Space-time high resolution reconstruction method for fluid data with unknown boundary and initial conditions

Abstract

The application belongs to the technical field of deep learning, and discloses a method for high-resolution reconstruction of fluid data in space-time with unknown boundary and initial conditions. The method determines the data source for processing the convection fluid data, and pre-processes the obtained data set. The method uses a feature extraction network to extract the implicit relationship between space and time between coordinates from the input low-resolution convection fluid data, and constructs a low-resolution implicit feature interpolatable grid. Based on the constructed low-resolution implicit feature interpolatable grid, the method obtains a fluid implicit high-resolution feature grid through trilinear interpolation processing. The fluid implicit high-resolution feature grid is decoded into original fluid physical features on each coordinate through a physical constraint network, so as to output high-resolution fluid data. The application realizes high-resolution construction of convection fluid in augmented reality.

Description

Technical Field

[0001] This invention belongs to the field of deep learning technology and relates to a physically constrained Transformer framework for spatiotemporal super-resolution of fluid data, particularly a method for spatiotemporal high-resolution reconstruction of fluid data with unknown boundaries and initial conditions. Background Technology

[0002] Modeling dynamic processes in high-resolution spatiotemporal data across continuous spatiotemporal scales is a fundamental task in science and engineering fields such as climate systems, physical oceanography, and fluid mechanics. This work plays a crucial role in understanding and reasoning about the natural physical world. Scientists attempt to model these processes in principle using conservation laws and physical laws, namely partial differential equations (PDEs), and further simulate these behaviors using computational devices. To this end, computational fluid dynamics (CFD) has become a powerful tool for numerically solving various PDEs over the past few decades. However, traditional CFD schemes are purely based on physical properties: solving step-by-step through grid-based numerical discretization or integration schemes, such as the finite difference method (FDM) and the finite element method (FEM). These methods are extremely time-consuming and require significant computational resources and expertise. In recent years, deep learning methods have achieved great success in accelerating the processing of computationally intensive scientific problems. Therefore, researchers have begun to replace parts of the solution process in CFD schemes with deep learning methods to improve the computational efficiency of numerical results and reduce computational costs. Hybrid learning simulations of physical constraints can be useful for real-world processes where the physical model, parameters, or boundary conditions are not fully known. When dealing with flow problems, only a handful of methods can simultaneously consider both physical principles and observed characteristics.

[0003] Therefore, handling flow simulations in marine and atmospheric sciences with uncertain boundaries and initial conditions presents new challenges that traditional spatiotemporal high-resolution methods lack. First, deep neural networks must be carefully designed to extract the intrinsic statistical correlations between pairs of low-resolution and high-resolution flow data during training. Second, the network should incorporate physical constraints to track the physical properties of partial differential equations on fine-scale grids. Finally, a successful STSR model should be able to handle flow dynamics under unknown boundaries and initial conditions and effectively represent high-resolution outputs.

[0004] Currently, there is no method that can reconstruct high-resolution spatiotemporal methods in ocean and atmospheric sciences by handling flow simulations with uncertain boundaries and initial conditions, while ensuring good visual effects. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions. Based on a deep learning model, a TransFlowNet network architecture is designed to solve the problem of being unable to handle flow simulations in marine and atmospheric sciences with uncertain boundaries and initial conditions (fluid horizontal motion and convection between horizontal plates with uncertain boundaries and initial conditions) to reconstruct spatiotemporal high-resolution results with physical constraints. This enables the construction of marine and atmospheric science models in augmented reality.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] First, this invention provides a method for high-resolution spatiotemporal reconstruction of fluid data with unknown boundaries and initial conditions, comprising the following steps:

[0008] Step 1: Determine the dataset for convective fluid data processing, including temperature, pressure, and velocity, and preprocess the dataset to obtain a low-resolution convective fluid dataset.

[0009] Step 2: Use a feature extraction network to extract the implicit spatial and temporal relationships between coordinates from the input low-resolution convective fluid data, and construct a low-resolution implicit feature interpolation grid.

