Spatial compression method for large-scale fine three-dimensional flow field in situ calculation

Abstract

The application discloses a method for spatial compression of large-scale fine three-dimensional flow field in situ computing on the way, comprising: building an in situ computing environment on the way, dividing computers in proportion; a part of computers is used for marking a region of interest, compressing flow field data, constructing a spatial super-resolution network, and establishing a mapping relationship between the compressed flow field and the original flow field; another part of computers is used for decompressing three-dimensional flow field data by using the spatial super-resolution network. The application relieves the computer input / output speed and storage limitations in the storage and analysis process based on the in situ computing environment on the way, and compresses and decompresses the data volume under the condition of ensuring the overall situation and the fine degree of the region of interest of the user for the large-scale fine spatial steady flow field which does not change with time. The application learns and restores the overall characteristics of the original data, and the generated flow line vortex position and speed change trend are basically consistent, and the decompression degree of the original data is high.

Description

Technical Field

[0001] This invention belongs to the field of fluid dynamics analysis, and more specifically, relates to a spatial compression and decompression method for a three-dimensional flow field based on an in-situ calculation environment. Background Technology

[0002] With the development of computer simulation technology, the scale of flow field data is constantly increasing, and the level of detail in this data is also steadily improving. Scientists increasingly need to manipulate large-scale, fine-grained steady-state flow fields. Traditional data preprocessing and visualization are mostly post-processing methods, where the computer saves the simulation results to disk, and then reads the data from the disk when visualization is needed. To reduce the amount of data transmitted, only low-precision flow field data is usually saved, resulting in the loss of accurate flow field information. Therefore, a method that can analyze and visualize flow field results in situ is urgently needed.

[0003] On the other hand, current research on the compression and decompression of large-scale, high-resolution 3D flow field data is mostly applied to 2D data. When using these methods to compress and decompress flow field data, details of various physical quantities contained in the flow field are lost. Since flow field data often operates on velocity vector fields, and streamlines are generated through line integration during visualization, the visualization results of flow field data are worse than those of decompressed 2D images when details are lost. Therefore, a method that allows users to save low-precision, large-scale, high-resolution 3D flow field data to more accurately obtain the overall and local situation of the dataset and perform holistic analysis of the dataset is currently a hot research topic.

[0004] In summary, large-scale, fine-grained steady-state flow fields not only pose challenges to computer input / output speed and storage capacity, but also to the compression of the overall flow field situation and the preservation of the local situation in the region of interest to the user. Summary of the Invention

[0005] The purpose of this invention is to propose a spatial compression method for large-scale, fine-grained three-dimensional flow fields under in-situ computation. For large-scale, fine-grained, steady-state spatial flow fields that do not change over time, the method compresses and decompresses the data while ensuring the overall situation and the fineness of the region of interest to the user. This solves the problems of input / output speed limitations and low storage precision that occur in the storage and analysis of large-scale, fine-grained three-dimensional flow fields in the prior art.

[0006] Firstly, a spatial compression method for large-scale, fine-grained three-dimensional flow fields under in-situ calculations is provided, including:

[0007] The original three-dimensional flow field data at the first resolution level is subjected to dimensionality reduction processing to obtain three-dimensional flow field data at the second resolution level, where the first resolution level is higher than the second resolution level.

[0008] Training a spatial super-resolution network using the second-resolution-level 3D flow field data specifically includes inputting the second-resolution-level 3D flow field data into the spatial super-resolution network to be trained to obtain the first-resolution-level 3D flow field estimation data. The 3D flow field estimation data is the prediction data based on the original 3D flow field data, and the parameters of the spatial super-resolution network are adjusted through a loss function.

[0009] In conjunction with the first aspect, in some implementations of the first aspect, the spatial super-resolution network includes a generator G and a discriminator D.

[0010] The generator G is used to generate corresponding single-time-step prediction data based on the input single-time-step data;

[0011] The discriminator D is used to match the predicted data with the original data in order to adjust the parameters of the spatial super-resolution network.

