A physical information and causality synergistic driven unsteady aerodynamic prediction framework

Abstract

This invention discloses an unsteady aerodynamic prediction framework driven by synergistic physical information and causal relationships, belonging to the interdisciplinary field of aerodynamics and artificial intelligence. The framework includes the following steps: Step 1: Constructing a spatiotemporal dataset of unsteady flow fields under multiple physical conditions; Step 2: Constructing an unsteady flow field prediction architecture based on front-door adjusted causal theory; Step 3: Constructing an upstream physical teacher network; Step 4: Defining the loss function of the upstream teacher network and optimizing network training; Step 5: Constructing a downstream student network; constructing a parameterized diffusion Transformer model as the student network, and inheriting the capabilities of the teacher network through a knowledge distillation strategy; Step 6: Defining the loss function of the downstream student network and jointly optimizing it, using distillation and diffusion losses to jointly optimize the student network. This framework aims to address the problem of insufficient generalization ability of existing data-driven models in complex unsteady flow fields.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of aerodynamics and artificial intelligence, and in particular to an unsteady aerodynamic prediction framework driven by the synergistic interaction of physical information and causal relationships. Background Technology

[0002] Fluid dynamics modeling is a key research topic in aerospace, earth sciences, and other fields. The evolution of unsteady flow fields is typically governed by complex partial differential equations (PDEs). Traditional methods mainly rely on computational fluid dynamics (CFD) for numerical solutions. However, the high dimensionality, nonlinearity, and chaotic nature of fluids make CFD methods computationally expensive and time-consuming, making it difficult to meet the needs for rapid prediction and real-time control of complex systems. In recent years, the rise of deep learning technology has provided a new paradigm for fluid dynamics modeling. Data-driven intelligent prediction methods, such as neural operators and various spatiotemporal prediction networks, utilize the powerful nonlinear fitting capabilities of neural networks to construct a mapping relationship between historical flow field data and future states, significantly improving prediction efficiency.

[0003] However, existing data-driven methods have significant limitations. First, purely data-driven models typically lack consideration of underlying physical laws, leading to predictions that do not conform to physical laws and exhibiting poor generalization ability. When the physical parameters (such as viscosity and Mach number) in the test data differ from those in the training data, model performance drops sharply. Second, although Physical Information Neural Networks (PINNs) attempt to incorporate physical equations into the loss function, they usually rely on fully known PDE equations, and their generalization ability and versatility in complex unsteady flow fields still need improvement. Currently, for unsteady flow field prediction tasks, most mainstream deep learning methods adopt a purely data-driven approach for training and prediction, lacking explicit consideration of physical parameters, resulting in poor model generalization performance. While PINNs incorporate physical information, they typically customize loss functions for specific problems, limiting their versatility. Existing solutions struggle to adapt to flow field variations under different physical settings without retraining or complex transfer learning.

[0004] Therefore, there is an urgent need to develop an unsteady aerodynamic prediction framework that combines high accuracy, high efficiency, physical consistency, and strong generalization ability. Summary of the Invention

[0005] The purpose of this invention is to provide an unsteady aerodynamic prediction framework driven by the synergy of physical information and causal relationships, addressing the challenges of existing models in terms of generalization ability and physical consistency.

[0006] This invention is achieved through the following scheme:

[0007] A framework for predicting unsteady aerodynamics driven by the synergistic interaction of physical information and causal relationships includes the following steps:

[0008] Step 1: Construct a spatiotemporal dataset of unsteady flow fields under multiple physics conditions;

[0009] Step 2: Construct an unsteady flow field prediction architecture based on front-door adjusted causal theory;

[0010] Step 3: Construct an upstream physics teacher network to create a network structure capable of capturing global spatiotemporal evolution patterns;

[0011] Step 4: Define the loss function of the upstream teacher network and optimize network training; train the teacher network through physical constraints and self-supervision so that the teacher network can learn the basic physical laws of the flow field;

[0012] Step 5: Construct the downstream student network; Construct a parameterized diffusion Transformer model as the student network, and inherit the capabilities of the teacher network through a knowledge distillation strategy;

[0013] Step 6: Define and jointly optimize the loss function of the downstream student network by jointly optimizing the student network through distillation and diffusion losses.

