Submesoscale flow field extraction method and apparatus based on boundary sensing and Poisson constraints

Abstract

This application provides a method and apparatus for extracting sub-mesoscale flow fields based on boundary awareness and Poisson constraints. The method includes: acquiring stationary ocean color satellite image data; inputting continuous satellite images into a flow field extraction model to obtain continuous feature maps; a boundary attention module extracting and enhancing the boundary structure features of the continuous feature maps, and a detail enhancement module extracting and enhancing the detail features of the continuous feature maps to obtain enhanced continuous feature maps; a volume construction module generating a multi-scale pyramid based on the enhanced continuous feature maps, determining the search radius based on each scale of the multi-scale pyramid, and constructing relevant volumes; a cyclic flow field refinement module using convolutional gated cyclic units to refine the relevant volumes through cyclic flow field refinement, iteratively updating to obtain a preliminary flow field; and a physical constraint correction module performing physical constraint correction on the preliminary flow field to obtain the final sea surface flow field.

Description

Technical Field

[0001] This application relates to the field of flow field extraction technology, and in particular to a method and apparatus for extracting sub-mesoscale flow fields based on boundary sensing and Poisson constraints. Background Technology

[0002] In the fields of marine science research and ecological environment monitoring, precise analysis of sub-mesoscale flow fields is a core requirement for revealing the complex dynamic mechanisms of the ocean. These flow fields not only drive the cross-scale transport of matter and energy in the ocean, directly affecting phytoplankton distribution, pollutant diffusion, and fishery resource fluctuations, but also play a crucial role in the global climate system. Their energy cascade processes can reshape sea surface temperature patterns, thereby influencing atmospheric circulation patterns. For example, in the equatorial sea, sub-mesoscale eddies influence the heat exchange between the ocean and atmosphere by regulating the intensity of sea rise, which is of great significance for predicting El Niño-Southern Oscillation phenomena. However, due to their small scale and dramatic spatiotemporal variations, traditional methods are insufficient for large-scale, detailed observational studies.

[0003] Currently, sub-mesoscale flow field extraction faces major technical bottlenecks. Traditional altimeter-based methods rely on the geostrophic equilibrium assumption, which cannot adapt to the non-geostrophic characteristics of sub-mesoscale flows, leading to distortion of the flow field structure. While optical flow algorithms can capture motion information using satellite imagery, they are limited by interferences such as cloud cover and differences in water optical properties, making them prone to feature mismatches in weakly textured regions. Emerging deep learning methods, although improving data-driven prediction capabilities, generally suffer from a lack of physical constraints: on the one hand, the flow fields output by the models often lack hydrodynamic physical convergence, making them prone to divergence anomalies; on the other hand, their ability to characterize key boundary structures such as fronts and filaments is insufficient, leading to biased predictions of material transport paths. These technical limitations make it difficult for existing flow field data to meet the high-precision application requirements of ocean numerical model calibration and ecosystem dynamic simulation.

[0004] Therefore, there is an urgent need for a method to solve the problems of insufficient accuracy and lack of physical meaning in traditional methods, and to achieve high-resolution, physically consistent sub-mesoscale flow field extraction. Summary of the Invention

[0005] In view of this, this application provides a sub-mesoscale flow field extraction method and apparatus based on boundary perception and Poisson constraints to solve the problems of insufficient accuracy and lack of physical meaning in traditional methods, and to achieve high-resolution, physically consistent sub-mesoscale flow field extraction.

[0006] Specifically, this application is implemented through the following technical solution:

[0007] The first aspect of this application provides a sub-mesoscale flow field extraction method based on boundary awareness and Poisson constraints, the method comprising:

[0008] Acquire geostationary ocean color satellite image data;

[0009] Continuous satellite images are input into a trained flow field extraction model, which downsamples the continuous satellite images to obtain continuous feature maps. The continuous feature maps are sea surface velocity field feature maps at two consecutive time points. The flow field extraction model includes a boundary attention module, a detail enhancement module, a volume construction module, a circulating flow field refinement module, and a physical constraint correction module.

[0010] The boundary attention module extracts and enhances the boundary structure of the continuous feature map, and the detail enhancement module extracts and enhances the detail features of the continuous feature map to obtain the enhanced continuous feature map.

[0011] The volume construction module generates a multi-scale pyramid based on the enhanced continuous feature map, determines the search radius based on each scale of the multi-scale pyramid, and constructs the relevant volume.

[0012] The circulating flow field refinement module uses a convolution gated circulating unit to refine the circulating flow field of the relevant volume, and obtains the preliminary flow field through iterative updates.

[0013] The physical constraint correction module performs physical constraint correction on the preliminary flow field, eliminates flow field divergence by solving the Poisson equation, and obtains the final sea surface flow field.

[0014] A second aspect of this application provides a sub-mesoscale flow field extraction device based on boundary-aware Poisson constraints, the device comprising an acquisition module and a processing module;

[0015] The acquisition module is used to acquire geostationary ocean color satellite image data;

[0016] The processing module is used to input continuous satellite images into a trained flow field extraction model. The flow field extraction model downsamples the continuous satellite images to obtain continuous feature maps. The continuous feature maps are sea surface velocity field feature maps at two consecutive time points. The flow field extraction model includes a boundary attention module, a detail enhancement module, a volume construction module, a circulating flow field refinement module, and a physical constraint correction module.

[0017] The boundary attention module extracts and enhances the boundary structure of the continuous feature map, and the detail enhancement module extracts and enhances the detail features of the continuous feature map to obtain the enhanced continuous feature map.

[0018] The volume construction module generates a multi-scale pyramid based on the enhanced continuous feature map, determines the search radius based on each scale of the multi-scale pyramid, and constructs the relevant volume.

[0019] The circulating flow field refinement module uses a convolution gated circulating unit to refine the circulating flow field of the relevant volume, and obtains the preliminary flow field through iterative updates.

[0020] The physical constraint correction module performs physical constraint correction on the preliminary flow field, eliminates flow field divergence by solving the Poisson equation, and obtains the final sea surface flow field.