[0012] In conjunction with the first aspect, in some implementations of the first aspect, the generator G includes a global network. The input of the global network is the three-dimensional flow field data at the second resolution level. The global network adopts a skip-link approach, first passing through three residual blocks with a convolution kernel size of 3×3×3, padding of 1, and stride of 1; then passing through a deconvolution DeConv layer with a convolution kernel size of 4×4×4, stride of 2, and padding of 0; then passing through two residual blocks, one deconvolution DeConv layer, two residual blocks, and one hyperbolic tangent function before output. The residual blocks consist of two parts: one part consists of three convolutional layers, where spectral normalization (SN) and instance normalization (IN) are performed after the first two convolutional layers, except for the last convolutional layer which only requires spectral normalization; the other part consists of only one convolutional layer and one spectral normalization layer. Before output, the results of the two parts of the residual block need to be added at corresponding positions.

[0013] In conjunction with the first aspect, in some implementations of the first aspect, the method includes:

[0014] A user-defined region of interest is extracted from the original three-dimensional flow field data to obtain the three-dimensional flow field data of the region of interest, wherein the resolution level of the three-dimensional flow field data of the region of interest is the first resolution level;

[0015] The three-dimensional flow field data of the region of interest is input into the spatial super-resolution network to be trained, so as to complete the training of the spatial super-resolution network.

[0016] In conjunction with the first aspect, in some implementations of the first aspect, the generator G further includes a local network. The input of the local network is local region data in the original three-dimensional flow field data at the first resolution level, and the local region data is data of the region of interest to the user. The local network adopts a convolutional neural network structure, first transforming the local region data into a 256×1×1×1 feature map through residual blocks, and without using fully connected layers and upsampling, restoring the feature map to its original size through deconvolutional layers, and calculating the loss accordingly.

[0017] In conjunction with the first aspect, in some implementations of the first aspect, in the discriminator D, except for the last convolutional layer, the kernel size of each other convolutional layer is 4×4×4, the stride is 2, the padding is 1, the stride of the last convolutional layer is 0, and each convolutional layer is followed by a spectral normalization layer and a leaky corrected linear unit layer.

[0018] In conjunction with the first aspect, in some implementations of the first aspect, the loss function of the spatial super-resolution network includes an adversarial loss function, which satisfies:

[0019]

[0020]

[0021] in, To minimize the loss of generator G, To obtain the expected operation, V represents the original data, V L Given low-resolution input data, D(·) is a function of the discriminator D, and G(·) is a function of the generator G. To minimize the loss of the discriminator D, To obtain the expected operation, V represents the original data, V H Given high-resolution input data, D(·) is a function of the discriminator D, and V L Given low-resolution input data, G(·) is a function of the generator G.

[0022] In conjunction with the first aspect, in some implementations of the first aspect, the loss function of the spatial super-resolution network includes a volumetric loss function, which satisfies:

[0023]

[0024] in, For volume loss, To obtain the expected operation, V′ is the data generated by the generator, V L The input is low-resolution data, where V represents the original data.H Given high-resolution input data, G(·) is a function of the generator G, and ||·|| is the L2 normal form.

[0025] In conjunction with the first aspect, in some implementations of the first aspect, the loss function of the spatial super-resolution network includes a feature loss function, which satisfies:

[0026]

[0027] in, For feature loss, To obtain the expected operation, V′ is the data generated by the generator, V L The input is low-resolution data, where V represents the original data. H Given high-resolution input data, N is the total number of convolutional layers in the discriminator D, and k represents the k-th convolutional layer. k F represents the number of elements in the k-th convolutional layer. k G represents the features extracted by the k-th convolutional layer in the discriminator D, G(·) is a function of the generator G, and ||·|| is the L2 norm.

[0028] In conjunction with the first aspect, in some implementations of the first aspect, the loss function of the spatial super-resolution network includes a local loss function, which satisfies:

[0029]

[0030] in, The loss is local, where i represents the i-th local region and n represents the total number of selected local regions. To obtain the expected operation, V′ li Generate data for the i-th local region for the generator. V is the low-resolution data for the entire selected local region. li Data representing the i-th local region, For the selected local regions, high-resolution data is used, G(·) is a function of the generator G, and ||·|| is the L2 normal form.

[0031] In conjunction with the first aspect, in some implementations of the first aspect, the loss function of the spatial super-resolution network satisfies:

[0032]

[0033] in, Let λ be the minimum value of the generator G loss, and λ1 be the weight corresponding to the first part of the loss. To obtain the expected operation, V represents the original data, V LGiven low-resolution input data, D(·) is a function of the discriminator D, G(·) is a function of the generator G, and λ² is the weight corresponding to the volumetric loss. λ3 represents the volumetric loss, and λ3 represents the weights corresponding to the feature loss. The feature loss is λ4, where λ4 is the weight corresponding to the local loss. This is a localized loss.