[0010] Step 3: Based on the constructed low-resolution implicit feature interpolable mesh, a fluid implicit high-resolution feature mesh is obtained through trilinear interpolation.

[0011] Step 4: The implicit high-resolution feature mesh of the fluid is decoded into the original fluid physical features at each coordinate by the physical constraint network, including temperature, pressure and velocity-related physical features, in order to output high-resolution fluid data.

[0012] Furthermore, the specific steps of step 1 are as follows: First, a high-resolution convective fluid dataset is constructed through numerical simulation, and a low-resolution convective fluid dataset DL is constructed by downsampling the high-resolution convective fluid data in space and time.

[0013] Furthermore, in step 2, a feature extraction network is constructed using deep learning to train low-resolution convective fluid data to generate an implicit feature interpolable grid. This specifically includes the following steps:

[0014] Step 201: Before the training process, the fluid dataset is randomly pruned and augmented to enable the feature extraction network to better adapt to spatial location features, and the velocity, temperature and pressure channels are normalized to eliminate the influence of scale.

[0015] Step 202: The feature extraction network includes a shallow feature network, a deep feature network, and a fusion convolutional layer. The shallow feature network includes several convolutional layers I for extracting shallow physical implicit features. The deep feature network includes three Transformer blocks, two convolutional layers II, four transposed convolutional layers, a convolutional layer III, a residual block, and a multilayer perceptron for extracting deep features and reconstructing fluid implicit features. The specific steps are as follows:

[0016] The feature extraction network extracts shallow physical implicit features of low-resolution fluids, including temperature, pressure, and velocity, through convolutional layer I.

[0017] Based on this, deep features are extracted through a deep feature network. Specifically, deep features are extracted through three Transformer blocks and two convolutional layers II. The physical implicit features of deeper layers are merged through the Transformer blocks to construct a hierarchical feature map.

[0018] In this process, in order to fuse shallow physical implicit features, skip connections are added between the first Transformer block and the second transposed convolutional layer, as well as between the second Transformer block and the first transposed convolutional layer.

[0019] The spatiotemporal structure of low-resolution fluid data is reconstructed using four transposed convolutional layers and two convolutional layers III. A residual block is added between the last two transposed convolutional layers, with each residual block including a convolutional layer, a linear rectified function, and a point addition operation. This approach avoids reducing the correlation of fluid features when reconstructing the spatiotemporal structure of low-resolution fluid data.

[0020] Finally, a multilayer perceptron is used to map the physical features of the spatiotemporal structure of the reconstructed low-resolution fluid data to multidimensional implicit features. Long skip connections connect the physical features of the low-resolution fluid after one convolution with the multidimensional implicit features through the channel dimension. Then, a fusion convolution layer is used to fuse the features, reconstruct the fluid implicit features, and finally form a low-resolution multichannel implicit feature grid.

[0021] Furthermore, the specific steps of step 4 are as follows:

[0022] During network training, spatiotemporal coordinates are randomly extracted from the fluid implicit high-resolution feature grid. A physical constraint network is constructed using a multilayer perceptron to receive the spatiotemporal coordinates and their corresponding implicit features, and output high-resolution fluid data, as well as the partial differential equation loss of the high-resolution fluid data calculated through the fluid nonlinear momentum equation. Backpropagation and parameter updates are used to train the feature extraction network and the physical constraint network, accelerating the network convergence speed and making the output high-resolution fluid data more consistent with physical reality. The implicit physical features Si and their normalized spatiotemporal coordinates Pi of each point are used as input to obtain the high-resolution fluid output, and the following formula is executed:

[0023]

[0024] Where DHR(Pi) is the high-resolution fluid output data at normalized spatiotemporal coordinates Pi, and GHR(Pi) is the physical implicit feature obtained at normalized spatiotemporal coordinates Pi. It reconstructs implicit physical features into high-resolution fluid physics features;

[0025] Through reasoning using a physical constraint network, predicted values ​​of low-resolution fluid physical variables at specific locations in high-resolution fluid data are obtained.