[0014] Step 1 specifically includes the following steps:

[0015] Step 1.1: Use a computational fluid dynamics solver to generate or collect multiple sets of unsteady flow field numerical simulation data, each set of data corresponding to a specific physical condition;

[0016] Step 1.2: Based on the data obtained in Step 1.1, preprocess the data, extract a fixed-length time window, and form a historical flow field sequence. and the corresponding future flow field truth value ,in To input the time step, The number of physical quantity channels. , Spatial resolution;

[0017] Step 1.3: Based on each flow field sequence in Step 1.2, label its corresponding k-dimensional physical condition parameters. Finally, the training dataset is obtained. ,in , and Let represent the i-th historical flow field sequence and the corresponding physical condition parameters and the true value of the future flow field, respectively, and N be the total number of samples.

[0018] Step 2 specifically includes the following steps:

[0019] Step 2.1: Construct a structural causal model, defining the historical flow field as the dependent variable. The true value of the future flow field is defined as the result variable. Unobserved physical environmental disturbances are defined as confounding factors. ;

[0020] Step 2.2: Based on the front-door adjustment theory, define a potential spatiotemporal feature that conforms to the laws of physical partial differential equations. As a mediating proxy variable to block confounding factors Interference with causal pathways;

[0021] Step 2.3: Based on the proxy variables defined in Step 2.2 Design an "upstream teacher network" to be used to learn from... Feature extraction And designed a "downstream student network" for use based on physical condition parameters. right Intervention and prediction .

[0022] Step 3 includes the following steps:

[0023] Step 3.1: Convert the historical flow field sequence from Step 1.2 into a sequence. Divided in spatial dimension Each generated patch consists of non-overlapping tiles, and after flattening, the feature dimension of each tile is mapped to... The token sequence;

[0024] Step 3.2: Add spatiotemporal location encoding;

[0025] Step 3.3: Construct the Transformer encoder;

[0026] Step 3.4: Decouple spatiotemporal feature representation;

[0027] Step 3.5: Calculate the spatiotemporal attention weight matrix;

[0028] Step 3.6: Aggregate spatiotemporal evolution features;

[0029] Step 3.7: Adaptive feature fusion;

[0030] Step 3.8: Build the Transformer decoder.

[0031] Step 3 specifically includes the following steps:

[0032] Step 3.1: Convert the historical flow field sequence from Step 1.2 into a sequence. Divided in spatial dimension There are 3 non-overlapping tiles, each tile being 1000 square meters in size. And after flattening each generated tile, the feature dimension is mapped to... A sequence of tokens;

[0033] Step 3.2: For each token in the token sequence generated in Step 3.1, add a learnable spatial location code. and time location encoding ;

[0034] Step 3.3: Input the token sequence processed in Step 3.2 into a multi-layer Transformer encoder, use a multi-head self-attention mechanism to calculate global associations, and output a high-dimensional latent feature sequence. ,in The sequence length;

[0035] Step 3.4: Using three independent linear transformation matrices The feature sequence output in step 3.3 This is mapped to three sets of vectors along the channel dimension:

[0036]

[0037] in, The spatial query vector represents the spatial structure at the current moment. The time key vector represents the evolutionary pattern of a historical moment; This represents a time value vector, which represents specific evolutionary feature values;

[0038] Step 3.5: Calculate the values ​​in step 3.4 and The correlation between the two;

[0039]

[0040] in, This is the spatiotemporal attention weight matrix; Indicates matrix transpose; This is a scaling factor for the feature dimension of the key vector, used to prevent the gradient from vanishing due to an excessively large dot product; It is a normalized exponential function;

[0041] Step 3.6: Apply the spatiotemporal attention weight matrix obtained in Step 3.5 Compared with the time value vector in step 3.4 Multiplying them yields a feature vector containing historical evolution information;

[0042]

[0043] in, It is a contextual evolution feature after spatiotemporal interaction aggregation, containing historical evolution information most relevant to the current spatial state;

[0044] Step 3.7: Introduce gating parameters The evolutionary features obtained in step 3.6 Compared with the high-dimensional latent feature sequence output before step 3.5 Perform residual connections to obtain the final evolutionary features;

[0045]

[0046] in, Characteristics of teachers;

[0047] Step 3.8: Extract the features output from Step 3.7 Mapped back to the Token space and reassembled into the predicted flow field through a de-blocking operation. .

[0048] Step 4 specifically includes the following steps:

[0049] Step 4.1: Define the reconstruction loss function ;

[0050] Step 4.2: Define the physical constraint loss function ;

[0051] Step 4.3: Based on the reconstruction loss function and physical constraint loss function Constructing the total loss function of the teacher network ;

[0052] Step 4.4: Conduct online training for teachers.