[0021] The sub-mesoscale flow field extraction method and apparatus based on boundary awareness and Poisson constraints provided in this application, firstly, selectively extracts and enhances the boundary structure and detailed features of continuous feature maps through a boundary attention module and a detail enhancement module. This enables the enhanced feature map to more accurately depict the spatial contours and subtle changes of sea surface fluid boundaries at small and medium scales, providing a more reliable feature basis for the subsequent volume construction module to generate multi-scale pyramids and determine the search radius. This processing method effectively highlights the motion characteristics of key boundary regions such as the front edges and vortex contours of the filamentary structure of sea surface tracer particles, making the construction of relevant volumes more closely match the actual fluid motion range and avoiding flow field estimation deviations caused by feature ambiguity. Especially in complex flow field boundaries such as fronts and turbulent mixing zones, it can significantly improve the flow field's ability to capture boundary motion trends, ensuring the integrity and positioning accuracy of sub-mesoscale flow field details. Secondly, by using a physical constraint correction module to solve the Poisson equation and eliminate flow field divergence, the data-driven preliminary flow field prediction is deeply integrated with the incompressible physical laws of fluid mechanics. Through Jacobi iteration to solve the potential function and correct the flow field velocity components, divergence or convergence phenomena that do not conform to the law of mass conservation are eliminated point by point. This processing mechanism effectively removes non-physical artifacts from the preliminary flow field, making the final flow field more consistent with the motion characteristics of real fluids in processes such as vortex evolution and water transport. Simultaneously, gradient correction preserves the fluid motion details enhanced by the boundary sensing module, avoiding the loss of sub-mesoscale features due to excessive smoothing. This ensures that the flow field meets physical consistency requirements while maintaining a fine motion structure, making it better suited for applications with high physical realism requirements, such as ocean dynamics simulation and ecological material transport analysis. Attached Figure Description

[0022] Figure 1 A flowchart of the sub-mesoscale flow field extraction method based on boundary sensing and Poisson constraints provided in Embodiment 1 of this application;

[0023] Figure 2 This is a schematic diagram of the sub-mesoscale flow field extraction device based on boundary sensing and Poisson constraints provided in Embodiment 2 of this application. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0025] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0026] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0027] The following specific embodiments are given to illustrate the technical solution of this application in detail.

[0028] Figure 1 The flowchart illustrates the sub-mesoscale flow field extraction method based on boundary awareness and Poisson constraints provided in Embodiment 1 of this application. Please refer to... Figure 1 The method provided in this embodiment may include:

[0029] S101. Acquire geostationary ocean color satellite image data.

[0030] Specifically, geostationary ocean color satellite imagery data is two-dimensional imagery data acquired through observations of the Earth's surface using remote sensing sensors (such as optical cameras, microwave radiometers, and synthetic aperture radar) mounted on satellites. Satellite imagery data uses pixels as the basic unit and records electromagnetic wave reflection or radiation information of surface targets, reflecting the physical state of the ocean surface through dimensions such as spectrum, texture, and geometric features.

[0031] It should be noted that satellite imagery data was chosen as the dataset for flow field extraction because the sub-mesoscale flow field (1-100 km) is naturally compatible with the medium resolution of satellite imagery (10-1000 m). Texture variations in satellite images (such as the drift of plankton aggregation areas and differences in sea surface roughness) can serve as tracer signals for flow field motion. Furthermore, compared to in-situ observations such as those using buoys, satellite imagery data can compensate for the sparseness of sub-mesoscale observations with its "area-like" coverage. It can also be directly used for numerical model calibration, overcoming the accuracy bottleneck of traditional methods in analyzing small-scale ocean dynamic processes. In this embodiment, we used sea surface chlorophyll a concentration data from the Korea Ocean Satellite Center's second-generation geostationary ocean color satellite GOCI-II. This data provides 10 effective hourly observations per day (07:30-16:30, Beijing time) with a spatial resolution of 250 m. The observation center is located at 130°E, 36°N, covering an area of ​​2500 km × 2500 km, encompassing the Bohai Sea, Yellow Sea, East China Sea, and other Northeast Asian sea areas. After downloading, using the official processing tools and an iterative scheme based on the near-infrared (NIR) atmospheric correction algorithm, normalized water ionization radiance (Lwn) was calculated for the raw data in 13 bands (380 nm to 865 nm). The 443 nm, 490 nm, and 555 nm bands were selected, and Chl-a concentration was estimated using the three-band ocean color algorithm (OC3). Finally, data format conversion and verification were performed to generate satellite image data for sub-mesoscale flow field extraction. It has the capability to capture sea surface velocity field changes at two consecutive time points in a sub-mesoscale process.

[0032] S102. Input the continuous satellite images into the trained flow field extraction model. The flow field extraction model downsamples the continuous satellite images to obtain continuous feature maps.

[0033] The continuous feature map is a sea surface velocity field feature map at two consecutive time points; the flow field extraction model includes a boundary attention module, a detail enhancement module, a volume construction module, a circulating flow field refinement module, and a physical constraint correction module.

[0034] Specifically, the flow field extraction model is an image processing system based on a deep learning architecture. Through the collaborative work of multiple modules, it extracts the velocity field of fluid motion (such as ocean currents and atmospheric currents) from continuous satellite images to characterize sub-mesoscale dynamic processes. The flow field extraction model includes a boundary attention module, a detail enhancement module, a volume construction module, a recurrent flow field refinement module, and a physical constraint correction module. The boundary attention module focuses on fluid boundaries in the image (such as vortex edges and fronts), enhancing the ability to identify dynamic interfaces and avoiding boundary blurring during flow field extraction. The detail enhancement module strengthens the extraction of sub-mesoscale features (such as vortices and filamentary structures at the kilometer scale), preserving small-scale details through convolution or attention mechanisms. The volume construction module fuses features from consecutive frames into spatiotemporal volume data, capturing the continuity of motion in the time series. The recurrent flow field refinement module iteratively optimizes the current frame flow field based on historical flow field prediction results using a recurrent neural network or recursive structure. The physical constraint correction module introduces constraints from ocean dynamics equations to perform physical rationality correction on the predicted flow field, reducing non-physical noise.

[0035] It is important to note that flow fields, as complex fluid motion phenomena that evolve over time, require time-series data to capture their trends and evolutionary patterns, whether it be the formation and dissipation of sub-mesoscale eddies in the ocean or the migration and reversal of airflow in the atmosphere. Single-frame satellite images only provide static information at a specific instant and cannot reflect changes in the direction and velocity of fluid motion. In contrast, continuous satellite images, formed at fixed time intervals (e.g., multiple observations per hour or per day), can completely record the entire process of flow field formation, development, and dissipation. For example, Chl-a images observed 10 times daily by the GOCI-II satellite can track the hourly displacement of phytoplankton fronts; hourly sea surface temperature images simulated by MITgcm LLC4320 can clearly show the rotational trajectory of sub-mesoscale eddies. Furthermore, continuous satellite images can be compared between adjacent frames to calculate the fluid velocity field, enabling dynamic analysis of sub-mesoscale flow fields.

[0036] In practice, continuous satellite images are converted into the format required by the flow field extraction model (such as NumPy arrays or Tensors) and arranged in chronological order to form a continuous frame sequence. The pixel values ​​of each frame are normalized and scaled to the same range, such as [0, 1], to eliminate numerical differences between different bands or sensors. The continuous frame images are batched, with two consecutive frames taken as a group of inputs, and the batch size is set to 60 (consistent with the flow field extraction model training phase). The continuous satellite images are input into the flow field extraction model. The initial convolutional layers in the flow field extraction model use four convolutional layers with a stride of 2 (such as 3×3 convolutional kernels with a stride of 2) to progressively reduce the image resolution, while doubling the number of channels (such as increasing from 32 channels to 256 channels) to preserve the feature dimension. Finally, the input image is downsampled to 1 / 8 of the original size as a continuous feature map.