[0026] Furthermore, during training, the loss function is the L1 error loss function. When optimizing network parameters for spatiotemporal super-resolution of fluid data, the loss function includes two parts:

[0027] The first part is the loss between the generated high-resolution fluid data corresponding to the downsampled low-resolution image and the real high-resolution fluid data, defined as regression loss. Regression loss It is the difference between the predicted output data and the actual data;

[0028] Let the data blocks sampled from the training data have a batch size B. For the j-th data block B j The i-th spatiotemporal coordinate P i In high-resolution real fluid data D GT Querying the same location in the middle, regression loss The formula is as follows:

[0029]

[0030] Among them, D HR (Pi) is the normalized spacetime coordinate P i High-resolution fluid output data; D GT (P i ) is the normalized spacetime coordinate P i High-resolution real fluid data;

[0031] The second part, under the control of the fluid nonlinear momentum equation, obtains the loss between the current spatiotemporally predicted physical characteristics and the actual physical characteristics, defined as the partial differential equation loss. This can be calculated using a differentiable multilayer perceptron, for a batch of fluid data blocks, Represented as:

[0032]

[0033] in, These are nonlinear partial differential equations for fluid data;

[0034] Finally, total loss yes and Weighted sum:

[0035]

[0036] Where α is the weight.

[0037] Secondly, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to perform the spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions as described above.

[0038] Compared with the prior art, the advantages of this invention are:

[0039] This invention maps raw physical variables to latent features through a feature extraction network. These features encode the correlations between random data patches, generating a low-resolution implicit feature interpolation grid. Based on the constructed low-resolution implicit feature interpolation grid, a fluid implicit high-resolution feature grid is obtained through trilinear interpolation. The high-resolution feature grid is then processed by a physical constraint network to decode the latent features at each coordinate into raw fluid physical features (temperature, pressure, velocity, etc.) to construct high-resolution output data. This solves the problem of being unable to handle horizontal fluid motion and convection between horizontal plates with uncertain boundaries and initial conditions, in order to reconstruct high-resolution spatiotemporal results of fluid simulations with physical constraints.

[0040] This invention enables a variety of applications and the recovery of a wide range of important physical quantities (e.g., including Rayleigh kinetic energy, Kolmogorov microscale, length gauge, etc.). Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a flowchart of the spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions according to Embodiment 1 of the present invention.

[0043] Figure 2 This is a flowchart of the process of generating implicitly interpolable meshes at low resolution using a feature extraction network in Embodiment 1 of the present invention.

[0044] Figure 3 This is a schematic diagram of Embodiment 1 of the present invention, which uses a physical constraint network to decode latent features into the values ​​of original physical variables in order to construct high-resolution output data for feedback and adjustment.

[0045] Figure 4 This is a schematic diagram of the feature extraction network structure in Embodiment 1 of the present invention;

[0046] Figure 5 This is a visualization result of constructing a high-resolution fluid data velocity component v from low-resolution fluid data according to Embodiment 1 of the present invention. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0048] Example 1

[0049] This embodiment is based on deep learning and designs the TransFlowNet network architecture. Using this network architecture, a spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions is implemented. First, low-resolution data is generated from numerical simulation. The low-resolution data is then converted into an implicit interpolable grid through a feature extraction network. The implicit interpolable grid is then processed by three-dimensional interpolation to obtain a high-resolution grid. Based on a physical constraint network, the implicit features at each coordinate are decoded into the values ​​of the original physical variables to construct high-resolution output data and generate beautiful and accurate spatiotemporal high-resolution results.

[0050] Combination Figures 1-3 As shown, the specific implementation method includes the following steps:

[0051] Step 1: Determine the dataset for convective fluid data processing, including temperature, pressure, velocity, etc., and preprocess the dataset to obtain a low-resolution convective fluid dataset.

[0052] More specifically, the steps of step 1 are as follows: First, a high-resolution convective fluid dataset (Rayleigh-B'enard Convection dataset) is constructed through numerical simulation. Then, a low-resolution convective fluid dataset (DL) is constructed by downsampling the high-resolution convective fluid data in both spatial and temporal dimensions. In this embodiment, downsampling factors of dt=4 and ds=8 are used to create low-resolution convective fluid data in the temporal and spatial dimensions, respectively. dt is the downsampling factor in the time dimension, and ds is the downsampling factor in the spatial dimension.