[0053] Step 4 specifically includes the following steps:

[0054] Step 4.1: Calculate the predicted flow field output from Step 3.8 Compared with the true value of the future flow field in step 1.2 The mean squared error between them yields the reconstruction loss function. This is used to constrain the model's reconstruction capability and ensure that the model can learn the flow field characteristics;

[0055] Step 4.2: Employ the physical constraint loss function based on the Navier-Stokes equations. Step 3.8: Predict the flow field The momentum residuals and mass residuals are obtained; the physical constraint loss function is then derived. ;

[0056] Step 4.3: Introduce weighting coefficients The reconstruction loss function defined in step 4.1 The physical constraint loss function defined in step 4.2 By performing a weighted summation, we obtain the total loss function of the teacher network. The formula is:

[0057]

[0058] Step 4.4: Teacher Network Total Loss Function Based on Step 4.3 The backpropagation algorithm is used to optimize the parameters of the teacher network constructed in step 3, and the teacher network parameters are frozen after optimization.

[0059] Step 5 includes the following steps:

[0060] Step 5.1: Construct an environmental parameter mapping network;

[0061] Step 5.2: Construct the time step embedding module;

[0062] Step 5.3: Generate adaptive normalization parameters;

[0063] Step 5.4: Construct the parameterized Transformer module;

[0064] Step 5.5: Perform teacher feature extraction;

[0065] Step 5.6: Perform student feature extraction;

[0066] Step 5.7: Construct the feature alignment layer.

[0067] Step 5 specifically includes the following steps:

[0068] Step 5.1: Receive the physical condition parameters marked in Step 1.3 using a multilayer perceptron. Map it to a dimension of Environmental feature vector ;

[0069] Step 5.2: Use sinusoidal position encoding to divide the diffusion time step Encoded as a temporal embedding vector ;

[0070]

[0071] in, Index representing the dimension of a vector ;

[0072] Step 5.3: The output of Step 5.1 Compared with the output of step 5.2 The data is stitched together, and the scaling factor is obtained by regression through the linear layer of a multilayer perceptron. and bias factor ;

[0073]

[0074] in, This is a vector concatenation operation; It is the Sigmoid linear unit activation function; It is a linear fully connected layer; ;

[0075] Step 5.4: Introduce an adaptive layer normalized AdaLN(x) into the Transformer layer, using the value generated in Step 5.3. and Features of the input Modulation:

[0076]

[0077] Among them, features This represents the sequence of intermediate feature tokens within the Transformer module, before entering the self-attention mechanism. Indicates standard layer normalization; This indicates element-wise multiplication;

[0078] Step 5.5: Input the historical flow field sequence from Step 1 into the upstream teacher network with frozen parameters from Step 4.4, and extract the teacher features output from Step 3.7. ;

[0079] Step 5.6: Input the noisy flow field latent variables into the downstream student network and extract the feature output of its Transformer intermediate layer. .

[0080] Step 5.7: Introduce a linear projection layer to transform the process in Step 5.6. Mapped to step 5.5 The same dimension is denoted as the aligned student feature. .

[0081] Step 6 specifically includes the following steps:

[0082] Step 6.1: Define the feature knowledge distillation loss function L KD ; Calculate the teacher features extracted in step 5.5 Student characteristics aligned with step 5.7 The Euclidean distance between them yields the feature knowledge distillation loss function, which is formulated as follows:

[0083] ;

[0084] Step 6.2: Define the diffusion generation loss function L diff ;

[0085] Calculate the noise predicted by the student network based on the modulation features from step 5.4. With sampled Gaussian noise The mean square error between the two values ​​yields the diffusion generation loss function, which is expressed as follows:

[0086] ;

[0087] in, It is Gaussian noise. Noise predicted for student networks For a moment The noise-adding characteristics, This represents the initial flow field state;

[0088] Step 6.3: Construct the total loss function L of the student network student ;

[0089] Introducing distillation weighting coefficient Combining the diffusion generation loss function defined in step 6.2 with the knowledge distillation loss function defined in step 6.1, we obtain the total loss function of the student network, as shown in the formula:

[0090] ;

[0091] Step 6.4: Jointly optimize the student network; calculate the total loss function of the student network. To optimize the student network so that it can simultaneously grasp the laws of physical evolution and the ability to control parameters.

[0092] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0093] 1. Overcoming the limitations of local receptive fields and achieving global long-range spatiotemporal dependency modeling: Compared to existing technologies based on convolutional neural networks (CNNs), this proposal adopts a Transformer architecture. Utilizing the global interconnectivity of the self-attention mechanism, the model can directly compute the correlation between any two spatial points in the flow field. This gives the model significant advantages in capturing large-scale structures and solves the problem that CNNs cannot effectively model long-range physical dependencies.