[0037] Optionally, the flow field extraction model uses endpoint error as the loss function, and the method further includes: for each pixel position, calculating the Euclidean distance between the flow field vector extracted by the flow field extraction model and the corresponding real flow field vector; summing the squared Euclidean distances of all pixel positions and then dividing by the total number of pixels to obtain the endpoint error value; the endpoint error is the velocity error.

[0038] Specifically, endpoint error is a core indicator for measuring the accuracy of flow field estimation, referring to the mean Euclidean distance between the predicted and actual flow field vectors at the pixel level. Choosing endpoint error as the loss function for the flow field extraction model is closely related to the marine sub-mesoscale flow field extraction application scenario of this application. In marine environmental monitoring, the core objective of flow field extraction is to accurately obtain the fluid motion vector at each pixel location to reflect the actual direction and velocity of seawater movement. Endpoint error directly measures the pixel-level deviation between the predicted and actual flow field vectors, providing an intuitive assessment of the flow field prediction model's ability to characterize flow field details. For example, when tracking sub-mesoscale phenomena such as phytoplankton fronts and eddy migration, even small velocity errors can lead to misjudgments of material transport paths. Endpoint error, by quantifying pixel-level deviations, can accurately guide the flow field extraction model to optimize the flow field estimation for each pixel. Furthermore, this application relies on satellite imagery to extract the flow field. This data provides accurate and real flow field labels as a reference, making the calculation of endpoint errors feasible. At the same time, as a differentiable function, the endpoint error can work in conjunction with the boundary attention module and physical constraint module in the flow field extraction model. This not only enhances the extraction of fluid boundary features but also ensures the physical rationality of the flow field. Ultimately, it outputs high-precision flow field data that conforms to the laws of ocean dynamics, meeting the application needs of marine ecological monitoring, climate model calibration, and other applications.

[0039] In practical implementation, the endpoint error loss function can be expressed as:

[0040] ;

[0041] Among them, the The endpoint error loss function; The flow field vector extracted by the flow field extraction model; The actual flow field vector; This represents the total number of pixels.

[0042] S103. The boundary attention module extracts and enhances the boundary structure of the continuous feature map, and the detail enhancement module extracts and enhances the detail features of the continuous feature map to obtain the enhanced continuous feature map.

[0043] Specifically, the boundary attention module focuses on feature extraction and enhancement of boundary structures in continuous feature maps. Specifically, by identifying edge regions in the flow field (such as fluid interfaces, vortex boundaries, etc.), the module uses an attention mechanism to strengthen the feature representation of these boundaries, enabling the flow field extraction model to more accurately capture the structural contours of fluid motion. For example, in ocean flow fields, boundaries may correspond to the division of different water masses or the edges of ocean currents; enhancing these features helps subsequent estimations of the direction and velocity of flow field vectors to better reflect the dynamic characteristics of actual fluid boundaries.

[0044] Furthermore, the detail enhancement module focuses on extracting and enhancing detailed features in continuous feature maps. These details typically refer to small-scale motion information in the flow field (such as sub-mesoscale eddies, local velocity changes, etc.). By using a multi-layer feature extraction network (such as convolutional layers or residual structures), subtle velocity gradients or texture changes are amplified, ensuring that high-frequency, small-scale motion features in the flow field are not ignored. For example, when tracking phytoplankton distribution or heat transport, the accuracy of detailed features directly affects the prediction accuracy of material transport paths.

[0045] It should be noted that the boundary attention module and the detail enhancement module process the input continuous feature maps in parallel: the boundary attention module outputs an enhanced boundary feature map, and the detail enhancement module outputs an enhanced detail feature map. Subsequently, the outputs of both are integrated through feature fusion operations (such as element-wise addition, channel concatenation, or weighted fusion) to form an enhanced feature map that simultaneously contains clear boundary structures and rich detail information. This design enables the flow field extraction model to capture both the macroscopic structure of the flow field and preserve microscopic motion details, providing higher-quality feature inputs for subsequent steps such as volume construction and flow field refinement, thereby improving the overall accuracy and physical plausibility of the flow field extraction.

[0046] In specific implementation, the boundary attention module performs feature extraction and enhancement on the boundary structure in the continuous feature map, including: using the Sobel operator to perform edge detection on the continuous feature map to obtain edge features; performing channel attention and spatial attention calculations on the edge features to generate channel weights and spatial weights; multiplying the channel weights and spatial weights and then fusing them with the continuous feature map to obtain the enhanced continuous feature map.

[0047] Specifically, the Sobel operator is used to perform edge detection on the input continuous feature map. Gradients are calculated using horizontal and vertical convolutional kernels to obtain the edge feature map. Global average pooling and global max pooling are then performed on the edge feature map. The pooling results are input into two fully connected network layers respectively. Channel-dimensional weight vectors are generated through activation functions (such as Sigmoid), and these weight vectors adaptively reweight the importance of each semantic channel. Average pooling and max pooling are then performed on the edge feature map separately. The pooling results are concatenated and passed through a 7×7 convolutional layer, followed by Sigmoid activation to generate a spatial weight matrix. This spatial weight matrix is ​​used to highlight significant edge regions. The channel weights and spatial weights are multiplied element-wise to obtain joint attention weights. These joint attention weights are then multiplied element-wise with the original continuous feature map. Finally, the multiplication result is fused with the original continuous feature map through residual connections to obtain the boundary-enhanced continuous feature map.

[0048] The method provided in this embodiment uses the gradient calculation of the Sobel operator to make fluid boundaries (such as vortex edges and fronts) explicit, providing a spatial localization basis for subsequent attention mechanisms and effectively identifying real physical boundaries. Channel attention adaptively allocates channel weights through global pooling and a fully connected network to enhance semantic features related to the boundary, while spatial attention focuses on the real boundary region through 7×7 convolution to suppress false edges. The combination of the two achieves semantic fine-tuning of boundary features. Residual fusion ensures that the enhancement process does not lose basic information in the original features, improving training stability. These designs make the flow field boundary localization more accurate, the flow field estimation in the boundary region more in line with physical laws, and retain more sub-mesoscale structural details. In terms of application effects, the boundary attention module can more accurately capture velocity abrupt changes at the fluid interface, improve the ability to characterize key structures such as ocean fronts and vortices, and has stronger anti-interference ability in complex environments (such as cloudy areas). In addition, the boundary attention module and the detail enhancement module complement each other and provide more reasonable boundary conditions for the physical constraint module, ultimately achieving "clearer boundaries, physical consistency, and complete details" in sub-mesoscale flow field extraction.

[0049] Optionally, the detail enhancement module performs feature extraction and enhancement on the detail features in the continuous feature map, including: using multiple parallel dilated convolution branches with different dilation rates to perform multi-scale feature extraction on the continuous feature map, obtaining the outputs of multiple different branches; concatenating the outputs of each branch and fusing them through convolution to obtain the detail enhancement features; determining whether the preliminary flow field exists, and when the preliminary flow field is determined to exist, bilinearly upsampling the preliminary flow field to the size of the continuous feature map, concatenating it with the detail enhancement features, and fusing it through convolution to obtain the enhanced continuous feature map.

