A three-dimensional mesoscale vortex detection method based on surface-to-volume physical constraint

Abstract

This application provides a three-dimensional mesoscale eddy detection method based on surface-to-volume physical constraints, belonging to the field of ocean observation and intelligent detection technology. Addressing the shortcomings of existing intelligent detection technologies, a three-dimensional mesoscale eddy inversion model is constructed. The model training method first constructs a dedicated dataset based on ocean physical reanalysis data, and generates three-dimensional eddy semantic segmentation labels by combining the VG algorithm, inter-layer matching, and spatial mapping. Eddypower prediction physical labels are obtained using ocean current field physical calculations. Then, a model is built based on the U-Net architecture, with an attention mechanism and cross-level feature fusion module added to optimize performance. Finally, eddypower physical constraints are introduced into the cross-entropy loss function, and combined with edge gradient information for joint optimization, enhancing the model's feature extraction capability. This invention overcomes the limitations of traditional methods in boundary characterization, effectively improving the accuracy of inferring three-dimensional eddy structures from sea surface data, and can provide reliable technical support for ocean dynamics research.

Description

Technical Field

[0001] This application relates to the field of intelligent mesoscale eddy detection technology, and in particular to a three-dimensional mesoscale eddy detection method based on surface-to-volume physical constraints. Background Technology

[0002] Mesoscale eddies are a ubiquitous energy feature in the global ocean, ranging in spatial scale from tens to hundreds of kilometers and in temporal scale from days to months. Accompanied by high eddy kinetic energy, significant temperature and salinity anomalies, and relatively isolated water masses, they influence thermohaline redistribution, nutrient transport, and the marine ecosystem. A typical observable feature of mesoscale eddies is their cyclonic or anticyclonic rotating flow and local sea-level height anomalies. Satellite remote sensing provides long-term, wide-coverage, and high-resolution observations, including sea-level height (SSH), sea-level temperature (SST), and surface currents (SSU, SSV). These data have greatly facilitated the development of eddy detection and statistical analysis, leading to the proposal and widespread application of many mature algorithms.

[0003] However, mesoscale eddies are three-dimensional structures whose vertical stratification strongly influences the internal dynamic structure of the ocean at depths of hundreds or even thousands of meters. Vertical variations in eddies dominate the subsurface redistribution of heat, salinity, and nutrients, which is crucial for understanding ocean dynamics, interlayer mass exchange, and changes in the underwater environment. Accurate and efficient reconstruction of the three-dimensional structure of mesoscale eddies can provide vital support for marine applications such as naval operations, ocean engineering, and environmental monitoring. Therefore, studies limited to surface features are insufficient; the three-dimensional structure and subsurface evolution of mesoscale eddies are equally important.

[0004] Since the late 20th century, researchers have been studying the vertical structure of mesoscale eddies and their impact on subsurface hydrological conditions. In recent years, the quantitative extraction and geometric reconstruction of three-dimensional eddy structures have attracted increasing attention. Unlike conservative physical quantities, mesoscale eddies cannot be directly derived from original equations or analytical formulas; they must be detected, identified, and reconstructed from three-dimensional hydrological and velocity fields. However, existing deep learning-based three-dimensional eddy extraction methods suffer from insufficient physical constraints and inaccurate boundary localization, limiting their practical applications. Summary of the Invention

[0005] In view of the above problems, embodiments of this application provide a model training method, a mesoscale eddy recognition method, and an apparatus to improve the detection accuracy of artificial intelligence models, so as to overcome the above problems or at least partially solve the above problems.

[0006] In a first aspect, embodiments of this application provide a method for training a three-dimensional mesoscale eddy detection model guided by multi-source, multi-scale fusion of surface-volume physical information, the method comprising:

[0007] Acquire multi-source sample data and preprocess the multi-source sample data to obtain a mesoscale eddy dataset.

[0008] Input the sample mesoscale eddy dataset into the mesoscale eddy detection model to output the mesoscale eddy vortex of the three-dimensional structure;

[0009] Construct the total loss function of the mesoscale eddy detection model, and determine the total loss value of the model based on the mesoscale eddy in the three-dimensional structure;

[0010] Based on the total loss value of the model, the model parameters of the mesoscale eddy detection model are adjusted to obtain a three-dimensional mesoscale eddy detection model guided by the surface-volume physical information fused from multiple sources and at multiple scales of the target.

