Cross-domain flow field prediction method and system based on neural operator and multi-target transfer learning

Abstract

The invention relates to the technical field of artificial intelligence, and provides a cross-domain flow field prediction method based on a neural operator and multi-target transfer learning, and the method comprises the steps: building a multi-input and multi-output general neural operator converter, combining the multi-input and multi-output general neural operator converter with the multi-target transfer learning, carrying out the multi-modal input coding and Fourier spectrum embedding through the steps S1 to S5, and carrying out the coding and embedding, thereby obtaining a multi-target flow field prediction result. The inputs of the physical domains are mapped to a shared potential feature space by their corresponding parameterized encoders. Coding features of all the domains are input into a shared computing layer, and features processed by the shared computing layer are mapped to physical quantity prediction of the domains through independent parameterization decoders of all the domains. The invention further discloses a system which achieves the technical effects. In the reasoning stage, the efficiency is improved, the flow field simulation time is greatly shortened, and rapid design iteration and parameter optimization are assisted. The method is not only suitable for airfoil flow field prediction, but also can be expanded to multi-scene engineering problems such as hydrodynamics and thermal management.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a cross-domain flow field prediction method and system based on neural operators and multi-objective transfer learning. Background Art

[0002] In engineering fields such as aerospace design and fluid machinery optimization, accurately predicting steady-state flow fields, such as velocity and pressure fields, around objects like airfoils and blades is crucial. While traditional computational fluid dynamics (CFD) methods offer high accuracy, they rely on partial differential equations, such as the Navier-Stokes equations. Numerical solutions require significant computational effort, and the iterative solution process is time-consuming.

[0003] CN118468455B discloses a deep operator learning compressible flow field prediction method fused with radial basis, S1, generating a sample data set required for building a neural network, and normalizing the sample data; S2, building a deep operator neural network model based on the normalized sample data set; S3, using the deep operator neural network for flow field prediction under compressible flow; in S2, the deep operator neural network model is built by fusion of radial basis functions, and the network structure of the deep operator neural network model includes: separate processing of the branch network and the trunk network, and feature splicing of the output of the processed trunk network with the output of the branch network.

[0004] CN119720739A discloses a method for inverting the external flow field of an aircraft based on a Fourier neural operator, comprising: obtaining training data; constructing a neural network proxy model using a Fourier neural operator to obtain a Fourier neural operator model; randomly initializing the Fourier neural operator model, and training the Fourier neural operator model using the training data to fit the mapping relationship between the pressure measurement points on the aircraft surface and the external flow field of the aircraft; and inputting the external flow field data of the aircraft into the trained Fourier neural operator model to invert the real external flow field of the aircraft.

[0005] CN119577376A discloses a wake field prediction method and device based on an adversarial neural network and transfer learning. The method comprises: obtaining a local wake field collected in a ship's observation area during navigation, as well as the ship's physical parameters; inputting the local wake field and the physical parameters into a pre-trained wake field prediction model, and using the wake field prediction model to determine whether the physical parameters conform to preset physical parameters; if it is determined that the physical parameters conform to the preset physical parameters, predicting and outputting a global wake field corresponding to the local wake field; if it is determined that the physical parameters do not conform to the preset physical parameters, optimizing the wake field prediction model based on the local wake field and the physical parameters, and using the optimized wake field prediction model to predict and output a global wake field corresponding to the local wake field; wherein the wake field prediction model is trained based on the adversarial neural network, global wake field samples, and physical parameter samples.

[0006] As an emerging paradigm in the field of scientific machine learning, neural operators, with their ability to learn mapping relationships in infinite-dimensional function spaces, provide a new approach to replacing traditional numerical solvers. Their reasoning speed significantly surpasses traditional computational fluid dynamics (CFD) methods. In existing technologies, neural operators still face challenges in model generalization when dealing with complex and changing geometries and strongly coupled physical operating parameters. In particular, when the data in the target domain (such as new parameter combinations) is sparse, the model often requires large-scale retraining or adaptive adjustment, resulting in high computational costs. Transfer learning technology can transfer knowledge learned in a data-rich source domain to a data-sparse target domain, but its traditional single-target transfer model is limited in efficiency when dealing with multi-target domain scenarios (such as simultaneous adaptation of multiple new airfoils and multiple operating conditions). Adaptation must be completed by independently migrating each target domain, which makes it difficult to meet the efficient optimization requirements of complex engineering scenarios. Summary of the Invention

[0007] Long-term practice has found that when evaluating and optimizing a large number of different design parameters in multiple physical domains, such as geometric shape, incoming flow conditions, angle of attack, and Reynolds number, the high computational cost of CFD severely limits the efficiency of design iterations and the ability to evaluate real-time performance. The limitations of processing multiple physical domains, multiple targets, and sparse data make it difficult to achieve rapid and accurate predictions of cross-domain flow fields. Furthermore, existing CFD-based flow field prediction methods have high computational costs, and existing neural operator methods have insufficient generalization capabilities across multiple physical domains, such as variable airfoil geometry, angle of attack, and Reynolds number, and low efficiency in multi-target domain migration.