[0053] Step 2: Use a feature extraction network to extract the implicit spatial and temporal relationships between coordinates from the input low-resolution convective fluid data, and construct a low-resolution implicit feature interpolation grid.

[0054] As a preferred implementation, step 2 involves using deep learning to construct a feature extraction network to train low-resolution convective fluid data to generate an implicit feature interpolable grid, specifically including the following steps:

[0055] Step 201: Before the training process, the fluid dataset is randomly pruned and augmented to enable the feature extraction network to better adapt to spatial location features. The velocity, temperature, pressure and other channels are normalized to eliminate the influence of scale.

[0056] In this practical application, an Adam optimizer with a learning rate of 0.001 and 200 epochs is used. Each epoch contains 3000 randomly pruned data blocks. The batch size is 30. Each implicit feature grid contains 512 sample points. The weighting coefficient α is 0.02. The convective fluid dataset is solved using FDM, employing a common positive time-space center scheme. Considering the Coriolis force, predictions of u and v are first found, and then their values ​​are corrected to include the Coriolis term. Furthermore, this embodiment incorporates wind stress into the flow simulation to better adapt the network model to spatial location characteristics. This is achieved by varying the H value and the amplitude of the wind stress to generate another set of ground-based data for evaluation; and each channel (velocity, temperature, pressure, etc.) is normalized to eliminate scale effects.

[0057] Step 202: The feature extraction network includes a shallow feature network, a deep feature network, and a fusion convolutional layer, such as... Figure 4 As shown, the shallow feature network includes several convolutional layers I, which are used to extract shallow physical implicit features (temperature, pressure, speed, etc.). In this embodiment, the convolutional layers I are illustrated by three 3×3×3 convolutional layers.

[0058] The deep feature network comprises three Transformer blocks, two convolutional layers II, four transposed convolutional layers, a convolutional layer III, a residual block, and a multilayer perceptron, used to extract deep features and reconstruct fluid implicit features. In this embodiment, a 4×4×1 linear embedding layer is first applied, followed by Transformer blocks to extract deep features. A 2×2×2 convolutional layer II is added after each of the first two Transformer blocks. These layers are used to merge features from 4×4×4 to 1×1×1. In other words, the deep feature network sequentially includes Transformer blocks, convolutional layer II (2×2×2), Transformer blocks, convolutional layer II (2×2×2), Transformer blocks, transposed convolution (4×4×4), convolutional layer III (1×1×1), transposed convolution (4×4×4), convolutional layer III (1×1×1), transposed convolution (4×4×4), residual blocks, transposed convolution (4×4×4), and a multilayer perceptron.

[0059] The specific steps are as follows:

[0060] The feature extraction network extracts shallow physical implicit features of low-resolution fluids, including temperature, pressure, and velocity, through convolutional layer I.

[0061] Based on this, deep features are extracted through a deep feature network. Specifically, deep features are extracted through three Transformer blocks and two convolutional layers II. The physical implicit features of deeper layers are merged through the Transformer blocks to construct a hierarchical feature map. The structure and working principle of the Transformer blocks can be referred to existing technologies, and will not be elaborated here.

[0062] In this process, to fuse shallow physical implicit features, skip connections are added between the first Transformer block and the second transposed convolutional layer, and between the second Transformer block and the first transposed convolutional layer. In each connection, features are connected along the channel dimension, and subsequent 1×1×1 convolutional layers III will merge them in an appropriate manner.

[0063] This embodiment reconstructs the spatiotemporal structure of low-resolution fluid data using four transposed convolutional layers and two convolutional layers III (with a kernel of 1). Simultaneously, a residual block is added between the last two transposed convolutional layers. Each residual block includes three convolutional layers (1x1, 3x3, 1x1), a linear rectified function, and a point-addition operation. This avoids the problem of reduced correlation of fluid features when reconstructing the spatiotemporal structure of low-resolution fluid data.