[0050] In practical implementation, multiple parallel dilated convolutional branches are configured, each with a different dilation rate. For example, in this embodiment, four parallel dilated convolutional branches are configured with dilation rates of 1, 2, 3, and 4, respectively. Each branch uses a 3×3 convolutional kernel to process the continuous feature map, maintaining the same number of input and output channels. The output size of each branch is the same as the input continuous feature map, capturing contextual information at different spatial scales. Further, the outputs of the four branches are concatenated along the channel dimension to form a feature map with a channel number expanded by 4 times. The number of channels in the concatenated feature map is compressed to twice the original input using a 1×1 convolutional kernel. Batch normalization and ReLU activation function are applied to obtain detail enhancement features. It is determined whether a preliminary flow field exists before this step. If so, bilinear interpolation is used to upsample the preliminary flow field (usually low resolution) to the size of the continuous feature map. The upsampled preliminary flow field and detail enhancement features are concatenated along the channel dimension. The concatenated features are fused using a 3×3 convolutional kernel, keeping the number of channels unchanged. Batch normalization and ReLU activation function are applied again to obtain the final enhanced continuous feature map. The final enhanced continuous feature map is fused with the original continuous feature map using residual addition. If the initial flow field does not exist, the detailed enhancement features are used as the enhanced continuous feature map.

[0051] The method provided in this embodiment enhances the expressive power of continuous feature maps from three key dimensions through a design that fuses multi-scale dilated convolution with the preliminary flow field, thereby optimizing the accuracy and physical rationality of the final flow field extraction. The multi-scale dilated convolution employs parallel branches with different dilation rates, enabling it to capture multi-scale information from local texture to global context while maintaining the spatial resolution of the feature map. This avoids the information loss inherent in traditional convolution at a single scale, allowing the flow field extraction model to simultaneously retain the compact structure and diffusion characteristics of the sub-mesoscale flow field. The dynamic guidance mechanism of the preliminary flow field uses it as prior knowledge to guide the flow field extraction model to focus on regions of drastic flow field changes, suppress irrelevant background noise, and enhance key detail features such as frontal boundaries. This processing mechanism, through a strategy of "multi-scale perception - motion guidance - feature complementarity," makes the flow field topology closer to the characteristics of real ocean dynamics, the generated flow field more consistent with the law of mass conservation, reduces non-physical velocity fluctuations, and improves the self-consistency and spatiotemporal continuity of fluid dynamics. The detail enhancement module and the boundary attention module complement each other, jointly constructing a complete flow field representation system. This provides richer spatiotemporal cues for the subsequent volume construction module, enabling the model to more accurately capture the two-dimensional spatial structure and temporal evolution of the flow field. It significantly improves the model's ability to depict the complex details of the sub-mesoscale flow field, achieving a better balance between physical rationality, spatial resolution, and temporal continuity in the flow field extraction results.

[0052] S104. The volume construction module generates a multi-scale pyramid based on the enhanced continuous feature map, determines the search radius based on each scale of the multi-scale pyramid, and constructs the relevant volume.

[0053] Specifically, the volume construction module is the spatiotemporal correlation engine in the flow field extraction model. It is used to establish pixel-level spatiotemporal correspondences in the enhanced continuous feature map, providing motion cues for subsequent flow field estimation. The volume construction module achieves feature matching at different granularities through a multi-scale pyramid structure and captures the spatiotemporal continuity of fluid motion by explicitly encoding the similarity between features through related volumes.

[0054] A multi-scale pyramid is a feature set that organizes enhanced continuous feature maps into different resolution levels. Each level reduces the spatial dimension through downsampling (e.g., a convolution stride of 2) while increasing the number of channels (e.g., doubling the number) to preserve semantic information. For example, if the enhanced continuous feature map is H×W×C, the size of the Lth layer feature map in the multi-scale pyramid is H / 2. L ×W / 2 L ×C×2 L .

[0055] Furthermore, the correlation volume is a 4D tensor that records the similarity of all pixel pairs between the reference feature map (at time t) and the target feature map (at time t+Δt). For each pixel position (x, y) in the reference feature map, the feature similarity is calculated in the target feature map within a neighborhood centered at (x, y) with a radius of R, forming a (2R+1)×(2R+1) similarity matrix. The similarity matrices of all pixel positions are combined to form the correlation volume, with dimensions H×W×(2R+1)×(2R+1).

[0056] In specific implementation, the volume construction module generates a multi-scale pyramid based on the enhanced continuous feature map, determines the search radius based on each scale of the multi-scale pyramid, and constructs a relevant volume, including: reshaping the enhanced continuous feature map to obtain different three-dimensional matrices under a unified dimension; calculating the dot product of each pair of pixels in the different three-dimensional matrices through matrix multiplication, dividing each dot product result by the norm product of the corresponding pixel feature vector, and generating a four-dimensional relevant volume; each element of the four-dimensional relevant volume represents the correlation coefficient of different pixels in the second continuous feature map; performing four-level pyramid downsampling processing on the four-dimensional relevant volume, with each level of downsampling generating a four-level relevant volume pyramid with linearly decreasing resolution through average pooling operation; determining the search radius based on the exponential power of the relevant volumes at each level, and determining the relevant volume in a local region with the velocity component of each pixel in the current flow field as the center and the search radius.

[0057] Specifically, the enhanced continuous feature maps (such as two consecutive feature maps F1 and F2) are adjusted to the same dimension through padding or cropping to ensure consistent spatial size. The enhanced continuous feature maps F1 and F2 are then reshaped into three-dimensional matrices with dimensions [H×W, C], where H×W is the total number of pixels and C is the number of feature channels. Pixel pair similarity is calculated for different three-dimensional matrices F1 and F2 using matrix multiplication. For each pixel feature vector in F1... and the feature vector of each pixel in F2 Calculate the dot product · Normalize each dot product result by dividing each dot product result by . and L2 norm product (|| ||·|| The standardized correlation coefficients are obtained by using the normalized correlation coefficients of all pixel pairs. The normalized correlation coefficients of all pixel pairs are organized into a four-dimensional tensor [H, W, H, W], which is the four-dimensional correlation volume Corr, where Corr [i, j, k, l] represents the correlation between pixel (i, j) in F1 and pixel (k, l) in F2.

[0058] ;

[0059] Among them, the The four-dimensional related volume; For pixels in the continuous feature map F1, the These are the pixels in the continuous feature map F2.