[0011] Furthermore, the multi-source, multi-scale fused surface-volume physical information-guided 3D mesoscale eddy detection model includes interconnected 2D physical feature extraction, 3D feature inversion, and 3D semantic segmentation modules; wherein:

[0012] The two-dimensional physical feature extraction module is used to extract multi-scale spatial features from multi-source sea surface observation data;

[0013] The 3D feature inversion module is used to establish a correlation mapping from sea surface features to deep volume features, thereby enhancing the spatial dimension.

[0014] The 3D semantic segmentation module adopts a U-Net-like architecture that includes spatial attention and channel attention mechanisms, and outputs 3D pixel-level vortex boundary depictions.

[0015] Furthermore, the two-dimensional physical feature extraction module adopts a topology structure of a shared backbone and a task-specific branch; the shared backbone is a shared feature encoder, used to map input data into 128-channel shared features containing texture and geometric information; the task-specific branch is a vortex prediction branch, used to extract dynamic information and provide physical information regularization, outputting 16-channel physical features; the two-dimensional physical feature extraction module compresses shared features and splices physical features through 1×1 convolution, and then completes deep fusion of multi-source information through a convolutional block attention module (CBAM), and the end of the vortex prediction branch predicts the vortex map used to calculate the physical gradient loss through a 1×1 convolution head.

[0016] Furthermore, the three-dimensional feature inversion module uses a U-Net-like feature expander to achieve implicit size inversion. It takes 80-channel fused features as input, captures large-scale context through the encoding path, restores spatial resolution through the decoding path, and finally outputs 800-channel features through the convolutional layer. These features are then recombined into a three-dimensional feature volume through a shaping operation, thus decoupling the depth information of the embedded channel dimension.

[0017] Furthermore, the three-dimensional semantic segmentation module is based on the 3D U-Net architecture. The encoder extracts spatiotemporal features and maintains the integrity of the vertical structure through three-dimensional convolution and anisotropic max pooling. The decoder refines the features by combining the 3D CBAM module and a multi-scale adaptive fusion mechanism. Finally, the class probability of each voxel is generated through convolutional mapping and Softmax activation to achieve high-precision three-dimensional vortex reconstruction.

[0018] Furthermore, the construction of the total loss function for the mesoscale eddy detection model and the determination of the total model loss value include:

[0019] Based on the predicted classification category and sample labels, the Dice coefficients for cyclonic vortices, antivortices, and non-vortices are determined respectively.

[0020] The weighted average Dice coefficient is obtained by taking the weighted average Dice coefficient of cyclone vortex, anti-vortex and non-vortex. Then, the weighted average Dice coefficient is subtracted from 1 to obtain the Dice coefficient loss value.

[0021] Determine the physical loss constraint between the sample labels and the predicted classification category;

[0022] The physical loss of the vorticity branch is a weighted combination of the mean squared error (MSE) and the gradient consistency loss:

[0023]

[0024] The hyperparameter was set to 0.05 to balance fidelity and physical consistency.

[0025]

[0026] A total loss function is established based on the Dice coefficient loss and physical loss constraints, and the total loss value of the model is determined according to the total loss function:

[0027]

[0028] in, =0.1 to prevent vorticity branch from dominating training.

[0029] Secondly, embodiments of this application provide a three-dimensional mesoscale eddy detection method based on surface-to-volume physical constraints, the method comprising:

[0030] Acquire the image to be detected;

[0031] The image to be detected is input into the target mesoscale eddy detection model to identify the mesoscale eddy classification category;

[0032] Based on the mesoscale vortex classification category, the three-dimensional mesoscale vortex mask in the image to be detected is determined.

[0033] Thirdly, embodiments of this application provide a three-dimensional mesoscale eddy recognition device, the device comprising:

[0034] The data acquisition module is used to acquire multi-source sample data and preprocess the multi-source sample data to obtain the sample mesoscale eddy dataset.

[0035] The input / output module is used to input the sample mesoscale eddy dataset into the mesoscale eddy detection model and output a three-dimensional mesoscale eddy mask.

[0036] The loss determination module is used to construct the total loss function of the mesoscale eddy detection model and determine the total loss value of the model.

[0037] The parameter adjustment module is used to adjust the model parameters of the mesoscale eddy detection model based on the total model loss value, so as to obtain the target mesoscale eddy detection model.