[0008] In view of this, the present invention aims to propose a cross-domain flow field prediction method based on neural operators and multi-objective transfer learning, including:

[0009] Step S1: For the kth physical domain k∈{1,...,K}, input the grid coordinates Geometric parameters and operational parameters; among them, N k is the number of grid points in the kth physical domain, and the operating parameters include the angle of attack α (k) , incoming flow velocity or Reynolds number Re (k) ;

[0010] Step S2: input spatial coordinates p = (x, y) and the first parameter θ∈R C Encode and embed Φ(p) in the Fourier spectrum of the spatial coordinates; R C is a C-dimensional real vector;

[0011] Step S3, the input of the kth physical domain is parameterized by the encoder E k Mapped to the shared latent feature space, the encoding feature of the kth physical domain is obtained Among them, n c is the dimension of the latent feature space;

[0012] Step S4: Encoding features H of all physical domains k Input shared computing layer, which is composed of multiple core computing blocks stacked together; after being processed by the shared computing layer, the kth physical domain independent parameterized decoder D k Physical quantity prediction mapped to the kth physical domain through multi-layer perceptron

[0013] Preferably, in the source domain Pre-train the MIMO-GNOT model and optimize the loss function The pre-trained MIMO-GNOT model obtains the hyperparameters of the source domain encoder E1 and the hyperparameters of the source domain decoder D1

[0014] The hyperparameters and hyperparameters Copied to the target domain encoder E k and decoder D k middle.

[0015] Preferably, the predicted flow field is calculated on the target domain k∈{2,...,M} of all physical domains Compared with real CFD flow field data The sum of the mean square errors between

[0016] The global collaborative joint maximum mean difference loss is,

[0017]

[0018] Where M is the number of target domains in all physical domains; γ ij is the weighting coefficient between domain pairs; Domain P i ,P j Empirical estimate of the joint maximum mean difference between .

[0019] Preferably, an empirical estimate of the joint maximum mean difference for,

[0020]

[0021] Among them, n s and n t are the number of samples in the physical domain P and the physical domain Q respectively; and are the feature representations of the ath and bth samples in the physical domain P at the lth layer of the network; and are the feature representations of the ath and bth samples in the physical domain Q at the lth layer of the network; k l () Kernel function defined in the feature space of the network layer l; The set of network layers used to calculate JMMD;

[0022]

[0023] in, is the total mean square prediction error over all target domains; is the total loss function of the parallel fine-tuning stage; N′ k is the number of training samples in the k-th target domain; is the predicted flow field of the i-th sample in the k-th target domain; is the true flow field of the i-th sample in the k-th target domain; λ is a hyperparameter that balances the prediction error loss and distribution alignment loss.

[0024] Preferably, in step S2, the original coordinates and the harmonic terms are spliced ​​along the channel dimension to generate enhanced features; wherein the Fourier spectrum is embedded into Φ(θ) as follows:

[0025]

[0026] Among them, the C-dimensional input parameter vector θ∈R C , X (c) is the cth component of θ;

[0027] The generated feature dimension is d f =C×[1+2(2n+1)], where n is a positive integer that controls the frequency range, and C is the dimension of the parameter vector.

[0028] Preferably, in step S3, the encoding feature H k is,

[0029]

[0030] wherein E k is the encoder of the kth physical domain, X (k) is the input mesh coordinate of the kth physical domain, is the geometric parameter of the kth physical domain; a (k) is the angle of attack of the kth physical domain; is the incoming flow velocity of the kth physical domain.

[0031] Preferably, the hyperparameters of the shared computing layer are shared among all physical domains.

[0032] The application also discloses a system of the cross-domain flow field prediction method based on the neural operator and multi-target transfer learning as described above, and the system comprises,

[0033] an input unit configured to input, for the kth physical domain k∈{1,...,K}, the mesh coordinate geometric parameters and operating parameters; wherein N k is the number of mesh points of the kth physical domain, and the operating parameters comprise the angle of attack a (k) , the incoming flow velocity or the Reynolds number Re (k) ;

[0034] an encoding unit configured to encode the input spatial coordinate p=(x,y) and the first parameter θ∈R C and embed Φ(p) in the Fourier spectrum of the spatial coordinate; R C is a C-dimensional real vector;

[0035] a mapping unit configured to map the input of the kth physical domain by the parameterized encoder E k to a shared latent feature space, to obtain the encoding feature of the kth physical domain wherein n c is the dimension of the latent feature space;

[0036] a prediction unit configured to input the encoding features H k of all physical domains into a shared computing layer, and the shared computing layer is stacked by a plurality of core computing blocks; after being processed by the shared computing layer, the parameterized decoder D k of the kth physical domain is mapped to the physical quantity prediction of the kth physical domain by a multi-layer perceptron.