[0060] Furthermore, the four-dimensional correlation volume Corr is downsampled in four levels, with each level using 2×2 average pooling (step size 2). Level 0 is the original Corr (resolution H×W), level 1 is downsampled to H / 2×W / 2, level 2 to H / 4×W / 4, and level 3 to H / 8×W / 8, forming a pyramid structure with resolution decreasing by a factor of 2. For each level of the correlation volume pyramid, its exponent (e^Corr) is calculated to enhance peak significance. Based on the current flow field predicted velocity components (u, v), a search radius R is set for each pixel (i, j) (e.g., R = 8×2^l, where l is the pyramid level). Centered on each pixel (i, j), a local region of (u±R, v±R) is extracted in F2 to generate a local correlation volume.

[0061] The method provided in this embodiment generates a four-dimensional correlated volume through feature normalization processing in the volume construction module. It standardizes the correlation coefficients of pixel pairs to reduce interference from non-motion factors such as illumination, making the matching process more stable. It uses multi-scale pyramid downsampling to form correlated volume representations with different resolutions, covering motion patterns at different scales from fine to coarse. This can capture details of fast motion in a small area and handle slow displacement at a large scale, avoiding information loss at a single scale. The search radius is dynamically determined based on the exponential power of the correlated volume, enabling the model to adaptively adjust the search range according to the local motion intensity. In areas with high flow velocity, the search is expanded to cover possible displacements, while in areas with low flow velocity, the search range is narrowed to focus on details, achieving a reasonable allocation of computing resources. Local correlated volumes are extracted with the current flow field velocity component as the center, forming a "prediction-refinement" closed-loop mechanism. Combined with existing flow field estimation, this further locks the real displacement region and reduces irrelevant noise interference. This approach optimizes the relevant volume structure in multiple dimensions, enabling it to adapt to the motion characteristics of complex scenarios. It also improves matching accuracy and computational efficiency through dynamic mechanisms, ultimately enhancing the continuity of flow field extraction at different scales, the accuracy of local details, and the robustness of overall estimation. This ensures that the flow field prediction is closer to the real motion pattern.

[0062] S105. The circulating flow field refinement module uses a convolution gated circulating unit to refine the circulating flow field of the relevant volume, and obtains the preliminary flow field through iterative updates.

[0063] Specifically, the recurrent flow field refinement module uses convolutionally gated recurrent units to perform temporal processing on relevant volumes, gradually improving the accuracy of flow field estimation through an iterative optimization mechanism. A convolutionally gated recurrent unit is a neural network component that integrates convolution operations and gated recurrent structures. It replaces the fully connected operations used in traditional recurrent units for processing sequential data with convolution operations, enabling the model to capture temporal dependencies while preserving the local correlations of spatial features—through convolutional calculations of the input gate, forget gate, and output gate, it achieves selective memorization and updating of feature information at spatial locations, making it particularly suitable for processing dynamic data with spatial continuity, such as flow fields.

[0064] Furthermore, cyclic flow field refinement refers to utilizing the iterative characteristics of convolutionally gated cyclic units to transform the pixel correlation information contained in relevant volumes into a temporal update process for flow field estimation. In each iteration, the model adjusts the velocity component predictions at each location based on the current flow field state and the matching relationship in the relevant volumes through a convolutional gating mechanism. The flow field state at the previous moment is passed as a hidden state to the next moment, forming a cyclic optimization link of "estimation-update-re-estimation". This allows the flow field to gradually approach the real motion pattern in multiple iterations, effectively eliminating local noise and discontinuity errors in the initial estimation, and ultimately obtaining a smoother preliminary flow field result that conforms to physical laws. This processing method combines spatial feature matching with temporal series optimization, utilizing both the static matching information of pixel correlation in relevant volumes and introducing dynamic temporal constraints through a cyclic mechanism, thereby improving the overall accuracy and spatiotemporal consistency of flow field extraction.

[0065] In specific implementation, the cyclic flow field refinement module uses a convolutional gated cyclic unit to refine the flow field of the relevant volume, and obtains a preliminary flow field through iterative updates, including: generating a context code based on the target feature map in the enhanced continuous feature map, initializing the hidden state and static input code; the target feature map is the feature map that appears first in the continuous feature map; performing multiple iterative updates on the relevant volume, and fusing the context code, relevant features and hidden state through a convolutional gated cyclic unit in each iteration to generate a flow field increment; the relevant features are determined from the relevant volume based on the current flow field; and applying endpoint error supervision to intermediate results during the iteration process, accumulating the flow field increment to obtain the preliminary flow field.

[0066] Specifically, the previous frame is extracted as the target feature map from the enhanced continuous feature map. A 3×3 convolutional layer is used for global feature extraction to generate a context encoding vector. This context encoding is then input into a fully connected layer to generate the initial hidden state and static input encoding, where the hidden state dimension is consistent with the flow field dimension. Further, based on the initial flow field (all zeros or random initialization), bilinear interpolation sampling is performed on the four-dimensional related volume to extract the relevant feature vector corresponding to each pixel. The number of iterations is then set, preparing for the cyclic refinement process.

[0067] Furthermore, the flow field is iteratively updated through a convolutionally gated recurrent unit (CLU). In each iteration, the CLU performs the following calculations: Input gate calculation: The current flow field, relevant features, and hidden states are fused using a 3×3 convolution, and an input gate vector is generated by sigmoid activation to control the inflow of new information; Forget gate calculation: Similarly, a forget gate vector is generated by convolution and sigmoid activation to determine the retention ratio of old hidden states; Candidate state calculation: Candidate states are generated by convolution and Tanh activation, fusing context encoding with current relevant features; Hidden state update: Based on the input gate and forget gate, the hidden state is updated: H_t = Forget gate ⊙ H_{t-1} + Input gate ⊙ Candidate state; Flow field increment generation: The updated hidden state is mapped to the flow field increment (U increment, V increment) by a 1×1 convolution. After each iteration, the sampling coordinates are recalculated based on the current flow field (initial flow field + cumulative increment), and the updated relevant features are extracted from the relevant volumes, forming a closed-loop feedback of "flow field - relevant features". After each iteration, the endpoint error between the current flow field and the actual flow field is calculated, and the model parameters are optimized through backpropagation. The flow field increment generated in each iteration is accumulated into the initial flow field, and the final preliminary flow field is obtained after the iteration ends.

[0068] For example, in one embodiment, it is set This represents the relevant features extracted around the current flow field estimation, where, It is a related dimension. It is the spatial dimension of the continuous feature map. Let... Indicates from the target feature map The context encoding obtained by a separate convolutional encoder, where, This refers to the context channel size. Context encoding. Divided into two parts: initial hidden state and static input encoding .set up Iteration Optical flow estimation at time, This indicates an incremental update. Each iteration... The detailed calculation is as follows:

[0069] ;

[0070] ;

[0071] in, Indicates based on the current flow field Relevant features of the search It is time The hidden state, Static input encoding; For incremental updates; It is time The hidden state; It is iteration Optical flow estimation at time.