[0064] Finally, a multilayer perceptron is used to map the physical features of the spatiotemporal structure of the reconstructed low-resolution fluid data to multidimensional implicit features. Long skip connections connect the physical features of the low-resolution fluid after one convolution with the multidimensional implicit features through the channel dimension. Then, a fusion convolution layer is used to fuse the features, reconstruct the fluid implicit features, and finally form a low-resolution multichannel implicit feature grid.

[0065] Step 3: Based on the constructed low-resolution implicit feature interpolable mesh, a fluid implicit high-resolution feature mesh is obtained through trilinear interpolation.

[0066] Step 4: The implicit high-resolution feature mesh of the fluid is decoded into the original fluid physical features at each coordinate by the physical constraint network, including temperature, pressure and velocity-related physical features, in order to output high-resolution fluid data.

[0067] As a preferred embodiment, step 4 is as follows:

[0068] Step 401: When training the network, spatiotemporal coordinates are randomly extracted from the fluid implicit high-resolution feature grid. A physical constraint network is constructed using a multilayer perceptron (containing three fully connected layers) to receive the spatiotemporal coordinates and their corresponding implicit features, and output high-resolution fluid data (predicted values) and calculate the partial differential equation loss of the high-resolution fluid data through the fluid nonlinear momentum equation.

[0069] Step 402: Calculate the spatiotemporal partial derivatives of the physical variables and parameter updates through backpropagation. This information is used to train the feature extraction network and the physical constraint network, accelerating network convergence and making the output high-resolution fluid data more consistent with physical reality. When ft, fx, fxx, etc., are obtained, the function F can generate residuals of the PDE to contribute to the physical constraints, which will be used to construct the loss function. Here, F is a nonlinear function of time t and space x. Solve for f and its partial derivatives with respect to t, x, etc. The subscript of f indicates the specific variable of its partial derivative. In particular, fxx represents the second-order partial derivative with respect to x, and so on.

[0070] Step 401 receives implicit coordinates and outputs predicted values. The implicit physical features Si and their normalized spatiotemporal coordinates Pi of each point are used as inputs (Si can be regarded as time-dependent and position-dependent parameters). High-resolution fluid output is obtained by executing the following formula:

[0071]

[0072] Among them, D HR (P i G represents high-resolution fluid output data in normalized spatiotemporal coordinates Pi. HR (P iThis is to obtain the physical implicit features at the normalized spatiotemporal coordinates Pi. It reconstructs implicit physical features into high-resolution fluid physics features.

[0073] This embodiment uses a multilayer perceptron to construct a physical constraint network to generate the final output high-resolution fluid data. Since it does not enforce the use of boundary and initial conditions to assist training, this helps improve the network's versatility across physical systems under different conditions. Through inference by the physical constraint network, predicted values ​​of low-resolution fluid physical variables at specific locations in the high-resolution fluid data are obtained.

[0074] Combination Figure 3 As shown, high-resolution convective fluid data generated through numerical simulation is downsampled to obtain low-resolution fluid data. A high-resolution implicit feature grid is constructed using a feature extraction network. The implicit feature Si of each point and its corresponding normalized spatiotemporal coordinate Pi constitute the input vector, and the formula is executed. Subsequently, through inference via the physical constraint network, the predicted values ​​of low-resolution fluid physical variables at specific locations in the high-resolution fluid data are obtained. The loss function selected during training is the L1 error loss function, which consists of two parts: the arbitrary spatiotemporal derivatives of the output are efficiently calculated via backpropagation of the multilayer perceptron, and the high-resolution implicit feature grid parameters are optimized by minimizing the total loss. Figure 3 In the middle, f i It predicts high-resolution fluid data, where Si is the implicit eigenvector at Pi in the normalized spatiotemporal coordinates of the GHR, and the set of solutions to the nonlinear partial differential equations of the fluid data (f t ,f x ,f xx (,…) is a nonlinear function whose partial derivatives are obtained with respect to time t, space x, etc. In particular, f xx Let x represent the second-order partial derivative, and so on.