[0094] 2. Dynamic adaptive fusion of spatiotemporal information is achieved, improving the predictive sensitivity for unsteady evolution: Compared to existing techniques that simply stack spatiotemporal modules or use global Fourier transform, this proposal's spatiotemporal cross-attention mechanism achieves efficient fusion of spatiotemporal features. In regions of drastic flow field changes, the model automatically assigns higher attention to historical evolution information through attention weights and gating parameters, while maintaining structural stability in stable regions. This dynamic on-demand retrieval mechanism significantly improves adaptability to complex unsteady flows.

[0095] 3. This proposal addresses the problem of poor generalization ability of purely data-driven models under unseen physical conditions: Existing purely data-driven models typically use physical parameters as ordinary input channels, making it difficult for the model to distinguish between "physical laws" and "operating conditions," leading to prediction failures in scenarios outside the parameter distribution. This proposal, based on causal inference, implements explicit intervention of physical parameters through the AdaLN mechanism. During training, the model learns how physical parameters specifically change the distribution of flow field characteristics. Therefore, when testing new operating conditions, only new parameters need to be input to generate a high-precision flow field that conforms to the physical characteristics of that condition.

[0096] 4. It ensures a high degree of physical consistency in the generated flow field, avoiding "non-physical illusions": While existing diffusion models generate visually realistic flow fields, they often violate fundamental physical laws. This proposal employs a distillation architecture of "physics teacher + parameter student," transferring the constraints of the Navier-Stokes equations to the student network through knowledge distillation. This is equivalent to implanting a "physical kernel" into the generative model, ensuring that the prediction results numerically and rigorously approximate the solutions to the fluid dynamics equations, thus possessing reliable engineering application value. Attached Figure Description

[0097] Figure 1 This invention proposes an unsteady flow field prediction architecture based on the front-door adjustment causality theory.

[0098] Figure 2 This is the overall prediction flowchart of the present invention. Detailed Implementation

[0099] All features disclosed in this specification, or steps in all methods or processes disclosed herein, may be combined in any way, except for mutually exclusive features and / or steps.

[0100] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0101] In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a predetermined orientation, or be constructed and operated in a predetermined orientation. Therefore, they should not be construed as limitations on this invention.

[0102] Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature.

[0103] Example 1

[0104] like Figures 1-2 As shown, the present invention provides a technical solution:

[0105] A framework for predicting unsteady aerodynamics driven by the synergistic interaction of physical information and causal relationships, specifically comprising the following steps:

[0106] Step 1: Construct a spatiotemporal dataset of unsteady flow fields under multiple physical conditions.

[0107] Step 1.1: Use a computational fluid dynamics (CFD) solver to generate or collect multiple sets of unsteady flow field numerical simulation data, each set of data corresponding to a specific physical condition;

[0108] Step 1.2: Based on the data obtained in Step 1.1, preprocess the data, extract a fixed-length time window, and form a historical flow field sequence. and the corresponding future flow field truth value ,in To input the time step, The number of physical quantity channels. , Spatial resolution;

[0109] Step 1.3: Based on each flow field sequence in Step 1.2, label its corresponding k-dimensional physical condition parameters. (such as Reynolds number) ,Mach number (etc.), ultimately obtaining the training dataset. ,in , and Let represent the i-th historical flow field sequence and the corresponding physical condition parameters and the true value of the future flow field, respectively, and N be the total number of samples.

[0110] Step 2: Construct an unsteady flow field prediction architecture based on front-door adjusted causal theory.

[0111] Step 2.1: Construct a structural causal model (SCM) and define the historical flow field as the dependent variable. The true value of the future flow field is defined as the result variable. Unobserved physical environmental disturbances are defined as confounding factors. ;

[0112] Step 2.2: Based on the front-door adjustment theory, define a potential spatiotemporal feature that conforms to the laws of physical partial differential equations. As a mediating proxy variable to block confounding factors Interference with causal pathways;

[0113] Step 2.3: Based on the proxy variables defined in Step 2.2 Design an "upstream teacher network" to be used to learn from... Feature extraction And designed a "downstream student network" for use based on physical condition parameters. right Intervention and prediction .

[0114] Step 3: Construct an upstream physics teacher network. This step aims to build a network structure that can capture the global spatiotemporal evolution.