[0034] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:

[0035] The computers are divided into a first computer cluster and a second computer cluster to build an in-situ computing environment. The first computer cluster is used to preprocess the data and train the spatial super-resolution network. The second computer cluster is used to generate three-dimensional flow field estimation data at the first resolution level based on the three-dimensional flow field data at the second resolution level through the trained spatial super-resolution network, and to perform visualization operations on the three-dimensional flow field data.

[0036] Secondly, a method for decompressing three-dimensional flow field data is provided, including:

[0037] Acquire 3D flow field data at the third resolution level;

[0038] The three-dimensional flow field data at the third resolution level is input into the spatial super-resolution network as described in any of the implementations of the first aspect above to obtain three-dimensional flow field estimation data at the fourth resolution level, wherein the fourth resolution level is higher than the third resolution level.

[0039] Based on the three-dimensional flow field estimation data at the fourth resolution level, perform visualization operations on the three-dimensional flow field data.

[0040] In conjunction with the second aspect, in some implementations of the second aspect, the method further includes:

[0041] The user-defined region of interest data is input into the spatial super-resolution network to obtain the third-dimensional flow field estimation data at the fourth resolution level.

[0042] The advantages of this invention compared to the prior art are:

[0043] (1) This invention trains spatial super-resolution networks based on in-situ computing environments, which effectively alleviates the problem that large-scale fine three-dimensional flow field data cannot be reasonably compressed and stored due to computer input / output speed and storage limitations.

[0044] (2) By constructing a spatial super-resolution network, this invention obtains a more detailed mapping relationship between the compression and decompression of large-scale fine three-dimensional flow fields. Compared with direct downsampling dimensionality reduction compression and upsampling decompression recovery, this invention can more effectively compress the overall situation and corresponding physical quantities of large-scale fine three-dimensional flow fields, and obtain higher accuracy results during decompression.

[0045] (3) By introducing user-defined regions of interest and local networks, this invention can meet users' needs for higher-precision storage of certain specific regions. Compared with uniform data compression and decompression, this invention can more effectively save the flow field information of specific regions and display it with high precision during decompression.

[0046] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0047] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same components in the exemplary embodiments of the invention.

[0048] Figure 1 A schematic diagram of the overall process of a spatial compression method for large-scale fine three-dimensional flow fields based on in-situ calculations according to an embodiment of the present invention is shown.

[0049] Figure 2 A schematic diagram of an in-situ computational application of a spatial compression method for large-scale fine three-dimensional flow fields based on in-situ computation according to an embodiment of the present invention is shown.

[0050] Figure 3 A schematic diagram of a large-scale fine three-dimensional flow field compression process according to an embodiment of the present invention is shown. This method is based on in-situ calculation of large-scale fine three-dimensional flow fields.

[0051] Figure 4 The illustration shows the original data and a visualization of the downsampled original data of a spatial compression method for large-scale fine three-dimensional flow fields based on in-situ calculations according to an embodiment of the present invention.

[0052] Figure 5 A schematic diagram of a spatial super-resolution network is shown, illustrating a spatial compression method for large-scale, fine three-dimensional flow fields based on in-situ computation according to an embodiment of the present invention.

[0053] Figure 6The diagram illustrates the global network architecture and IB block schematic of a spatial super-resolution network based on a spatial compression method for large-scale fine three-dimensional flow fields under in-situ computation according to an embodiment of the present invention.

[0054] Figure 7 The global network layer parameters of a spatial super-resolution network based on a spatial compression method for large-scale fine three-dimensional flow fields under in-situ computation according to an embodiment of the present invention are shown.

[0055] Figure 8 A schematic diagram of the local network architecture of a spatial super-resolution network based on a spatial compression method for large-scale fine three-dimensional flow fields under in-situ computation according to an embodiment of the present invention is shown.

[0056] Figure 9 A schematic diagram of the parameters of each layer of a spatial super-resolution network according to an embodiment of the present invention is shown. This method is based on a spatial compression method for large-scale fine three-dimensional flow fields using in-situ computation.

[0057] Figure 10 A schematic diagram of a discriminator architecture for a spatial super-resolution network based on a spatial compression method for large-scale fine three-dimensional flow fields under in-situ computation according to an embodiment of the present invention is shown.