[0075] The loss function of this invention is described in detail below:

[0076] The loss function selected during training is the L1 error loss function. When optimizing network parameters for spatiotemporal super-resolution of fluid data, the loss function consists of two parts: the first part is the loss between the generated high-resolution fluid data corresponding to the downsampled low-resolution image and the real high-resolution fluid data. The second part is the loss between the currently predicted physical features and the real physical features obtained in the physically constrained network under the control of the fluid nonlinear momentum equation.

[0077] The loss in the first part is defined as regression loss. Regression loss It represents the difference between the predicted output data and the actual data. Let the data blocks sampled from the training data have a batch size B. For the j-th data block B... j The i-th spatiotemporal coordinate P i In high-resolution real fluid data D GT Querying the same location in the middle, regression loss The formula is as follows:

[0078]

[0079] Among them, D HR (Pi) is the normalized spacetime coordinate P i High-resolution fluid output data; D GT (P i ) is the normalized spacetime coordinate P i High-resolution real fluid data;

[0080] The loss in the second part is defined as the partial differential equation loss. Partial differential equation loss This is the loss between the currently predicted physical characteristics and the actual physical characteristics, which can be calculated using a differentiable multilayer perceptron. Similarly, for a batch of fluid data blocks, Represented as:

[0081]

[0082] in, These are nonlinear partial differential equations for fluid data;

[0083] Finally, total loss yes and Weighted sum:

[0084]

[0085] Where α is the weight.

[0086] The total loss is generated by interpolating the ground truth values ​​of high-resolution fluid data to produce a predictive loss. The gradient from the combined loss can be backpropagated to the feature extraction network for training. Due to the differentiability of the multilayer perceptron, any partial derivative of the output physical quantity with respect to the input spatiotemporal coordinates can be efficiently computed through backpropagation, which can be combined with partial differential equation constraints to produce an equation loss. On the other hand, by interpolating the generated values ​​from the high-resolution fluid data, a comparison can be made with the ground truth values ​​of the fluid data at these locations, thus generating a predictive loss. The gradient from the combined loss can be backpropagated to the network for training, adjusting the offset parameters of the fluid feature extraction network to improve the accuracy of generating high-resolution fluid data.

[0087] Example 2

[0088] The present invention also provides an electronic device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform a method for reconstructing a spatiotemporal high resolution based on a deep learning model as described in the previous embodiment 1, which will not be repeated here.

[0089] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for high-resolution spatiotemporal reconstruction of fluid data with unknown boundaries and initial conditions, characterized in that, Includes the following steps: Step 1: Determine the dataset for convective fluid data processing, including temperature, pressure, and velocity, and preprocess the dataset to obtain a low-resolution convective fluid dataset. Step 2: Use a feature extraction network to extract the implicit spatial and temporal relationships between coordinates from the input low-resolution convective fluid data, and construct a low-resolution implicit feature interpolation grid. Step 3: Based on the constructed low-resolution implicit feature interpolable mesh, a fluid implicit high-resolution feature mesh is obtained through trilinear interpolation. Step 4: The implicit high-resolution feature mesh of the fluid is decoded into the original fluid physical features at each coordinate by the physical constraint network, including temperature, pressure and velocity-related physical features, in order to output high-resolution fluid data.

2. The spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions according to claim 1, characterized in that, The specific steps of step 1 are as follows: First, a high-resolution convective fluid dataset is constructed through numerical simulation. Then, a low-resolution convective fluid dataset (DL) is constructed by downsampling the high-resolution convective fluid data in space and time.