[0037] Preferably, the system further comprises: the shared computing layer comprises a heterogeneous normalized attention mechanism module and a self-attention mechanism module, or a geometric gated hybrid expert mechanism module;

[0038] The heterogeneous normalized attention mechanism module integrates the attention mechanism into the normalization process, dynamically adjusting the weights of different channels or spatial positions; it is used to normalize feature maps from different sources and different scales;

[0039] The self-attention mechanism module is used to calculate the similarity between each position in the feature map and all other positions and redistribute the weights;

[0040] The geometric gated hybrid expert mechanism module is used to pass a gating function G(y t ), using the coordinates of grid points to modulate the weight distribution of multiple expert networks.

[0041] The present invention provides an electronic device, at least one processor; and

[0042] a memory communicatively connected to the at least one processor; wherein,

[0043] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the above-mentioned cross-domain flow field prediction method based on neural operators and multi-objective transfer learning.

[0044] The present invention provides a machine-readable storage medium having instructions stored thereon, which are used to enable a machine to execute the cross-domain flow field prediction method based on neural operators and multi-objective transfer learning as described above in the present application.

[0045] The cross-domain flow field prediction method based on neural operators and multi-target transfer learning disclosed in the present invention is combined by establishing a multi-input and output general neural operator transformer (Multi-Input Multiple-Output General Neural Operator Transformer, MIMO-GNOT) and multi-target domain transfer learning (Multi-Target Domain Transfer Learning, MTDTL). Through steps S1 to S5, multimodal input is encoded and Fourier spectrum embedded. After encoding and embedding, the input of the kth physical domain is mapped to a shared potential feature space by its corresponding parameterized encoder. The encoded features of all domains are input to the shared computing layer, and the features processed by the shared computing layer are then mapped to the physical quantity prediction of the domain through independent parameterized decoders of each domain. The present invention also discloses a system for the above method, and the technical effects achieved include:

[0046] (1) Compared to traditional CFD (Computational Fluid Dynamics) methods, the proposed method and system can achieve a thousand-fold speed increase in the inference phase while maintaining acceptable prediction accuracy. This significantly shortens flow field simulation time, enabling rapid design iterations and large-scale parameter optimization.

[0047] (2) The MIMO-GNOT architecture effectively decouples the specific influences of different physical domains by combining domain-specific encoding / decoding with a shared computing layer, while learning the general laws of fluid physics, thereby making accurate predictions with fewer parameter combinations and improving the generalization capability across multiple domains.

[0048] (3) The MTDTL strategy, especially the GC-JMMD (Global Collaborative JMMD Loss) loss function, enables parallel knowledge transfer from source domains to multiple target domains. It effectively utilizes sparse target domain data by globally aligning the feature distributions of all relevant domain pairs, avoiding the inefficiency of traditional transfer methods that require adapting each target domain separately. It also prevents feature space fragmentation and ensures physical consistency.

[0049] (4) Fourier spectrum embedding helps to capture the multi-scale physical phenomena of the flow field. The geometric gating MoE mechanism enables the model to adaptively activate the most appropriate "expert" network for calculation according to the spatial position, thereby improving the modeling ability of complex flow areas and the utilization efficiency of computing resources.

[0050] (5) Reducing dependence on large amounts of labeled data. Through effective transfer learning, the present invention can achieve performance superior to that of training from scratch or simple transfer methods even when the target domain samples are very sparse. This is particularly important for scenarios in actual engineering where it is difficult to obtain large amounts of high-quality CFD data.

[0051] (6) The framework of the present invention has a certain degree of versatility. It is not limited to airfoil flow field prediction, but can also be extended to other engineering problems that require fast and multi-scenario simulation, such as hydrodynamics and thermal management. At the same time, it can adapt to more complex input and output by adding or modifying encoders / decoders.

[0052] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0054] In the attached figure:

[0055] Figure 1 A schematic diagram of the architecture of a general neural operator transformer (GNOT) according to an embodiment of the present application;

[0056] Figure 2 A schematic diagram of the architecture of a multi-input-output general neural operator transformer (MIMO-GNOT) according to an embodiment of the present application;

[0057] Figure 3 A schematic diagram of the architecture of a Fourier spectrum embedding encoding procedure according to an embodiment of the present application;

[0058] Figure 4 A schematic diagram of the architecture of a two-stage multi-target domain transfer learning (MTDTL) strategy according to an embodiment of the present application. DETAILED DESCRIPTION

[0059] The specific embodiments of the present application will be described below in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely intended to illustrate and explain the present application, and are not intended to limit the present application.

