space or grid. The system first maps the input to the frequency domain using a Fast Fourier Transform (FFT) to obtain the complex spectral distribution in the frequency domain: .

[0034] This process can extract the energy distribution of the input physical field at different frequencies, capturing the information structure of low-frequency global modes and high-frequency local details. Subsequently, the system divides the entire frequency spectrum into a fixed window size. Divide the frequency axis so that it is evenly divided into sections. Each frequency band is defined as follows: .

[0035] Among them, the The segment corresponds to the low-frequency fundamental region, and the remaining part is divided into the high-frequency enhancement region.

[0036] Through this spectrum partitioning mechanism, this module discretizes continuous frequency signals into several independent sub-intervals, enabling subsequent expert modules to perform targeted processing on different frequency bands and achieve structured modeling in the frequency dimension. Simultaneously, the frequency domain data output by this module... Maintaining a consistent format ensures the consistency of input and the continuity of processing for subsequent expert scheduling and frequency band modeling.

[0037] Sparse Expert Activation and Inference Execution Module: This module is primarily responsible for the sparse activation and computation of high-frequency experts during the model inference phase. This ensures that the model maintains prediction accuracy while reducing redundant computation and improving overall operational efficiency. During the training phase, all high-frequency experts participate in optimization to fully learn spectral features. However, during the inference phase, to reduce complexity, only the experts with the highest gating scores are activated. One expert is selected, while the remaining experts remain frozen and do not participate in the calculation. The specific reasoning formula is as follows: .

[0038] in, This indicates the top gating score in the current frequency band. A set of experts. Furthermore, during the training phase, to prevent the gating mechanism from frequently activating too many experts and causing computational redundancy, this module introduces a sparse regularization term to constrain the expert activation probability: .

[0039] This regularization term encourages the model to adopt sparse expert usage strategies during optimization, allowing each expert to focus on processing specific types of spectral signals, thus improving the stability and computational efficiency of the model structure. Through this module, the system can significantly reduce computational resource overhead during inference while maintaining accuracy, exhibiting good engineering deployability and general adaptability.

[0040] Frequency band expert scheduling and task allocation module: This module is used to implement dynamic scheduling and task allocation of expert networks in the frequency domain. The system includes a basic low-frequency expert. And several expert subnetworks for processing high-frequency regions. For the input spectrum block The system uses a learnable gating network to determine which experts should participate in processing a particular frequency band. The core calculation formula for this process is: , in, For the Sigmoid function, For the gating parameter vector, The temperature coefficient is used to adjust the smoothness of the gating distribution. Based on the gating output value, the system performs weighted control on the expert selection for different frequency bands, thereby achieving an adaptive mapping relationship from frequency bands to experts. The output of each frequency band is generated by the following rules: .

[0041] This mechanism ensures that basic low-frequency experts focus on global pattern learning, while high-frequency experts are dynamically activated based on signal characteristics, thus achieving targeted modeling. Through this design, this module can automatically match the optimal expert structure under different input conditions, enabling adaptive computation of the model in multi-frequency domain tasks.

[0042] High-Frequency Expert Initialization and Weight Inheritance Module: This module is used to initialize and inherit weights for the high-frequency expert subnetwork, ensuring that the model has good high-frequency expressive capabilities while maintaining a controllable parameter scale. In traditional FNO models, the number of weight parameters increases dramatically with resolution and frequency band expansion. This invention employs a low-rank parameter upcycling strategy, which, while keeping the low-frequency base expert weights unchanged, generates learnable high-frequency incremental weights in a lower-dimensional space by performing low-rank decomposition and parameter recombination on their weight tensors. This strategy is essentially a parameter reuse and expansion mechanism based on pre-trained weights, enabling high-frequency experts to inherit low-frequency knowledge while performing targeted refinement, thus achieving progressive transfer learning from low-frequency to high-frequency. The weights of each high-frequency expert are shared base weights. and low-rank update weights composition: .

[0043] in, and It is a low-rank matrix. Represents rank constraint. This is the scaling factor.

[0044] This design significantly reduces the parameter size, originally with a complexity of... After low-rank decomposition, it is reduced to Meanwhile, by sharing low-frequency weights, this scheme allows high-frequency experts to inherit the stable feature distribution of the basic model, avoiding instability caused by training the high-frequency part from scratch. This ensures that the system can achieve gradual transfer of high and low frequency information under limited parameters, effectively improving the parameter efficiency and generalization ability of the overall structure.

[0045] Frequency domain synthesis and physics field recovery module: This module is used to reconstruct the expert output results from different frequency bands in the frequency domain and restore them to the spatial domain to generate the final predicted physical field. After processing by the high and low frequency expert module, the outputs of each frequency band are obtained. The system stitches these spectral fragments together in the frequency dimension to form a complete spectral tensor. For inactive or uncomputed frequency bands, the system automatically performs zero-padding to ensure spectral continuity and structural integrity. After spectral reconstruction, the system performs an inverse fast Fourier transform (iFFT) to convert the frequency domain signal back to the spatial domain, obtaining the final output. .

[0046] This output It represents the physical field prediction result of the system at a given time. Its shape is consistent with the original input and contains multiple physical channels (such as velocity field, density field or pressure field, etc.).