[0072] The method provided in this embodiment uses a recurrent flow field refinement module to iteratively update relevant volumes using convolutionally gated recurrent units to determine the initial flow field. This process generates context encoding based on the target feature map in the enhanced continuous feature map and initializes the hidden state and static input encoding, incorporating global motion information and a reasonable iteration starting point into the flow field estimation. This allows the model to avoid local motion ambiguity by leveraging context constraints during processing. In multiple iterations of relevant volumes, the flow field increment is generated by fusing context encoding, dynamically updated relevant features, and hidden states through convolutionally gated recurrent units. This iterative mechanism optimizes the flow field from coarse to fine, first capturing large-scale motion trends and then gradually refining local details. Furthermore, the feedback loop that dynamically extracts relevant features based on the current flow field allows the model to adaptively focus on key areas based on real-time flow field estimation. Combined with the gating mechanism to retain historical effective information and filter noise, the temporal consistency of the flow field is improved. The endpoint error supervision applied during the iteration process directly affects the intermediate flow field. By accumulating the flow field increment through residual learning, each iteration is driven closer to the real motion, avoiding error accumulation. The preliminary flow field obtained through this process possesses geometric accuracy and temporal coherence, providing high-quality input for subsequent physical constraint correction. Its implicit motion continuity constraint brings the divergence closer to zero, reducing the number of iterations required to solve the Poisson equation. At the same time, the accuracy of the flow field details ensures more precise calculation of the potential function gradient. This allows the final flow field to satisfy physical incompressibility while, through reasoning about occluded regions, phased optimization of large displacements, and improved noise resistance, more closely approximating real motion in complex scenarios, achieving end-to-end optimization from visual motion laws to physical constraints.

[0073] S106. The physical constraint correction module performs physical constraint correction on the preliminary flow field, eliminates the flow field divergence by solving the Poisson equation, and obtains the final sea surface flow field.

[0074] Specifically, the physical constraint correction module is used to optimize the initial flow field at the physical rule level. By solving the Poisson equation, it eliminates the divergence in the flow field, so that the flow field satisfies the incompressibility constraint in fluid mechanics (i.e., volume conservation during fluid flow), and obtains the final sea surface flow field that conforms to physical laws.

[0075] It's important to note that the initial flow field may exhibit non-zero divergence, meaning there might be unreasonable phenomena of fluid "divergence" or "convergence" within the flow field. For example, when the divergence is positive, it means the fluid "disappears out of thin air" in that region; when the divergence is negative, the fluid "appears out of thin air," which contradicts the incompressible properties of real fluids (such as water and air). This type of problem stems from the fact that neural networks may lack explicit modeling of physical constraints when predicting the flow field, learning motion patterns only through data-driven methods, leading to predictions that are not physically rigorous. Therefore, it is necessary to perform physical constraint correction on the initial flow field to adjust for these physical inconsistencies in the prediction results.

[0076] In specific implementation, the physical constraint correction module performs physical constraint correction on the preliminary flow field, eliminates flow field divergence by solving the Poisson equation, and obtains the final sea surface flow field. This includes: upsampling the preliminary flow field to the original resolution of the continuous satellite image; calculating the divergence of the upsampled preliminary flow field using the Sobel operator, and establishing the Poisson equation based on the relationship between flow field divergence and potential function; solving the Poisson equation using the Jacobi iteration method to obtain the potential function; calculating the gradient of the potential function using the Sobel operator, and subtracting the gradient from the preliminary flow field to obtain the final sea surface flow field.

[0077] Specifically, a bilinear interpolation algorithm is used to enlarge the initial flow field (usually the size of a continuous feature map resolution) output by the cyclic flow field refinement module to the original size of the satellite image, ensuring that the flow field corresponds one-to-one with the pixels of the satellite image.

[0078] The final sea surface current field can be expressed as:

[0079] ;

[0080] Among them, the For the final sea surface current field; the aforementioned This is the initial flow field; the For gradient.

[0081] The method provided in this embodiment involves a physical constraint correction module that restores the initial flow field resolution through upsampling, establishing pixel-level alignment with the original satellite image to provide a foundation for subsequent image-space-based divergence calculation. The Sobel operator is used to calculate the flow field divergence, conforming to the physical definition of divergence in fluid mechanics and leveraging its edge-sensitivity to capture fluid boundary motion. The divergence field is transformed into a potential function problem using the Poisson equation, introducing the physical constraint of incompressible fluids to force the flow field to satisfy the law of mass conservation. The Jacobi iteration method is used to update the potential function point-by-point, ensuring numerical stability and gradually reducing the divergence value, bringing the flow field closer to a divergence-free state. Finally, the gradient of the potential function is subtracted from the initial flow field, combining data-driven motion estimation with physical constraints to directionally adjust the non-zero divergence region, eliminating non-physical artifacts while preserving high-frequency details of the flow field. This processing flow, through multi-stage collaborative optimization, ensures that the final flow field conforms to physical laws globally and preserves motion characteristics locally, improving the realism, consistency, and engineering practicality of the flow field estimation. It is suitable for physical modeling and environmental monitoring of complex fluid scenarios.

[0082] Optionally, the step of calculating the divergence of the initial flow field after upsampling using the Sobel operator includes: calculating the lateral partial derivative of the horizontal velocity component and the longitudinal partial derivative of the vertical velocity component using the Sobel operator; and adding the lateral partial derivative and the longitudinal partial derivative to obtain the divergence of the initial flow field.

[0083] In practice, the initial flow field after upsampling is decomposed into horizontal velocity components. and vertical velocity component Both the horizontal and vertical velocity components are two-dimensional matrices of the same size as the feature map. The preliminary flow field is represented as follows: For the horizontal velocity component Calculate the lateral partial derivatives using the horizontal Sobel operator (3×3 convolution kernel). For the vertical velocity component Calculate the longitudinal partial derivatives using the Sobel operator in the vertical direction. By adding the lateral and longitudinal partial derivatives point by point, the divergence of the initial flow field is obtained: .

[0084] The formula for calculating the divergence of the initial flow field can be expressed as:

[0085] ;

[0086] Among them, the The divergence of the initial flow field; the For the preliminary flow field; the The position in the image plane; The lateral partial derivative; This is the longitudinal partial derivative.

[0087] Optionally, the step of solving the Poisson equation using the Jacobi iteration method to obtain the potential function includes: initializing the potential function matrix by setting all elements of the potential function matrix to zero; the number of rows and columns of the potential function matrix being the same as the initial flow field matrix after upsampling; performing multiple iterations to update the potential function matrix, calculating the average potential function of the four adjacent grid points (east, west, south, and north) for each grid point in each iteration, and subtracting a specified multiple of the flow field divergence value of the grid point from the average value; the specified multiple being determined based on the Laplace operator template after discretization of the Poisson equation; after each iteration, calculating the mean square error between the current potential function matrix and the result of the previous iteration; if the mean square error is less than a preset threshold, the iteration is terminated; otherwise, the next iteration continues, and the potential function is determined based on the results of multiple iterations.