[0038] Fourthly, embodiments of this application provide an electronic device, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the model training method described above, or a three-dimensional mesoscale eddy detection method guided by multi-source, multi-scale fusion surface-volume physical information.

[0039] Fifthly, embodiments of this application provide a readable storage medium storing a program or instructions, which, when executed by a processor, implements the model training method described above, or a three-dimensional mesoscale eddy detection method guided by multi-source, multi-scale fusion surface-volume physical information.

[0040] The specific beneficial effects are as follows:

[0041] First, this application uses data from different sources, such as a combination of remote sensing data and reanalysis data, to make up for the deficiencies of single-source data through multi-source data;

[0042] Second, this application constructs an improved U-Net network model, which introduces a channel attention mechanism to the input of multi-source data, enabling it to adaptively focus on the importance of features of different channels and amplify the feature information of the object to highlight its main factors; at the same time, multi-source data is fused at the feature level at each level in the model to ensure that early data features are not lost.

[0043] Third, this application constructs a new loss function and adds a gradient difference constraint term to the loss function, which further strengthens the training features and thus further increases the feature difference of the model.

[0044] In summary, this invention can significantly improve the model's ability to identify mesoscale eddies, and is of great significance for the intelligent detection of ocean mesoscale eddies. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart of a model training method provided in Embodiment 1 of this application;

[0047] Figure 2 This is a flowchart of the inter-layer matching algorithm;

[0048] Figure 3 The overall mode structure for three-dimensional mesoscale vortex detection;

[0049] Figure 4 Here is a flowchart for loss calculation;

[0050] Figure 5 This is the architecture diagram of the baseline model;

[0051] Figure 6 Figures (a)-(f) show the visualization results of the three-dimensional vortex structures constructed using each scheme; where, Figure 6 (a) is a label; Figure 6 (b) is the baseline model; Figure 6 (c) represents ablation model 1; Figure 6 (d) represents ablation model 2; Figure 6 (e) is the 3D U-Res-Net model; Figure 6 (f) represents the final model;

[0052] Figure 7 In Figures (a)-(f), the boundary differences of the multi-layered vortices for each scheme are shown. Figure 7 (a) is the label. Figure 7 (b) is the baseline model. Figure 7 (c) represents ablation model 1. Figure 7 (d) represents ablation model 2. Figure 7 (e) is the 3D U-Res-Net model. Figure 7 (f) represents the final model;

[0053] Figure 8 Figures (a)-(f) visualize the model from different inputs; where, Figure 8 (a) is the label. Figure 8 (b) represents SSH. Figure 8 In the middle (c), SST is represented. Figure 8 In the middle (d), SSU / V is represented. Figure 8 In the middle (e), SSH+SST is used. Figure 8 In the middle (f), SSH+SST+SSU / V is used.

[0054] Figure 9 This section compares the vorticity prediction results. Among them, Figure 9 In (a), only MSE loss, Figure 9 In (b), the mixed loss (MSE + gradient consistency loss) is represented. For each, from left to right, the three columns represent the true vorticity, predicted vorticity, and prediction error, respectively. Detailed Implementation

[0055] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0056] Example 1

[0057] Reference Figure 1 , Figure 1 A flowchart of a three-dimensional mesoscale eddy detection method based on surface-to-volume physical constraints provided in this application embodiment is included, the method comprising the following steps:

[0058] Step 1: Obtain multi-source sample data and preprocess the multi-source sample data to obtain a mesoscale eddy dataset. Calculate the relative eddy and perform Z-score standardization.

[0059] Optionally, step 1 includes the following sub-steps:

[0060] Sub-step 101: Obtain sample reanalysis data;

[0061] Since mesoscale eddies are mainly concentrated above 1000m, and to avoid the shortcomings of low accuracy and weak signal in deep-sea data, this embodiment acquires sample reanalysis data within a depth of 1000m. The reanalysis data uses Global Ocean Reanalysis (GLORYS) data, sourced from the Copernicus Marine Environmental Monitoring Service (CMEMS), with a time range of 2015 and a spatial resolution of 1 / 12°. In this embodiment, the selected sea area for sample reanalysis data is (100°E~100°W, 5°N~65°N). Multi-layer ocean current field data for this region are extracted. The sample reanalysis data is thus the Global Ocean Reanalysis data.