[0060] In order to enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts should fall within the scope of the present application.

[0061] It should be noted that the terms "first", "second", "third", and the like in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or a chronological sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but can include other steps or units that are not clearly listed or inherent to the process, method, product or device.

[0062] In order to solve the technical problems existing in the prior art, in the case of needing to evaluate and optimize a large number of different design parameters in multiple physical domains, such as geometric shape, incoming flow condition, attack angle, Reynolds number and the like, the high computational cost of CFD seriously limits the design iteration efficiency and real-time performance evaluation capability. The limitations in processing multiple physical domains, multiple targets and sparse data scenes make it difficult to realize fast and accurate prediction of cross-domain flow field. Moreover, the existing flow field prediction method based on CFD has high computational cost, and the existing neural operator method has insufficient generalization ability in multiple physical domains, such as variable airfoil geometry, attack angle, Reynolds number, and low efficiency of multi-target domain migration. The present application provides a cross-domain flow field prediction method based on neural operator and multi-target transfer learning, as shown in Figure 1-4 The cross-domain flow field prediction method based on neural operator and multi-target transfer learning of an embodiment of the present application is shown in the schematic diagram. The cross-domain flow field prediction method based on neural operator and multi-target transfer learning comprises,

[0063] Step S1, for the kth physical domain k∈{1,...,K}, input the grid coordinates Geometric parameters and operating parameters; wherein, N k is the number of grid points of the kth physical domain, the operating parameters include attack angle α (k) , incoming flow velocity or Reynolds number Re (k) ;

[0064] Step S2, encode the input spatial coordinates p=(x,y) and the first parameter θ∈R C , and embed Φ(p) in the Fourier spectrum of the spatial coordinates; R C is a C-dimensional real vector;

[0065] Step S3, the input of the kth physical domain is mapped to a shared latent feature space by a parameterized encoder E k , to obtain the encoded feature of the kth physical domain wherein, n c is the dimension of the latent feature space;

[0066] Step S4, input the encoded features H k of all physical domains into a shared calculation layer, and the shared calculation layer is stacked by a plurality of core calculation blocks; after being processed by the shared calculation layer, the independent parameterized decoder D k of the kth physical domain is mapped to the physical quantity prediction of the kth physical domain by a multi-layer perceptron

[0067] By combining a multi-input-output general neural operator transformer (MIMO-GNOT) with multi-target domain transfer learning (MTDTL), through steps S1 to S5, multimodal input is encoded and Fourier spectrum embedded. After encoding and embedding, the input of the kth physical domain is mapped to a shared latent feature space by its corresponding parameterized encoder. The encoded features of all domains are input to the shared computation layer. The features processed by the shared computation layer are then mapped to the physical quantity prediction of each domain through independent parameterized decoders in each domain. The technical effects achieved include:

[0068] Compared to traditional CFD methods, the proposed method achieves thousands of times faster inference speed while maintaining engineering-acceptable prediction accuracy. This significantly shortens flow simulation time, enabling rapid design iterations and large-scale parameter optimization. The MIMO-GNOT architecture effectively decouples the specific influences of different physical domains by combining domain-specific encoding / decoding with a shared computational layer, while simultaneously learning universal fluid physics laws. This enables accurate predictions with fewer parameter combinations, improving cross-domain generalization. The MTDTL strategy, specifically the GC-JMMD loss function, enables parallel knowledge transfer from a source domain to multiple target domains. By globally aligning the feature distributions of all relevant domain pairs, it effectively utilizes sparse target domain data, avoiding the inefficiency of traditional transfer methods that require separate adaptation for each target domain. It also prevents feature space fragmentation and ensures physical consistency. Fourier spectral embedding helps capture the multi-scale physics of the flow field, and the geometrically gated MoE (Mixture of Experts) mechanism enables the model to adaptively activate the most appropriate "expert" network based on spatial location for computation, improving modeling capabilities for complex flow regions and utilizing computational resources. By reducing reliance on large amounts of labeled data and through effective transfer learning, the present invention can achieve performance superior to that of de novo training or simple transfer methods even when target domain samples are very sparse. This is particularly important for practical engineering scenarios where it is difficult to obtain large amounts of high-quality CFD data. The framework of the present invention has a certain degree of versatility and is not limited to airfoil flow field prediction. It can also be extended to other engineering problems requiring fast, multi-scenario simulation, such as hydrodynamics and thermal management. Furthermore, by adding or modifying encoders / decoders, it can accommodate more complex inputs and outputs.