[0088] In practice, a potential function matrix of the same size as the initial flow field matrix after upsampling is constructed, and all elements of the potential function matrix are initialized to 0. A maximum number of iterations and a convergence threshold are set. The relaxation factor is determined based on the Laplace operator template after discretization of the Poisson equation; for example, the relaxation factor for a two-dimensional Laplace operator is one-quarter. For each iteration, the result of the previous iteration is first saved, and the current potential function matrix is ​​copied to a temporary matrix. Then, each grid point is traversed, and for each internal point in the matrix, the potential function values ​​of its four neighbors (east, west, south, and north neighbors) are obtained, and the average value of the four neighbors' potential functions is calculated. The potential function of the current point is updated based on the calculated average value, while keeping the potential function value of the boundary points at 0 during the iteration process. Furthermore, after each iteration, the mean square error between the current iteration result and the previous iteration result is calculated. If the mean square error is less than a preset threshold, the iteration is terminated; otherwise, the next iteration is executed. After the iteration terminates, the potential function is determined.

[0089] For example, in one embodiment, a potential function is introduced to correct the flow field. This allows its gradient to be subtracted from the initial flow field: Among them, the aforementioned For divergence; the stated This is the initial flow field; the It is a potential function.

[0090] To ensure that the corrected flow field is incompressible, the following is specified:

[0091] ;

[0092] in, For the Laplace operator; the stated For divergence; the stated This is the initial flow field; the The potential function; This represents the spatial gradient.

[0093] Therefore, the potential function The Poisson equation must be satisfied:

[0094] ;

[0095] Among them, the For the Laplace operator; the stated The potential function; For spatial gradient; the This represents the initial flow field.

[0096] The Laplace operator uses a discrete kernel approximation: ;

[0097] Therefore, the discrete Laplace is:

[0098] ;

[0099] Among them, the For discrete Laplace; the For the Laplace operator; the stated It is a potential function.

[0100] Then, the differentially comparable iteration is used to solve the problem. The update rules are as follows:

[0101] ;

[0102] in, The , The potential function for adjacent iterations; the For the Laplace operator; This represents the divergence.

[0103] Therefore, the above formula can be expressed as:

[0104] .

[0105] Among them, the , The potential function for adjacent iterations; the For the Laplace operator; This represents the divergence.

[0106] The method provided in this embodiment, in its first aspect, achieves targeted feature enhancement through a boundary attention module and a detail enhancement module. It utilizes the Sobel operator to extract edge features and combines channel and spatial attention mechanisms to highlight the spatial continuity of key boundaries such as ocean current edges and vortex contours. Simultaneously, it employs multi-scale dilated convolution and preliminary flow field guidance to capture detailed features such as sub-mesoscale vortices. This processing method enables the enhanced feature map to accurately depict the spatial contours and subtle changes of fluid boundaries, providing a reliable feature foundation for subsequent volume construction, avoiding flow field estimation bias caused by feature ambiguity, and significantly improving the motion capture capability and detail integrity at complex flow field boundaries. In its second aspect, it relies on a multi-scale iterative optimization mechanism formed by a volume construction module and a cyclic flow field refinement module. By generating a multi-scale pyramid and a dynamic search radius to construct relevant volumes, it achieves coarse-to-fine motion pattern coverage. Then, it utilizes convolutionally gated cyclic units to fuse context encoding and dynamically related features, generating flow field increments through iterative updates. This mechanism enables the model to adaptively focus on key regions, gradually approximating the actual motion pattern through a closed-loop iteration of "prediction-update-re-estimation," effectively eliminating noise and discontinuities in the initial estimation, improving the spatiotemporal consistency and geometric accuracy of the flow field, and providing high-quality input for physical constraint correction. Thirdly, a Poisson equation solution mechanism is introduced using a physical constraint correction module. After upsampling the flow field to the original resolution, divergence is calculated, and the potential function is solved based on Jacobi iteration to correct the flow field velocity components. This approach deeply integrates data-driven flow field prediction with fluid dynamics incompressibility constraints, eliminating non-physical divergence or convergence phenomena in the flow field point by point, ensuring that the final flow field satisfies the law of mass conservation. Simultaneously, gradient correction preserves boundary and detailed features, making the flow field both conform to physical laws and maintain a fine motion structure, significantly improving its practicality and reliability in scenarios such as ocean dynamics simulation and ecological material transport analysis.

[0107] Corresponding to the aforementioned embodiment of a sub-mesoscale flow field method based on boundary-aware Poisson constraints, this application also provides an embodiment of a sub-mesoscale flow field device based on boundary-aware Poisson constraints.

[0108] Figure 2 This is a schematic diagram of the sub-mesoscale flow field device based on boundary sensing and Poisson constraints provided in Embodiment 2 of this application. Please refer to... Figure 2 The apparatus provided in this embodiment includes an acquisition module 210 and a processing module 220;

[0109] The acquisition module 210 is used to acquire geostationary ocean color satellite image data;

[0110] The processing module 220 is used to input continuous satellite images into a trained flow field extraction model. The flow field extraction model downsamples the continuous satellite images to obtain continuous feature maps. The continuous feature maps are sea surface velocity field feature maps at two consecutive time points. The flow field extraction model includes a boundary attention module, a detail enhancement module, a volume construction module, a circulating flow field refinement module, and a physical constraint correction module.

[0111] The boundary attention module extracts and enhances the boundary structure of the continuous feature map, and the detail enhancement module extracts and enhances the detail features of the continuous feature map to obtain the enhanced continuous feature map.

[0112] The volume construction module generates a multi-scale pyramid based on the enhanced continuous feature map, determines the search radius based on each scale of the multi-scale pyramid, and constructs the relevant volume.

[0113] The circulating flow field refinement module uses a convolution gated circulating unit to refine the circulating flow field of the relevant volume, and obtains the preliminary flow field through iterative updates.

[0114] The physical constraint correction module performs physical constraint correction on the preliminary flow field, eliminates flow field divergence by solving the Poisson equation, and obtains the final sea surface flow field.

[0115] The apparatus of this embodiment can be used to perform... Figure 1 The steps of the method embodiment shown are similar in principle and process, and will not be repeated here.

[0116] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0117] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0118] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for submesoscale flow field extraction based on boundary awareness and Poisson constraint, characterized in that, The method comprises: acquiring static ocean color satellite image data; inputting continuous satellite images into a trained flow field extraction model, the flow field extraction model down-samples the continuous satellite images to obtain continuous feature maps; the continuous feature maps are sea surface velocity field feature maps at two continuous time points; the flow field extraction model comprises a boundary attention module, a detail enhancement module, a volume construction module, a cyclic flow field refinement module, and a physical constraint correction module; the boundary attention module extracts and enhances the boundary structure of the continuous feature maps, and the detail enhancement module extracts and enhances the detail features in the continuous feature maps to obtain enhanced continuous feature maps; the volume construction module generates a multi-scale pyramid based on the enhanced continuous feature maps, determines a search radius based on each scale of the multi-scale pyramid, and constructs a relevant volume; the cyclic flow field refinement module uses a convolution gate cycle unit to perform cyclic flow field refinement on the relevant volume, and updates the relevant volume through multiple rounds of iteration to obtain a preliminary flow field; the preliminary flow field is a stage result after multiple rounds of iteration, and the detail enhancement module is fed back using the generated preliminary flow field during the iteration optimization process; the physical constraint correction module corrects the preliminary flow field based on physical constraints, solves a Poisson equation to eliminate the divergence of the flow field, and obtains a final sea surface flow field.