[0058] Figure 11 The diagram illustrates the streamline visualization results obtained by a running spatial super-resolution network based on a spatial compression method for large-scale fine three-dimensional flow fields under in-situ computation according to an embodiment of the present invention. Detailed Implementation

[0059] Preferred embodiments of the present invention will now be described in more detail.

[0060] The spatial compression method for large-scale, fine three-dimensional flow fields based on in-situ calculations according to the present invention, such as... Figure 1 As shown, it includes:

[0061] Set up an in-situ computing environment while en route and allocate the available computers;

[0062] Mark user-defined regions of interest and compress large-scale fine steady-state flow fields;

[0063] Construct a spatial super-resolution network to establish a mapping relationship between large-scale, fine-grained steady-state flow field compression and recovery;

[0064] A trained spatial super-resolution network is used to decompress large-scale, fine-grained three-dimensional flow field data.

[0065] This embodiment mainly describes the method from three aspects: building an in-situ computing environment, compressing a large-scale fine-grained spatial steady-state flow field, and decompressing a large-scale fine-grained spatial steady-state flow field.

[0066] 1. Set up an in-situ computing environment

[0067] In one example, the following steps can be used to perform large-scale, detailed three-dimensional flow field analysis and calculation in an in-situ environment:

[0068] like Figure 2 As shown, the number of computers was divided in an 8:2 ratio. The cluster consisting of 80% of the computers was used for data preprocessing and training the spatial super-resolution network. All training results were transferred via memory to the other 20% of the computers for in-situ analysis and computation, and the computational results from the global and local networks were visualized and analyzed.

[0069] 2. Compression of large-scale, fine-grained, spatial steady-state flow fields

[0070] Based on the in-situ computing environment built in section 1, in one example, using 80% of the computer space, the three-dimensional flow field data can be compressed using the following steps:

[0071] like Figure 3 As shown, the process can be divided into three steps: marking user-defined regions of interest; performing preprocessing operations such as compression on large-scale, fine-grained 3D flow fields; and constructing a super-resolution network to establish a mapping relationship between the compressed flow field and the original flow field data.

[0072] Step 1: In one example, the user can mark the region of interest in the 3D flow field data using the following steps:

[0073] Regions of interest in large-scale, fine-grained steady-state flow fields are marked using flow field visualization software such as ParaView, and the marked flow field files are used as input for subsequent methods.

[0074] Step 2: In one example, the three-dimensional flow field data can be preprocessed by compression and other operations through the following steps:

[0075] For the aforementioned large-scale, high-resolution 3D flow field data, the user-marked custom spatial regions are segmented. The high-resolution data in the spatial dimension is downsampled to reduce dimensionality, and the corresponding dimensions and starting coordinates, as well as the low-resolution data, are saved. Then, the saved data is normalized, and training and testing datasets are constructed.

[0076] Specifically, for the input data of the spatial super-resolution network, preprocessing is first performed, which involves truncating the original data and then downsampling the data using average pooling with a 4×4×4 kernel, a stride of 4, and zero padding. Next, a user-defined flow field spatial region is extracted from the original high-resolution data. For example... Figure 4 As shown, the left image is a cloud map obtained after visualizing the original high-resolution data, with an image size of L×W×H. The right image is a cloud map obtained after visualizing the downsampled data, with an image size of L / 4×W / 4×H / 4. It can be seen from the images that the cloud map of the downsampled low-resolution data clearly shows more jagged edges and blurry areas, and some details are even more difficult to distinguish.

[0077] Step 3: In one example, a spatial super-resolution network for a large-scale, high-resolution 3D flow field is constructed using the following method to establish a mapping relationship between the compressed flow field and the original flow field data:

[0078] By utilizing preprocessed low-resolution data and user-defined regions of interest, a spatial super-resolution network for large-scale, high-resolution 3D flow fields is trained to obtain the corresponding weights. The resulting parameterized model of this neural network represents the mapping relationship between the compressed flow field and the original flow field data.

[0079] The spatial super-resolution network for large-scale, high-resolution 3D flow field data mainly consists of two parts: a generator G and a discriminator D. The network input is a single time-step data point, which is fed into the generator G. After generating the corresponding single-time-step data, the generator D performs appropriate discrimination, thereby achieving a dynamic game-like effect. The network structure of the spatial super-resolution network is as follows: Figure 5 As shown.