[0047] Through the frequency domain synthesis and inverse transform operations of this module, the model prediction results achieve spatial smoothness and continuity, remain numerically stable, and physically comply with conservation constraints and energy consistency requirements. As the system's output unit, this module can directly interface with various partial differential equation scenarios such as fluid mechanics, weather forecasting, and material stress, achieving high-precision simulation and long-term stable prediction.

[0048] While some embodiments of this disclosure have been shown and described, those skilled in the art will understand that modifications may be made to these embodiments without departing from the principles and spirit of this disclosure, which are defined by the claims and their equivalents.

Claims

1. A fluid analysis data processing method based on frequency domain expert hybridization, characterized in that, In the fluid analysis process, the multi-channel physical field data of the fluid is first input into the spectrum partitioning and transformation processing module. The spectrum is extracted by fast Fourier transform, and low-frequency global information and high-frequency local information are divided according to the preset frequency range and output to the sparse expert activation and inference execution module. The sparse expert activation and inference execution module selects the top-scoring high-frequency experts to participate in the calculation based on the scores output by the gating network, and freezes the remaining experts so that they do not participate in the inference process. By introducing a sparse regularization term for optimization, the system is guided to minimize the number of activated experts while maintaining prediction accuracy. The frequency band expert scheduling and task allocation module sets up a low-frequency basic expert network and multiple high-frequency expert sub-networks. The low-frequency part of the signal is processed by the basic expert network, while the high-frequency part is processed by the high-frequency expert sub-modules corresponding to multiple high-frequency experts selected by the selective activation sparse expert activation and inference execution module to process specific frequency band information. The high-frequency expert sub-network is constructed in the system training phase through the high-frequency expert initialization and weight inheritance module. It uses the traditional FNO pre-training parameters as a shared weight basis and introduces a low-rank bias structure to perform lightweight expansion to construct the high-frequency expert sub-network. The processing results of the low-frequency and high-frequency components of the signal are then sent to the frequency domain synthesis and physical field recovery module to reconstruct the spectrum results, perform zero-filling processing on the inactive frequency bands, and restore the data to the physical field form in the spatial domain through inverse fast Fourier transform. The output data can be directly used for the simulation and analysis of systems such as fluid mechanics, and corresponding fluid mechanics method calculations are performed.

2. The fluid analysis data processing method based on frequency domain expert hybridization as described in claim 1, characterized in that, In the spectrum partitioning and transformation processing module, the input physical field is represented as: ,in Indicates the number of channels. Indicates the number of points in a space or grid. First, the input is mapped to the frequency domain using a Fast Fourier Transform, resulting in the complex spectral distribution in the frequency domain: ; Subsequently, the system divides the entire frequency spectrum into a fixed window size. Divide the frequency axis so that it is evenly divided into sections. Each frequency band is defined as follows: Among them, the first The segment corresponds to the low-frequency fundamental region, and the remaining part is divided into the high-frequency enhancement region.

3. The fluid analysis data processing method based on frequency domain expert hybridization as described in claim 1, characterized in that, The sparse expert activation and inference execution module is constructed in such a way that all high-frequency experts participate in the optimization during the training phase. During the reasoning phase, only the gating system with the highest score is activated. One expert is selected, while the remaining experts remain frozen and do not participate in the calculation; the specific reasoning formula is as follows: in, This indicates the top gating score in the current frequency band. A set of experts; to prevent the gating mechanism from frequently activating too many experts and causing computational redundancy, a regularization term is introduced to constrain the expert activation probability during the optimization phase and promote sparse learning: Indicates that the gating network is in the first stage. Frequency band input The activation probability output on This represents the expected calculation of the expert activation probability for all frequency bands.

4. The fluid analysis data processing method based on frequency domain expert hybridization as described in claim 1, characterized in that, The frequency band expert scheduling and task allocation module includes a basic low-frequency expert. And several expert subnetworks for processing high-frequency regions. For the input spectrum block The participation experts for this frequency band are determined through a learnable gating network. The core calculation formula for this process is: ， in, For the Sigmoid function, For the gating parameter vector, The temperature coefficient is used to adjust the smoothness of the gating distribution; the gating network consists of an input normalization layer, a feature extraction layer, and an output activation layer, with the input spectral block... The gated response value is obtained by combining linear transformation and nonlinear function, and then the gated probability is calculated by temperature scaling and the Sigmoid function. The output for each frequency band is generated according to the following rules: 。 5. The fluid analysis data processing method based on frequency domain expert hybridization as described in claim 1, characterized in that, The high-frequency expert initialization and weight inheritance module adopts a low-rank parameter loop strategy, which reuses the weights of low-frequency basic experts to achieve efficient initialization of high-frequency experts. Specifically, the weight of each high-frequency expert is composed of a shared base weight. and low-rank update weights composition: in, and It is a low-rank matrix. Represents rank constraint. This is the scaling factor.

6. The fluid analysis data processing method based on frequency domain expert hybridization as described in claim 1, characterized in that, The frequency domain synthesis and physical field reconstruction module outputs the spectral fragments of each frequency band obtained after processing by the high and low frequency expert module. The complete spectral tensor is formed by splicing the components along the frequency dimension. ; For inactive or uncomputed frequency bands, a zero-filling operation is performed, followed by an inverse fast Fourier transform to convert the frequency domain signal back to the spatial domain, yielding the final output: This output This represents the physical field prediction result of the system at a given time, and its shape is consistent with the original input.

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