2. The method of claim 1, wherein, The boundary attention module extracts and enhances the boundary structure in the continuous feature maps, comprising: performing edge detection on the continuous feature maps using a Sobel operator to obtain edge features; performing channel attention and spatial attention calculations on the edge features to generate channel weights and spatial weights; multiplying the channel weights and spatial weights and fusing them with the continuous feature maps to obtain enhanced continuous feature maps.

3. The method of claim 1, wherein, The detail enhancement module extracts and enhances the detail features in the continuous feature maps, comprising: performing multi-scale feature extraction on the continuous feature maps using multiple parallel dilation convolution branches with different dilation rates to obtain outputs of multiple branches; splicing the outputs of the branches and fusing them through convolution to obtain detail enhancement features; determining whether there is a preliminary flow field generated in the previous round of iteration, and when it is determined that there is, bilinearly up-sampling the preliminary flow field generated in the previous round of iteration to the size of the continuous feature maps, splicing the detail enhancement features, and fusing them through convolution to obtain enhanced continuous feature maps.

4. The method of claim 1, wherein, The volume construction module generates a multi-scale pyramid based on the enhanced continuous feature maps, determines a search radius based on each scale of the multi-scale pyramid, and constructs a relevant volume, comprising: reshaping the enhanced continuous feature maps to obtain different three-dimensional matrices under a unified dimension; calculating the dot product of each pixel pair in the different three-dimensional matrices through matrix multiplication, dividing each dot product result by the norm product of the corresponding pixel feature vectors, and generating a four-dimensional relevant volume; each element of the four-dimensional relevant volume represents the correlation coefficient of different pixel points in the second continuous feature map; The four-dimensional correlation volume is subjected to four-level pyramid down-sampling processing, and each level of down-sampling generates a correlation volume pyramid with four-level resolution linearly decreasing through an average pooling operation; A search radius is determined based on an exponential power of each level of correlation volume, and a correlation volume in a local region is determined within the search radius, with the speed component of each pixel in the current flow field as the center.

5. The method of claim 1, wherein, The circulation flow field refinement module utilizes a convolutional gated recurrent unit to refine the correlation volume to obtain a preliminary flow field through iterative updating, including: Context encoding is generated based on a target feature map in the enhanced continuous feature map, a hidden state is initialized, and static input encoding is initialized; the target feature map is a previous feature map in the continuous feature map; The correlation volume is subjected to multiple iterative updates, and each iteration fuses the context encoding, a correlation feature, and the hidden state through a convolutional gated recurrent unit to generate a flow field increment; the correlation feature is determined from the correlation volume based on a current flow field; End-point error supervision is applied to an intermediate result in the iteration process, and the flow field increment is accumulated to obtain the preliminary flow field.

6. The method of claim 1, wherein, The physical constraint correction module corrects the preliminary flow field based on physical constraints, eliminates flow field divergence by solving a Poisson equation, and obtains a final sea surface flow field, including: The preliminary flow field is up-sampled to the original resolution of the continuous satellite image; A Sobel operator is used to calculate the divergence of the up-sampled preliminary flow field, and a Poisson equation is established based on the relationship between the flow field divergence and the potential function; A Jacobi iteration method is used to solve the Poisson equation to obtain the potential function; A Sobel operator is used to calculate the gradient of the potential function, and the preliminary flow field is subtracted by the gradient to obtain the final sea surface flow field.

7. The method of claim 6, wherein, The method for calculating the divergence of the up-sampled preliminary flow field using a Sobel operator includes: A Sobel operator is used to calculate the transverse partial derivative of the horizontal velocity component and the longitudinal partial derivative of the vertical velocity component, respectively; The transverse partial derivative and the longitudinal partial derivative are added to obtain the divergence of the preliminary flow field.

8. The method of claim 6, wherein, The method for solving the Poisson equation using a Jacobi iteration method to obtain the potential function includes: A potential function matrix is initialized, and all elements of the potential function matrix are set to zero; the number of rows and columns of the potential function matrix is the same as that of the up-sampled preliminary flow field matrix; The potential function matrix is subjected to multiple iterative updates, and in each iteration, the average value of the potential functions of the east, west, south, and north adjacent grid points of each grid point is calculated, and the average value is subtracted by the flow field divergence value of the grid point multiplied by a specified multiple; the specified multiple is determined based on a Laplace operator template after the Poisson equation is discretized; After each iteration is completed, the mean square error between the current potential function matrix and the result of the last iteration is calculated, and if the mean square error is less than a preset threshold, the iteration is terminated, otherwise the next iteration is continued, and the potential function is determined based on the results of multiple iterations.

9. The method of claim 1, wherein, The flow field extraction model takes the end-point error as a loss function, and the method further includes: For each pixel position, the Euclidean distance between the flow field vector extracted by the flow field extraction model and the corresponding real flow field vector is calculated; The Euclidean distances of all pixel positions are squared and summed, and then divided by the total number of pixels to obtain an end-point error value; the end-point error is a velocity error.

10. A device for extracting a submesoscale flow field based on boundary awareness and Poisson constraint, characterized in that, The device comprises an acquisition module and a processing module; The acquisition module is configured to acquire static marine ocean color satellite image data; The processing module is configured to input continuous satellite images into a trained flow field extraction model, down-sample the continuous satellite images by using the flow field extraction model, and obtain continuous feature maps; the continuous feature maps are sea surface velocity field feature maps at two continuous time points; the flow field extraction model comprises a boundary attention module, a detail enhancement module, a volume construction module, a cyclic flow field refinement module, and a physical constraint correction module; The boundary attention module is configured to perform feature extraction and enhancement on boundary structures of the continuous feature maps, and the detail enhancement module is configured to perform feature extraction and enhancement on detail features in the continuous feature maps to obtain enhanced continuous feature maps; The volume construction module is configured to generate a multi-scale pyramid based on the enhanced continuous feature maps, determine a search radius based on each scale of the multi-scale pyramid, and construct a relevant volume; The cyclic flow field refinement module is configured to perform cyclic flow field refinement on the relevant volume by using a convolution gate cycle unit, and obtain a preliminary flow field through multiple rounds of iterative updates; the preliminary flow field is a stage result after multiple rounds of iterations, and the detail enhancement module is fed back by using the generated preliminary flow field during the iterative optimization process; The physical constraint correction module is configured to perform physical constraint correction on the preliminary flow field, eliminate flow field divergence by solving a Poisson equation, and obtain a final sea surface flow field.

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