[0069] Figures 1-4 In the above figure, MLP is a multi-layer perceptron (MLP), which is a feedforward neural network structure consisting of an input layer, several hidden layers and an output layer. The layers are connected in a fully connected manner. Figure 2In the proposed framework, the Trunk MLP is a shared feature extraction layer responsible for extracting common features from the original input. The Branch MLP performs specialized processing for different tasks based on the features output by the Trunk MLP.

[0070] The process of embedding Φ(p) in the Fourier spectrum of spatial coordinates p = (x, y) is,

[0071]

[0072] Among them, Φ(p) is the Fourier spectrum embedding vector of the spatial point p, and x and y are the horizontal and vertical coordinates of the spatial point p respectively. It is a vector concatenation operation, k is the frequency index, which is an integer ranging from -n to n; n is a positive integer that controls the frequency range.

[0073] In order to achieve parameter synchronization, in a more preferred embodiment of the present invention, in the source domain Pre-train the MIMO-GNOT model and optimize the loss function The pre-trained MIMO-GNOT model obtains the hyperparameters of the source domain encoder E1 and the hyperparameters of the source domain decoder D1

[0074] The hyperparameters and hyperparameters Copied to the encoder E in the target domain k and decoder D k middle.

[0075]

[0076] in, are the hyperparameters of the kth target domain encoder and target domain decoder, are the hyperparameters of the source domain encoder and source domain decoder. ← is the parameter assignment operation.

[0077] Among them, the traditional joint maximum mean discrepancy loss function JMMD (Joint Maximum Mean Discrepancy) method usually performs pairwise alignment of feature distributions between the source domain and a single target domain. However, in the multi-target domain migration scenario, this pairwise strategy may have limitations: (1) Changes in parameters of different target domains may cause implicit fragmentation of the learned feature space, that is, the feature representation is split into discontinuous and inconsistent regions, destroying the smoothness and coherence of the flow field solution space. (2) Independent alignment ignores the possible shared characteristics between target domains and weakens the role of the source domain as a knowledge hub. In order to better coordinate the feature distributions of all relevant domain pairs, including source domain-target domain pairs and domain pairs between different target domains from a global perspective. It aims to eliminate the risk of feature space fragmentation, ensure the physical continuity of the solution space, and make full use of the shared information between the source domain and multiple target domains, and strengthen the expression of cross-domain universal physical patterns through a global collaborative mechanism. In a more preferred case of the present invention, the target domain k∈{2,...,M} of all physical domains is calculated to predict the flow field Compared with real CFD flow field data The sum of the mean square errors between

[0078] The global collaborative joint maximum mean difference loss is,

[0079]

[0080] Where M is the number of target domains in all physical domains; γ ij is the weighting coefficient between domain pairs; Domain P i , P j Empirical estimate of the joint maximum mean difference between .

[0081] Although the boundary conditions or parameters of different domains, such as airfoil geometry and angle of attack, are different, the statistical characteristics of the solutions of their governing equations, such as turbulence structure scale, energy dissipation rate, boundary layer behavior, etc., should be inherently consistent. GC-JMMD adaptively extracts these implicit physical laws by aligning the characteristic distributions of all domain pairs. In a more preferred embodiment of the present invention, the empirical estimate of the joint maximum mean difference is for,

[0082]

[0083] Among them, n s and n t are the number of samples in the physical domain P and the physical domain Q respectively; and are the feature representations of the ath and bth samples in the physical domain P at the lth layer of the network; and are the feature representations of the ath and bth samples in the physical domain Q at the lth layer of the network; k l O is the kernel function defined in the feature space of the network layer l; The set of network layers used to calculate JMMD;

[0084]

[0085]

[0086] in, is the total mean square prediction error over all target domains; is the total loss function of the parallel fine-tuning stage; N′ k is the number of training samples in the k-th target domain; is the predicted flow field of the i-th sample in the k-th target domain; is the true flow field of the i-th sample in the k-th target domain; λ is a hyperparameter that balances the prediction error loss and distribution alignment loss.

[0087] In order to explicitly analyze high-frequency fluctuations in the flow field structure, such as boundary layer turbulence and low-frequency mean field characteristics, such as potential flow characteristics, and thus improve the model's ability to capture multi-scale physical phenomena. In a more preferred embodiment of the present invention, in step S2, the original coordinates and the harmonic terms are spliced ​​along the channel dimension to generate enhanced features; wherein, the Fourier spectrum is embedded in Φ(θ) as follows:

[0088]

[0089] Among them, the C-dimensional input parameter vector θ∈R C , X (c) is the cth component of θ;

[0090] The generated feature dimension is d f =C×[1+2(2n+1)], where n is a positive integer that controls the frequency range, and C is the dimension of the parameter vector.