[0080] First, in one example, the generator for the spatial super-resolution network is constructed as follows:

[0081] The generator G contains two types of networks: a global network responsible for extracting global features and a local network that focuses on local features of the flow field.

[0082] The input to the global network is unprocessed low-resolution data, which is downsampled from the original high-resolution data through average pooling during training.

[0083] The network employs a skip-link approach. First, it passes through three residual blocks with 3×3×3 kernels, padding of 1, and stride of 1. This configuration ensures the data volume remains unchanged after passing through the residual blocks. Next, it passes through a deconvolutional layer (DeConv) with a 4×4×4 kernel, stride of 2, and padding of 0, doubling the data's length, width, and height. This is followed by two more residual blocks and one more deconvolutional layer, then two more residual blocks, at which point the data's length, width, and height are four times the original. Finally, it passes through a hyperbolic tangent function (tanh) to obtain the output. The specific structure of the generator G of the spatial super-resolution network is as follows... Figure 6 As shown in (a).

[0084] The residual block consists of two parts. One part consists of three convolutional layers. Except for the last convolutional layer, which only requires spectral normalization, the first two convolutional layers each undergo spectral normalization (SN) and instance normalization (IN). The other part consists of only one convolutional layer and one spectral normalization layer. Before output, the results from these two parts need to be added at corresponding positions. The structure diagram of the residual block is shown below. Figure 6 As shown in (b), the names and output sizes of each layer in the global network of the spatial super-resolution network are as follows: Figure 7 As shown.

[0085] For the local network described above, its input is a user-labeled custom spatial flow field region within the original high-resolution flow field. The local network architecture of the spatial super-resolution network is as follows: Figure 8 As shown.

[0086] In local networks, the input region is small, and features need to be preserved. This invention employs a convolutional neural network structure. First, residual blocks are used to transform the input local region data into a 256×1×1×1 feature map. Fully connected layers and upsampling are not used; instead, deconvolutional layers restore the feature map to its original size, and this is used to calculate the loss. The names and output sizes of each layer in the local network of the spatial super-resolution network are as follows: Figure 9 As shown.

[0087] Then, in one example, the discriminator of the spatial super-resolution network is constructed as follows:

[0088] In the discriminator network architecture, except for the last convolutional layer, the kernel size of each convolutional layer is 4×4×4, the stride is 2, and the padding is 1. The stride of the last convolutional layer is 0, resulting in a final output data size of 1×1×1. Each convolutional layer is followed by a spectral normalization layer and a LeakyReLU layer. The architecture of the discriminator in the spatial super-resolution network is as follows: Figure 10 As shown.

[0089] Finally, in one example, the loss function of the spatial super-resolution network is composed as follows:

[0090] Loss functions for spatial super-resolution can be categorized into adversarial loss, volumetric loss, feature loss, and local loss.

[0091] The adversarial loss enables a dynamic game between the generator G and the discriminator D, making the intermediate time-step data generated by the generator G more similar to the corresponding time-step data in the original data, and allowing the discriminator D to better identify whether the data comes from the generator G or from the original data. Based on the definition of an adversarial generative network, the adversarial loss formula is as follows:

[0092]

[0093]

[0094] For the first expression, To minimize the loss of generator G, To obtain the expected operation, V represents the original data, V L Given low-resolution input data, D(·) is a function of the discriminator D, and G(·) is a function of the generator G.

[0095] For the second expression, To minimize the loss of the discriminator D, To obtain the expected operation, V represents the original data, V H Given high-resolution input data, D(·) is a function of the discriminator D, and V L Given low-resolution input data, G(·) is a function of the generator G.

[0096] Volumetric loss is used to ensure that the data generated by the generator has a low mean square error, making the obtained data closer to the original data. The formula is as follows:

[0097]

[0098] in, For volume loss, To obtain the expected operation, V′ is the data generated by the generator, V L The input is low-resolution data, where V represents the original data. H Given high-resolution input data, G(·) is a function of the generator G, and ||·|| is the L2 normal form.

[0099] Feature loss is used to ensure that the features of the data generated by the generator are similar to those of the corresponding original data as a whole.