[0115] Step 3.1: Convert the historical flow field sequence from Step 1.2 into a sequence. Divided in spatial dimension There are 3 non-overlapping patches, each patch being 1000 pixels in size. And after flattening each generated tile, the feature dimension is mapped to... The token sequence;

[0116] Step 3.2: Add spatiotemporal location encoding; add a learnable spatial location encoding to each token in the token sequence generated in Step 3.1. and time location encoding To preserve geometric and temporal information;

[0117] Step 3.3: Construct a Transformer encoder; input the token sequence processed in Step 3.2 into a multi-layer Transformer encoder, use a multi-head self-attention mechanism to calculate global associations, and output a high-dimensional latent feature sequence. ,in The sequence length;

[0118] Step 3.4: Decouple spatiotemporal feature representation; using three independent linear transformation matrices The feature sequence output in step 3.3 This is mapped to three sets of vectors along the channel dimension:

[0119]

[0120] in, The spatial query vector represents the spatial structure at the current moment. The temporal key vector represents the evolutionary pattern at a historical moment. The temporal value vector represents specific evolutionary feature values.

[0121] Step 3.5: Calculate the spatiotemporal attention weight matrix; calculate the values ​​in step 3.4. and The correlation between the two;

[0122]

[0123] in, This is the spatiotemporal attention weight matrix; Indicates matrix transpose; This is a scaling factor for the feature dimension of the key vector, used to prevent the gradient from vanishing due to an excessively large dot product; It is a normalized exponential function;

[0124] Step 3.6: Aggregate spatiotemporal evolution features; combine the features obtained in Step 3.5... Compared with the time value vector in step 3.4 Multiplying them yields a feature vector containing historical evolution information;

[0125]

[0126] in, It is a contextual evolution feature after spatiotemporal interaction aggregation, containing historical evolution information most relevant to the current spatial state;

[0127] Step 3.7: Adaptive feature fusion; introducing learnable gating parameters The evolutionary features obtained in step 3.6 Compared with the high-dimensional latent feature sequence output before step 3.5 Perform residual connections to obtain the final evolutionary features;

[0128]

[0129] in, Characteristics of teachers;

[0130] Step 3.8: Construct the Transformer decoder. This involves converting the features output from Step 3.7... Map back to the Token space and reassemble it into the predicted flow field through a de-blocking operation. .

[0131] Step 4: Definition of loss function for upstream teacher network and optimization of network training; This step aims to train the teacher network through physical constraints and self-supervision, so that the teacher network can learn the basic physical laws of the flow field.

[0132] Step 4.1: Define the reconstruction loss function ; Calculate the predicted flow field output in step 3.8 Compared with the true values ​​of the flow field in step 1.2 The mean square error (MSE) between the two is used to constrain the model's reconstruction capability and ensure that the model can learn the flow field characteristics;

[0133] Step 4.2: Define the physical constraint loss function The physical constraint loss function based on the Navier-Stokes equations is adopted. Step 3.8: Predict the flow field The momentum residuals and mass residuals;

[0134] Step 4.3: Construct the total loss function for the teacher network; introduce weight coefficients. The reconstruction loss defined in step 4.1 and the physical constraint loss defined in step 4.2 are weighted and summed, as shown in the formula:

[0135]

[0136] Step 4.4: Perform teacher network training; based on the total loss function in Step 4.3. The backpropagation algorithm is used to optimize the parameters of the teacher network constructed in step 3, and the teacher network parameters are frozen after optimization.

[0137] Step 5: Construct the downstream student network; This step constructs a parameterized diffusion Transformer model as the student network and inherits the capabilities of the teacher network through a knowledge distillation strategy.

[0138] Step 5.1: Construct an environmental parameter mapping network; use a multilayer perceptron (MLP) to receive the physical condition parameters labeled in step 1.3. Map it to a dimension of Environmental feature vector ;

[0139] Step 5.2: Construct the time step embedding module; use sinusoidal position coding to spread the time steps. Encoded as a temporal embedding vector ;

[0140]

[0141] in, Index representing the dimension of a vector .

[0142] Step 5.3: Generate adaptive normalization parameters; convert the output of Step 5.1... Compared with the output of step 5.2 The data is then stitched together, and the scaling factor is derived through linear layer regression of the MLP. and bias factor ;

[0143]

[0144] in, This is a vector concatenation operation; It is the Sigmoid linear unit activation function; It is a linear fully connected layer; ;

[0145] Step 5.4: Construct the parameterized Transformer module; introduce adaptive layer normalization (AdaLN(x)) into the Transformer layer, using the generated in Step 5.3. and Features of the input Modulation:

[0146]

[0147] Among them, features This represents the sequence of intermediate feature tokens within the Transformer module, before entering the self-attention mechanism. Indicates standard layer normalization; This indicates element-wise multiplication;

[0148] Step 5.5: Perform teacher feature extraction; input the historical flow field sequence from Step 1 into the upstream teacher network with frozen parameters from Step 4.4, and extract the teacher features output from Step 3.7. ;

[0149] Step 5.6: Perform student feature extraction; input the noisy flow field latent variables into the downstream student network and extract the feature output of its Transformer intermediate layer. .