[0091] In order to better input to the shared computing layer, in a more preferred embodiment of the present invention, in step S3, the encoding feature H of the kth physical domain is k for,

[0092]

[0093] Among them, E k is the encoder of the kth physical domain, X (k) is the input grid coordinate of the kth physical domain, is the geometric parameter of the kth physical domain; α (k) is the angle of attack of the kth physical domain; is the incoming flow velocity of the kth physical domain. The encoding characteristics H of all physical domains k Input to the shared computing layer. This shared computing layer inherits the core structure of GNOT and is composed of multiple core computing blocks (Core Blocks). Figure 1-Figure 2 In the shared computing layer, each core computing block usually contains an attention mechanism for capturing long-range dependencies, such as Heterogeneous Normalization Attention (HNA) and a module for modeling local relationships, such as Self-Attention (SA). This shared computing layer contains GNOT's original Geometric Gating Mixture-of-Experts (MoE) mechanism module. GeometricGating is a geometric gating module. Vector Encoder is a model component that converts input data (such as text, images, audio, etc.) into a dense vector representation. Points Encoder is a neural network component that specializes in processing three-dimensional point cloud data (Point Cloud). Its core function is to convert an unordered, sparse point set into a feature vector or feature map with semantic information. Figure 2 In the Query Points and Input Function, the query points correspond to the input grid coordinates. The input function is the specific geometric parameters or operation parameters. Figure 3 In the process, frequency generation and spatial point (Input Point), that is, the specific point in the spatial coordinate p = (x, y), are used as the input of harmonic feature generation (Harmonic Feature Generation), and output to the feature concatenation module (Feature Concatenation) to form an encoded vector structure (Encoded Vector Structure), completing Fourier spectrum embedding. The output of this module is output to the network model (To Network) as input using the feature vector (Output Feature Vector), and also forms a high-sample density part (High-Frequency Components) and a low-sample density part (Low-Frequency Components). Entering the second stage of domain alignment fine-tuning (Domain Alignment Fine-Tunning), Figure 4The samples in the high sample density space and the samples in the low sample density space are respectively input into the processor for calculation.

[0094] The MoE mechanism is a gate function G(y t ), using the coordinates of query points, such as grid points, to modulate the weight distribution of multiple expert networks. This allows the model to adaptively activate and combine the most appropriate expert networks based on spatial location for calculations. For example, in areas with rapidly changing geometry and complex flows, such as the trailing edge of an airfoil, the gating network can dynamically adjust the expert weights to prioritize the activation of expert networks specialized for phenomena like flow separation at the trailing edge. This enables compartmentalized reuse of domain knowledge and refined modeling of locally complex flows without significantly increasing network width.

[0095] In order to learn universal fluid dynamics laws, in a more preferred embodiment of the present invention, the hyperparameters of the shared computation layer are shared among all physical domains. The parameters of the shared computation layer, including the parameters of the expert network in HNA, SA, and MoE, but excluding the domain-specific parts that may exist in the gate function of MoE, are shared among all domains. The features processed by the shared computation layer are then passed through the parameterized decoder D k Prediction of physical quantities mapped to this domain Parameterized decoder D k Typically a lightweight multilayer perceptron.

[0096]

[0097] in, The flow field physical quantities predicted for the kth physical domain, such as velocity and pressure. k is the decoder of the kth physical domain, CoreBlock is a core block. Multiple core blocks form a shared computing layer.

[0098] The present invention also discloses a system for the cross-domain flow field prediction method based on neural operators and multi-objective transfer learning as described above, the system comprising:

[0099] Input unit, for inputting grid coordinates for the kth physical domain k∈{1,...,K} Geometric parameters and operational parameters; among them, N k is the number of grid points in the kth physical domain, and the operating parameters include the angle of attack α (k) , incoming flow velocity or Reynolds number Re (k) ;

[0100] Encoding unit, for inputting spatial coordinates p = (x, y) and first parameter θ∈R CEncode and embed Φ(p) in the Fourier spectrum of the spatial coordinates; R C is a C-dimensional real vector;

[0101] Mapping unit, used to transform the input of the kth physical domain from the parameterized encoder E k Mapped to the shared latent feature space, the encoding feature of the kth physical domain is obtained Among them, n c is the dimension of the latent feature space;

[0102] The prediction unit is used to transform the encoding features H of all physical domains k Input shared computing layer, which is composed of multiple core computing blocks stacked together; after being processed by the shared computing layer, the kth physical domain independent parameterized decoder D k Physical quantity prediction mapped to the kth physical domain through multi-layer perceptron