[0100]

[0101] in, For feature loss, To obtain the expected operation, V′ is the data generated by the generator, V L The input is low-resolution data, where V represents the original data. H Given high-resolution input data, N is the total number of convolutional layers in the discriminator D, and k represents the k-th convolutional layer. k F represents the number of elements in the k-th convolutional layer. k G represents the features extracted by the k-th convolutional layer in the discriminator D, G(·) is a function of the generator G, and ||·|| is the L2 norm.

[0102] The concept of local loss arises because flow field data often focuses on local regions such as vortices and the areas around key points. Therefore, this invention proposes a local loss method to preserve the characteristics of these local regions to a greater extent. Specifically, this local region loss method involves generating a corresponding local region G(V′) using a generator G. li ) and local regions V in the original high-resolution data li To make the data more similar, the goal is to achieve a low mean squared error in the overall data while also ensuring that the mean squared error in the local regions where most features need to be retained is low. This is achieved using L2 distance in this invention, as shown in the following formula:

[0103]

[0104] in, The loss is local, where i represents the i-th local region and n represents the total number of selected local regions. To obtain the expected operation, V′ li Generate data for the i-th local region for the generator. V is the low-resolution data for the entire selected local region. li Data representing the i-th local region, For the selected local regions, high-resolution data is used, G(·) is a function of the generator G, and ||·|| is the L2 normal form.

[0105] By multiplying and summing the aforementioned loss components according to their respective weights, the final loss function of the generator can be obtained as follows:

[0106]

[0107] in, Let λ be the minimum value of the generator G loss, and λ1 be the weight corresponding to the first part of the loss. To obtain the expected operation, V represents the original data, V LGiven low-resolution input data, D(·) is a function of the discriminator D, G(·) is a function of the generator G, and λ² is the weight corresponding to the volumetric loss. λ3 represents the volumetric loss, and λ3 represents the weights corresponding to the feature loss. The feature loss is λ4, where λ4 is the weight corresponding to the local loss. This is a localized loss.

[0108] Specifically, the original high-resolution data used in this invention is 3×64×64×64 in size, containing three channels: u, v, and w. The downsampled low-resolution data is 3×16×16×16 in size. The model with only the global network has 200 training epochs, and the model with the local network has 200 training epochs. The training data time step is 100, and the test data time step is 30.

[0109] 3. Decompression of large-scale, fine-grained spatial steady-state flow fields

[0110] Utilizing the additional 20% of the computer in the in-situ computing environment, based on the mapping relationship between flow field compression and decompression obtained in section 2, i.e., the neural network parameterization model, the spatial super-resolution network described above is run with low-resolution images, the neural network parameterization model, and user-defined regions of interest as input. The result is the corresponding decompressed high-resolution large-scale detailed 3D flow field file, and the final flow field image is output.

[0111] After inference using a spatial resolution network, the result is as follows: Figure 11 As shown, from left to right, the data represents the original high-resolution data, the data generated by a spatial super-resolution network with local networks, and the data generated by a spatial super-resolution network with only global networks. It can be seen that regardless of whether it's the architecture with only global networks or the architecture with local networks, the learning of the overall features of the original data is quite accurate. The vortex positions of the generated streamlines are basically consistent, and the velocity change trends are also largely consistent, indicating a high degree of decompression of the original data.

[0112] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

[0113] The contents not described in detail in this invention are well-known to those skilled in the art.

Claims

1. A spatial compression method for large-scale, fine-grained three-dimensional flow fields under in-situ calculations, comprising: The original three-dimensional flow field data at the first resolution level is subjected to dimensionality reduction processing to obtain three-dimensional flow field data at the second resolution level, where the first resolution level is higher than the second resolution level. Training a spatial super-resolution network using 3D flow field data at the second resolution level specifically includes inputting the 3D flow field data at the second resolution level into the spatial super-resolution network to be trained to obtain 3D flow field estimation data at the first resolution level. The 3D flow field estimation data is prediction data based on the original 3D flow field data, and the parameters of the spatial super-resolution network are adjusted through a loss function. The spatial super-resolution network includes a generator G and a discriminator D. The generator G is used to generate corresponding single-time-step prediction data based on the input single-time-step data; The discriminator D is used to match the predicted data and the original data in order to adjust the parameters of the spatial super-resolution network; The method further includes: A user-defined region of interest is extracted from the original three-dimensional flow field data to obtain the three-dimensional flow field data of the region of interest, wherein the resolution level of the three-dimensional flow field data of the region of interest is the first resolution level; The three-dimensional flow field data of the region of interest is input into the spatial super-resolution network to be trained, so as to complete the training of the spatial super-resolution network; The generator G also includes a local network. The input of the local network is local region data in the original three-dimensional flow field data at the first resolution level. The local region data is the data of the region of interest to the user. The local network adopts a convolutional neural network structure. First, the local region data is transformed into a 256×1×1×1 feature map through residual blocks. Without using fully connected layers and upsampling, the feature map is restored to its original size through deconvolution layers, and the loss is calculated based on this.