[0150] Step 5.7: Construct the feature alignment layer. Introduce a linear projection layer to align the features from step 5.6. Mapped to step 5.5 The same dimension is denoted as the aligned student feature. .

[0151] Step 6: Definition and joint optimization of the loss function of the downstream student network. This step optimizes the student network by jointly using distillation and diffusion losses.

[0152] Step 6.1: Define the feature knowledge distillation loss function L KD ; Calculate the teacher features extracted in step 5.5 Student characteristics aligned with step 5.7 The Euclidean distance between them is given by the formula:

[0153]

[0154] Step 6.2: Define the diffusion generation loss function L diff ; Calculate the noise predicted by the student network based on the modulation features from step 5.4. With sampled Gaussian noise The mean square error between them is given by the formula:

[0155]

[0156] in, It is Gaussian noise. Noise predicted for student networks For a moment The noise-adding characteristics, This represents the initial flow field state;

[0157] Step 6.3: Construct the total loss function L of the student network student Introducing distillation weighting coefficient Combining the diffusion generation loss defined in step 6.2 with the knowledge distillation loss defined in step 6.1, the formula is:

[0158]

[0159] Step 6.4: Jointly optimize the student network; calculate the total loss function of the student network. To optimize the student network so that it can simultaneously grasp the laws of physical evolution and the ability to control parameters.

[0160] This scheme employs a two-stage prediction architecture for unsteady flow fields based on causal front-door adjustment theory. The architecture, constructed in step 2, decouples the flow field prediction into two independent stages: the first stage utilizes an upstream teacher network as a causal agent to extract general physical evolution features independent of the environment through physical constraints; the second stage utilizes a downstream student network to causally intervene in these features based on physical parameters. This architecture effectively blocks interference from environmental confounding factors and achieves precise decoupling of the causal relationship between physical parameters and flow field evolution.

[0161] This scheme is a dynamic evolution method based on spatiotemporal cross-attention using Transformer. Specifically, in the feature processing logic of steps 3.4 to 3.7, Transformer features are explicitly decoupled into "spatial query vector (Query)" and "temporal value vector (Key / Value)". In step 3.5, the correlation between spatial structure and historical evolution trend is calculated; and in step 3.7, learnable gating parameters are introduced, ultimately realizing a technical solution for adaptive spatiotemporal feature residual fusion based on the real-time state of the flow field.

[0162] Meanwhile, this scheme employs a physics-prior-driven feature-level knowledge distillation strategy: in step 6, the teacher network "internalizes" physical laws into physical knowledge in the feature space and transmits this knowledge to the generative model. Specifically, during teacher network training, the reconstruction loss and Navier-Stokes physics residual loss are fused; the student network, by minimizing the feature distillation loss, forces its intermediate layer features to approximate the feature manifold containing physical conservation laws in the teacher network, thereby endowing the generative model with physical consistency without increasing the computational cost of inference.

[0163] Meanwhile, this scheme is an adaptive normalization (AdaLN) mechanism with explicit intervention of physical parameters: the parameter control logic implemented in steps 5.3 and 5.4. Specifically, it uses MLP to map physical condition parameters and time steps to scaling and bias factors of the normalization layer, and directly modulates the hidden state characteristics inside the Transformer through affine transformation, thereby realizing explicit causal intervention of physical parameters on the flow field generation process.