[0103] This system combines a multi-input and output general neural operator transformer (MIMO-GNOT) with multi-target domain transfer learning (MTDTL) through input units, encoding units, mapping units, and prediction units. Multimodal inputs are encoded and Fourier spectral embedded. After encoding and embedding, the input of the kth physical domain is mapped to a shared latent feature space by its corresponding parameterized encoder. The encoded features of all domains are input to the shared computing layer. The features processed by the shared computing layer are then mapped to the physical quantity prediction of the domain through independent parameterized decoders of each domain. The system proposed in the present invention can achieve a speed increase of thousands of times in the inference stage while maintaining engineering-acceptable prediction accuracy. It greatly shortens the flow field simulation time and provides the possibility for rapid design iteration and large-scale parameter optimization. The MIMO-GNOT architecture effectively decouples the specific influences of different physical domains through the combination of domain-specific encoding / decoding and shared computing layers, while learning universal fluid physics laws, so that accurate predictions can still be made under fewer parameter combinations, thereby improving the generalization ability across multiple domains. It can realize parallel knowledge transfer from the source domain to multiple target domains. It effectively utilizes sparse target domain data by globally aligning the feature distributions of all relevant domain pairs, preventing feature space fragmentation and ensuring physical consistency. Fourier spectral embedding helps capture the multi-scale physical phenomena of the flow field, and the geometrically gated MoE mechanism enables the model to adaptively activate the most appropriate "expert" network for calculations based on spatial location, improving the modeling capabilities of complex flow areas and the efficiency of computing resource utilization. Through effective transfer learning, the reliance on large amounts of annotated data is reduced. It is not limited to airfoil flow field prediction but can also be extended to other engineering problems requiring fast, multi-scenario simulation, such as hydrodynamics and thermal management.

[0104] The normalization operation, such as BatchNorm, LayerNorm, is deeply coupled with the attention mechanism, dynamically allocates weights according to feature importance, and strengthens key semantic channels such as target contour and texture features, and suppresses redundant information. In a more preferred case of the present application, the system further comprises that the shared computing layer comprises a heterogeneous normalization attention mechanism module and a self-attention mechanism module, or a geometric gating hybrid expert mechanism module.

[0105] In order to adaptively adjust the normalization parameters for different position feature saliency, such as the center region and the edge region of the image. The heterogeneous normalization attention mechanism module integrates the attention mechanism into the normalization process, dynamically adjusts the weights of different channels or spatial positions; for normalizing features of different sources and different scales. It is suitable for processing multi-source heterogeneous data, such as RGB image and depth image fusion, multi-scale features, etc.

[0106] By calculating the correlation degree of each position in the feature map with all other positions, that is, the "similarity matrix", the global context information is captured. The self-attention mechanism module is used to calculate the similarity between each position in the feature map and all other positions, and to redistribute the weights. The weight matrix reflects the semantic association between any two positions.

[0107] Compared with a single network, the hybrid expert mechanism can reduce the computational complexity, that is, only part of the experts are activated, while the representation ability of geometric features is improved. The geometric gating hybrid expert mechanism module is used to modulate the weight distribution of multiple expert networks by a gating function G(y t ), using the coordinates of the grid points. The feature processing is divided into multiple "expert sub-networks", each expert is responsible for processing specific geometric features, such as straight lines, curves, and topological structures.

[0108] The present application provides an electronic device, at least one processor; and

[0109] The memory is in communication connection with the at least one processor; wherein,

[0110] The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the construction method described above.

[0111] The present application provides a machine readable storage medium, the machine readable storage medium stores instructions for causing a machine to execute the construction method of the present application as described above.

[0112] It should be noted that for the aforementioned method embodiments, for simplicity of description, they are all expressed as a series of action combinations. However, those skilled in the art should be aware that the present invention is not limited by the order of the actions described, because according to the present invention, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present invention.

[0113] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0114] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0115] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A cross-domain flow field prediction method based on neural operators and multi-objective transfer learning, characterized by: The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning includes: Step S1: For the kth physical domain k∈{1,...,K}, input the grid coordinates Geometric parameters and operational parameters; among them, N k is the number of grid points in the kth physical domain, and the operating parameters include the angle of attack α (k) , incoming flow velocity or Reynolds number Re (k) ; Step S2: input spatial coordinates p = (x, y) and the first parameter θ∈R C Encode and embed Φ(p) in the Fourier spectrum of the spatial coordinates; R C is a C-dimensional real vector; Step S3, the input of the kth physical domain is parameterized by the encoder E k Mapped to the shared latent feature space, the encoding feature of the kth physical domain is obtained Among them, n c is the dimension of the latent feature space; Step S4: Encoding features H of all physical domains k Input shared computing layer, which is composed of multiple core computing blocks stacked together; after being processed by the shared computing layer, the kth physical domain independent parameterized decoder D k Physical quantity prediction mapped to the kth physical domain through multi-layer perceptron 2. The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to claim 1 is characterized in that: In the source domain Pre-train the MIMO-GNOT model and optimize the loss function The pre-trained MIMO-GNOT model obtains the hyperparameters of the source domain encoder E1 and the hyperparameters of the source domain decoder D1 The hyperparameters and hyperparameters Copied to the encoder E in the target domain k and decoder D k middle.