2. The method according to claim 1, characterized in that, The generator G includes a global network whose input is the 3D flow field data at the second resolution level. The global network adopts a skip-link approach, first passing through three residual blocks with a kernel size of 3×3×3, padding of 1, and stride of 1; then passing through a deconvolutional DeConv layer with a kernel size of 4×4×4, stride of 2, and padding of 0; then passing through two residual blocks, one deconvolutional DeConv layer, two residual blocks, and one hyperbolic tangent function layer before outputting. The residual block consists of two parts. One part consists of three convolutional layers. Except for the last convolutional layer, which only requires spectral normalization, the first two convolutional layers each have a spectral normalization (SN) and an instance normalization (IN) performed. The other part consists of only one convolutional layer and one spectral normalization layer. Before output, the results of the two parts of the residual block need to be added at corresponding positions.

3. The method according to claim 1, characterized in that, In the discriminator D, except for the last convolutional layer, the kernel size of each other convolutional layer is 4×4×4, the stride is 2, and the padding is 1. The stride of the last convolutional layer is 0. Each convolutional layer is followed by a spectral normalization layer and a leaky corrected linear unit layer.

4. The method according to claim 1, characterized in that, The loss function of the spatial super-resolution network includes an adversarial loss function, which satisfies the following: in, To minimize the loss of generator G, To obtain the expected operation, V represents the original data. For the input low-resolution data, Let D be a function of the discriminator. A function relating to the generator G, To minimize the loss of the discriminator D, This is the input high-resolution data.

5. The method according to claim 1, characterized in that, The loss function of the spatial super-resolution network includes a volumetric loss function, which satisfies: in, For volume loss, Data generated by the generator It is an L2 paradigm.

6. The method according to claim 1, characterized in that, The loss function of the spatial super-resolution network includes a feature loss function, which satisfies: in, For feature loss, N is the total number of convolutional layers in the discriminator D, and k represents the k-th convolutional layer. k F represents the number of elements in the k-th convolutional layer. k This represents the features extracted by the k-th convolutional layer in discriminator D.

7. The method according to claim 1, characterized in that, The loss function of the spatial super-resolution network includes a local loss function, which satisfies: in, The loss is local, where i represents the i-th local region and n represents the total number of selected local regions. Generate data for the i-th local region for the generator. For the selected local region of low-resolution data, Data representing the i-th local region, High-resolution data for the entire selected local area.

8. The method according to claim 1, characterized in that, The loss function of the spatial super-resolution network satisfies: in, To minimize the loss of generator G, The weights corresponding to the first part of the loss are... The weights corresponding to the volume loss. The weights corresponding to the feature loss. The weights are those corresponding to the local loss.

9. The method according to claim 1, characterized in that, The method further includes: The computers are divided into a first computer cluster and a second computer cluster to build an in-situ computing environment. The first computer cluster is used to preprocess the data and train the spatial super-resolution network. The second computer cluster is used to generate three-dimensional flow field estimation data at the first resolution level based on the three-dimensional flow field data at the second resolution level through the trained spatial super-resolution network, and to perform visualization operations on the three-dimensional flow field data.

10. A method for decompressing three-dimensional flow field data, characterized in that, include: Acquire 3D flow field data at the third resolution level; The three-dimensional flow field data at the third resolution level is input into the spatial super-resolution network as described in any one of claims 1 to 9 to obtain three-dimensional flow field estimation data at the fourth resolution level, wherein the fourth resolution level is higher than the third resolution level. Based on the three-dimensional flow field estimation data at the fourth resolution level, perform visualization operations on the three-dimensional flow field data.

11. The method according to claim 10, characterized in that, The method further includes: The user-defined region of interest data is input into the spatial super-resolution network to obtain the third-dimensional flow field estimation data at the fourth resolution level.

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