[0164] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting unsteady aerodynamics driven by the synergistic interaction of physical information and causal relationships, characterized in that: Includes the following steps: Step 1: Construct a spatiotemporal dataset of unsteady flow fields under multiple physics conditions; Step 2: Construct an unsteady flow field prediction architecture based on front-door adjusted causal theory; Step 2 specifically includes the following steps: Step 2.1: Construct a structural causal model, defining the historical flow field as the dependent variable. The true value of the future flow field is defined as Unobserved physical environmental disturbances are defined as confounding factors. ; Step 2.2: Based on the front-door adjustment theory, define a potential spatiotemporal feature that conforms to the laws of physical partial differential equations. As a mediating proxy variable to block confounding factors Interference with causal pathways; Step 2.3: Based on the proxy variables defined in Step 2.2 Design an "upstream teacher network" to be used to learn from... Feature extraction And designed a "downstream student network" for use based on physical condition parameters. right Intervention and prediction ; Step 3: Construct an upstream physics teacher network to create a network structure capable of capturing global spatiotemporal evolution patterns; Step 3 includes the following steps: Step 3.1: Convert the historical flow field sequence from Step 1.2 into a sequence. Divided in spatial dimension Each generated patch consists of non-overlapping tiles, and after flattening, the feature dimension of each tile is mapped to... The token sequence; Step 3.2: Add spatiotemporal location encoding; Step 3.3: Construct the Transformer encoder; Step 3.4: Decouple spatiotemporal feature representation; Step 3.5: Calculate the spatiotemporal attention weight matrix; Step 3.6: Aggregate spatiotemporal evolution features; Step 3.7: Adaptive feature fusion; Step 3.8: Build the Transformer decoder; Step 4: Define the loss function of the upstream teacher network and optimize network training; train the teacher network through physical constraints and self-supervision so that the teacher network can learn the basic physical laws of the flow field; Step 5: Construct the downstream student network; Construct a parameterized diffusion Transformer model as the student network, and inherit the capabilities of the teacher network through a knowledge distillation strategy; Step 6: Define and jointly optimize the loss function of the downstream student network by jointly optimizing the student network through distillation and diffusion losses.

2. The unsteady aerodynamic prediction method driven by the synergistic interaction of physical information and causal relationships as described in claim 1, characterized in that: Step 1 specifically includes the following steps: Step 1.1: Use a computational fluid dynamics solver to generate or collect multiple sets of unsteady flow field numerical simulation data, each set of data corresponding to a specific physical condition; Step 1.2: Based on the data obtained in Step 1.1, preprocess the data, extract a fixed-length time window, and form a historical flow field sequence. and the corresponding true values ​​of the future flow field ,in To input the time step, The number of physical quantity channels. , Spatial resolution; Step 1.3: Based on each flow field sequence in Step 1.2, label its corresponding k-dimensional physical condition parameters. Finally, the training dataset is obtained. ,in , and Let represent the i-th historical flow field sequence and the corresponding physical condition parameters and the true value of the future flow field, respectively, and N be the total number of samples.

3. The unsteady aerodynamic prediction method driven by the synergistic effect of physical information and causal relationships as described in claim 2, characterized in that: Step 3 specifically includes the following steps: Step 3.1: Convert the historical flow field sequence from Step 1.2 into a sequence. Divided in spatial dimension There are 3 non-overlapping tiles, each tile being 1000 square meters in size. And after flattening each generated tile, the feature dimension is mapped to... The token sequence; Step 3.2: For each token in the token sequence generated in Step 3.1, add a learnable spatial location code. and time location encoding ; Step 3.3: Input the token sequence processed in Step 3.2 into a multi-layer Transformer encoder, use a multi-head self-attention mechanism to calculate global associations, and output a high-dimensional latent feature sequence. ,in The sequence length; Step 3.4: Using three independent linear transformation matrices The high-dimensional latent feature sequence output from step 3.3 will be used. This is mapped to three sets of vectors along the channel dimension: in, The spatial query vector represents the spatial structure at the current moment. The time key vector represents the evolutionary pattern of a historical moment; This represents a time value vector, which represents specific evolutionary feature values; Step 3.5: Calculate the values ​​in step 3.4 and The correlation between the two; in, This is the spatiotemporal attention weight matrix; Indicates matrix transpose; This is a scaling factor for the feature dimension of the key vector, used to prevent the gradient from vanishing due to an excessively large dot product; It is a normalized exponential function; Step 3.6: Apply the spatiotemporal attention weight matrix obtained in Step 3.5 Compared with the time value vector in step 3.4 Multiplying them yields a feature vector containing historical evolution information; in, It is a contextual evolution feature after spatiotemporal interaction aggregation, containing historical evolution information most relevant to the current spatial state; Step 3.7: Introduce gating parameters The evolutionary features obtained in step 3.6 Compared with the high-dimensional latent feature sequence output before step 3.5 Perform residual connections to obtain the final evolutionary features; in, Characteristics of teachers; Step 3.8: Extract the features output from Step 3.7 Mapped back to the Token space and reassembled into the predicted flow field through a de-blocking operation. .