3. The spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions according to claim 1, characterized in that, In step 2, a feature extraction network is constructed using deep learning to train low-resolution convective fluid data to generate an implicit feature interpolable grid. This specifically includes the following steps: Step 201: Before the training process, the fluid dataset is randomly pruned and augmented to enable the feature extraction network to better adapt to spatial location features, and the velocity, temperature and pressure channels are normalized to eliminate the influence of scale. Step 202: The feature extraction network includes a shallow feature network, a deep feature network, and a fusion convolutional layer. The shallow feature network includes several convolutional layers I for extracting shallow physical implicit features. The deep feature network includes three Transformer blocks, two convolutional layers II, four transposed convolutional layers, a convolutional layer III, a residual block, and a multilayer perceptron for extracting deep features and reconstructing fluid implicit features. The specific steps are as follows: The feature extraction network extracts shallow physical implicit features of low-resolution fluids, including temperature, pressure, and velocity, through convolutional layer I. Based on this, deep features are extracted through a deep feature network. Specifically, deep features are extracted through three Transformer blocks and two convolutional layers II. The physical implicit features of deeper layers are merged through the Transformer blocks to construct a hierarchical feature map. In this process, in order to fuse shallow physical implicit features, skip connections are added between the first Transformer block and the second transposed convolutional layer, as well as between the second Transformer block and the first transposed convolutional layer. The spatiotemporal structure of low-resolution fluid data is reconstructed using four transposed convolutional layers and two convolutional layers III. A residual block is added between the last two transposed convolutional layers, with each residual block including a convolutional layer, a linear rectified function, and a point addition operation. This approach avoids reducing the correlation of fluid features when reconstructing the spatiotemporal structure of low-resolution fluid data. Finally, a multilayer perceptron is used to map the physical features of the spatiotemporal structure of the reconstructed low-resolution fluid data to multidimensional implicit features. Long skip connections connect the physical features of the low-resolution fluid after one convolution with the multidimensional implicit features through the channel dimension. Then, a fusion convolution layer is used to fuse the features, reconstruct the fluid implicit features, and finally form a low-resolution multichannel implicit feature grid.

4. The spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions according to claim 1, characterized in that, The specific steps for step 4 are as follows: During network training, spatiotemporal coordinates are randomly extracted from the fluid implicit high-resolution feature grid. A physical constraint network is constructed using a multilayer perceptron to receive the spatiotemporal coordinates and their corresponding implicit features, and output high-resolution fluid data, as well as the partial differential equation loss of the high-resolution fluid data calculated through the fluid nonlinear momentum equation. Backpropagation and parameter updates are used to train the feature extraction network and the physical constraint network, accelerating the network convergence speed and making the output high-resolution fluid data more consistent with physical reality. The implicit physical features Si and their normalized spatiotemporal coordinates Pi of each point are used as input to obtain the high-resolution fluid output, and the following formula is executed: Among them, D HR (P i G represents high-resolution fluid output data in normalized spatiotemporal coordinates Pi. HR (P i This is to obtain the physical implicit features at the normalized spatiotemporal coordinates Pi. It reconstructs implicit physical features into high-resolution fluid physics features; Through reasoning using a physical constraint network, predicted values ​​of low-resolution fluid physical variables at specific locations in high-resolution fluid data are obtained.

5. The spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions according to claim 1, characterized in that, During training, the loss function is the L1 error loss function. When optimizing network parameters for spatiotemporal super-resolution of fluid data, the loss function consists of two parts: The first part is the loss between the generated high-resolution fluid data corresponding to the downsampled low-resolution image and the real high-resolution fluid data, defined as regression loss. Regression loss It is the difference between the predicted output data and the actual data; Let the data blocks sampled from the training data have a batch size B. For the j-th data block B j The i-th spatiotemporal coordinate P i In high-resolution real fluid data D GT Querying the same location in the middle, regression loss The formula is as follows: Among them, D HR (Pi) is the normalized spacetime coordinate P i High-resolution fluid output data; D GT (P i ) is the normalized spacetime coordinate P i High-resolution real fluid data; The second part, under the control of the fluid nonlinear momentum equation, obtains the loss between the current spatiotemporally predicted physical characteristics and the actual physical characteristics, defined as the partial differential equation loss. This can be calculated using a differentiable multilayer perceptron, for a batch of fluid data blocks, Represented as: in, These are nonlinear partial differential equations for fluid data; Finally, total loss yes and Weighted sum: Where α is the weight.

6. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the spatiotemporal high-resolution reconstruction method for fluid data with unknown boundaries and initial conditions as described in any one of claims 1-5.

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