3. The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to claim 2 is characterized in that: Calculate the predicted flow field on the target domain k∈{2,...,M} of all physical domains Compared with real CFD flow field data The sum of the mean square errors between The global collaborative joint maximum mean difference loss is, Where M is the number of target domains in all physical domains; γ ij is the weighting coefficient between domain pairs; Domain P i ,P j Empirical estimate of the joint maximum mean difference between .

4. The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to claim 3 is characterized in that: Empirical estimate of the joint maximum mean difference for, Among them, n s and n t are the number of samples in the physical domain P and the physical domain Q respectively; and are the feature representations of the ath and bth samples in the physical domain P at the lth layer of the network; and are the feature representations of the ath and bth samples in the physical domain Q at the lth layer of the network; k l () Kernel function defined in the feature space of the network layer l; The set of network layers used to calculate JMMD; in, is the total mean square prediction error over all target domains; is the total loss function of the parallel fine-tuning stage; N′ k is the number of training samples in the k-th target domain; is the predicted flow field of the i-th sample in the k-th target domain; is the true flow field of the i-th sample in the k-th target domain; λ is a hyperparameter that balances the prediction error loss and distribution alignment loss.

5. The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to claim 1 is characterized in that: In step S2, the original coordinates and harmonic terms are spliced ​​along the channel dimension to generate enhanced features; wherein, the Fourier spectrum embedding Φ(θ) process is, Among them, the C-dimensional input parameter vector θ∈R C , X (c) is the cth component of θ; The generated feature dimension is d f =C×[1+2(2n+1)], where n is a positive integer that controls the frequency range, and C is the dimension of the parameter vector.

6. The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to claim 1 is characterized in that: In step S3, the encoding feature H of the kth physical domain k for, Among them, E k is the encoder of the kth physical domain, X (k) is the input grid coordinate of the kth physical domain, is the geometric parameter of the kth physical domain; α (k) is the angle of attack of the kth physical domain; is the incoming flow velocity of the kth physical domain.

7. The cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to any one of claims 1 to 6, characterized in that: The hyperparameters of the shared computation layer are shared among all physical domains.

8. A system for cross-domain flow field prediction based on neural operators and multi-objective transfer learning according to any one of claims 1 to 7, characterized in that: The system comprises, Input unit, used to input grid coordinates for the k-th physical domain k∈{1,...,K} Geometric parameters and operational parameters; among them, N k is the number of grid points in the kth physical domain, and the operating parameters include the angle of attack α (k) , incoming flow velocity or Reynolds number Re (k) ; Encoding unit, for inputting spatial coordinates p = (x, y) and first parameter θ∈R C Encode and embed Φ(p) in the Fourier spectrum of the spatial coordinates; R C is a C-dimensional real vector; The mapping unit is used to transform the input of the k-th physical domain from the parameterized encoder E k Mapped to the shared latent feature space, the encoding feature of the kth physical domain is obtained Among them, n c is the dimension of the latent feature space; The prediction unit is used to convert the encoding features H of all physical domains k Input shared computing layer, which is composed of multiple core computing blocks stacked together; after being processed by the shared computing layer, the kth physical domain independent parameterized decoder D k Physical quantity prediction mapped to the kth physical domain through multi-layer perceptron 9. The system according to claim 7, wherein: The system further includes that the shared computing layer includes a heterogeneous normalized attention mechanism module and a self-attention mechanism module, or a geometric gated hybrid expert mechanism module; The heterogeneous normalized attention mechanism module integrates the attention mechanism into the normalization process, dynamically adjusting the weights of different channels or spatial positions; it is used to normalize feature maps from different sources and different scales; The self-attention mechanism module is used to calculate the similarity between each position in the feature map and all other positions and redistribute the weights; The geometric gated hybrid expert mechanism module is used to pass a gating function G(y t ), using the coordinates of grid points to modulate the weight distribution of multiple expert networks.

10. A machine-readable storage medium, characterized in that The machine-readable storage medium stores instructions for enabling a machine to execute the cross-domain flow field prediction method based on neural operators and multi-objective transfer learning according to any one of claims 1 to 6 of the present invention.

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