4. The unsteady aerodynamic prediction method driven by the synergistic effect of physical information and causal relationships as described in claim 3, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Define the reconstruction loss function ; Step 4.2: Define the physical constraint loss function ; Step 4.3: Based on the reconstruction loss function and physical constraint loss function Constructing the total loss function of the teacher network ; Step 4.4: Conduct online training for teachers.

5. The unsteady aerodynamic prediction method driven by the synergistic effect of physical information and causal relationships as described in claim 4, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Calculate the predicted flow field output from Step 3.8 Compared with the true value of the future flow field in step 1.2 The mean squared error between them yields the reconstruction loss function. This is used to constrain the model's reconstruction capability and ensure that the model can learn the flow field characteristics; Step 4.2: Employ the physical constraint loss function based on the Navier-Stokes equations. Step 3.8: Predict the flow field The momentum residuals and mass residuals are obtained; the physical constraint loss function is then derived. ; Step 4.3: Introduce weighting coefficients The reconstruction loss function defined in step 4.1 The physical constraint loss function defined in step 4.2 By performing a weighted summation, we obtain the total loss function of the teacher network. The formula is: Step 4.4: Teacher Network Total Loss Function Based on Step 4.3 The backpropagation algorithm is used to optimize the parameters of the teacher network constructed in step 3, and the teacher network parameters are frozen after optimization.

6. The unsteady aerodynamic prediction method driven by the synergistic effect of physical information and causal relationships as described in claim 5, characterized in that: Step 5 includes the following steps: Step 5.1: Construct an environmental parameter mapping network; Step 5.2: Construct the time step embedding module; Step 5.3: Generate adaptive normalization parameters; Step 5.4: Construct the parameterized Transformer module; Step 5.5: Perform teacher feature extraction; Step 5.6: Perform student feature extraction; Step 5.7: Construct the feature alignment layer.

7. The unsteady aerodynamic prediction method driven by the synergistic effect of physical information and causal relationships as described in claim 6, characterized in that: Step 5 specifically includes the following steps: Step 5.1: Receive the physical condition parameters marked in Step 1.3 using a multilayer perceptron. Map it to a dimension of Environmental feature vector ; Step 5.2: Use sinusoidal position encoding to divide the diffusion time step Encoded as a temporal embedding vector ; in, Index representing the dimension of a vector ; Step 5.3: The output of Step 5.1 Compared with the output of step 5.2 The data is stitched together, and the scaling factor is obtained by regression through the linear layer of a multilayer perceptron. and bias factor ; in, This is a vector concatenation operation; It is the Sigmoid linear unit activation function; It is a linear fully connected layer; ; Step 5.4: Introduce an adaptive layer normalized AdaLN(x) into the Transformer layer, using the value generated in Step 5.

3. and Features of the input Modulation: Among them, features This represents the sequence of intermediate feature tokens within the Transformer module, before entering the self-attention mechanism. Indicates standard layer normalization; This indicates element-wise multiplication; Step 5.5: Input the historical flow field sequence from Step 1 into the upstream teacher network with frozen parameters from Step 4.4, and extract the teacher features output from Step 3.

7. ; Step 5.6: Input the noisy flow field latent variables into the downstream student network and extract the feature output of its Transformer intermediate layer. ; Step 5.7: Introduce a linear projection layer to transform the process in Step 5.

6. Mapped to step 5.5 The same dimension is denoted as the aligned student feature. .

8. The unsteady aerodynamic prediction method driven by the synergistic effect of physical information and causal relationships as described in claim 7, characterized in that: Step 6 specifically includes the following steps: Step 6.1: Define the feature knowledge distillation loss function L KD ;Calculate the teacher features extracted in step 5.5 Student characteristics aligned with step 5.7 The Euclidean distance between them yields the feature knowledge distillation loss function, which is formulated as follows: ; Step 6.2: Define the diffusion generation loss function L diff ; Calculate the noise predicted by the student network based on the modulation features from step 5.

4. With sampled Gaussian noise The mean square error between the two values ​​yields the diffusion generation loss function, which is expressed as follows: ; in, It is Gaussian noise. Noise predicted for student networks For a moment The noise-adding characteristics, This represents the initial flow field state; Step 6.3: Construct the total loss function L of the student network student Introducing distillation weighting coefficient Combining the diffusion generation loss function defined in step 6.2 with the knowledge distillation loss function defined in step 6.1, we obtain the total loss function of the student network, as shown in the formula: ; Step 6.4: Jointly optimize the student network by calculating the total loss function of the student network. To optimize the student network so that it can simultaneously grasp the laws of physical evolution and the ability to control parameters.

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