[0062] Sub-step 102: Using vector geometry algorithms and interlayer vertical matching, identify and integrate vertically coherent three-dimensional vortex structures from multi-layer ocean data;

[0063] First, in the embodiments of this application, the VG algorithm is used to detect mesoscale vortices layer by layer according to depth. Table 1 summarizes the key parameters obtained by the VG algorithm.

[0064] Table 1 Output parameters of the VG algorithm

[0065]

[0066] Secondly, after obtaining the mesoscale vortices detected layer by layer based on depth using the VG method, an inter-layer matching procedure is applied to link the vertically continuous vortex features, such as... Figure 2 As shown, daily vortex instances are spatially matched at different depth levels, preserving a consistent 3D structure based on depth constraints, regional overlap, and vertical continuity. Vortices with the same identifier (belonging to the same vortex volume) are sorted by depth and integrated into a unified 3D vortex record.

[0067] Finally, to support standardized annotation and model training, global 3D features were extracted for each vortex, including top and bottom depth layers, total vertical extent, average geographic center, average area, average radius, and total tilt angle. These descriptors characterize the 3D geometry of each vortex and support subsequent cropping into 48×48 pixel patches.

[0068] Sub-step 103: By cropping, filtering, physical field extraction and layer-by-layer polygon annotation, the three-dimensional vortex data is converted into a pixel-level classification template. Based on the annotated sample reanalysis data and the unannotated sample reanalysis data, a sample mesoscale vortex dataset is constructed, and the sample mesoscale vortex dataset is divided into a training set and a test set.

[0069] Pixel-level 3D segmentation templates were generated from the vortex dataset, with each sample cropped into a fixed 48×48 pixel region (approximately 600 km wide), which fully covers the typical horizontal scale of a mesoscale vortex.

[0070] Effective vortices are filtered according to three criteria to ensure structural integrity: i) a maximum depth threshold of 1000m with a complete surface layer and continuous vertical morphology; ii) sufficient effective depth layers with no missing data; and iii) strict vertical continuity between all included levels.

[0071] Surface physics (SSH, SST, U / V) was extracted centered on the surface geometry of each vortex. For labeling, ten depth levels were defined with a vertical spacing of approximately 100m. For each layer, the boundary coordinates were converted to closed polygons using the Shapely library, and pixels were categorized into three classes: background (0), cyclonic vortex (1), and anticyclonic vortex (2). Land areas were masked as background. A total of over 3400 high-quality 3D vortex samples were prepared for training and testing.

[0072] Sub-step 104: To provide a supervision label for the physical constraint branch, calculate the relative vorticity and perform Z-score standardization, using it as a regression target to calculate the gradient consistency loss.

[0073] First, since the physical constraint (vortex prediction) branch of the proposed algorithm requires a reliable vortex map as a supervision label, the vortex is calculated based on the current velocity data. Relative vortex characterizes the rotational intensity of the fluid package and is mathematically defined as the vertical component of the curl of the velocity vector field, as shown in (1) below:

[0074] (1)

[0075] in and Let x and y represent the latitudinal and latitudinal components of the flow velocity, respectively. The program uses the gradient operator from the NumPy library and employs the second-order precision central difference method to calculate the spatial derivatives of the flow velocity field in the x and y directions.

[0076] Secondly, in order to eliminate the adverse effects of physical size differences on deep learning model training and prevent gradient vanishing due to excessively small numerical ranges, the calculated original vortex field... Further standardization was performed, as shown in formula (2):

[0077] (2)

[0078] In the formula, and These represent the mean and standard deviation of the vorticity samples in the training set, and the vorticity label after Z-score standardization. With zero mean and unit variance, it serves as the regression objective for the physics branch and is used to calculate gradient consistency loss along with the model's predicted output.

[0079] Step 2: Input the sample mesoscale eddy dataset into the mesoscale eddy detection model and output the mesoscale eddies of the three-dimensional structure;

[0080] The mesoscale eddy current 3D structure detection model integrates multi-source data such as SSH, SST, and surface velocity (UV), and adopts a cascaded structure of "shared backbone encoding → physical constraint branching → 3D feature inversion → 3D fine segmentation," combined with multiple fusion strategies. The architecture of this model is as follows: Figure 3 As shown.

[0081] To effectively mitigate the vanishing gradient problem and accelerate model convergence in deep networks, almost all basic convolutional units in the model use residual blocks as basic building blocks. The residual block structure consists of two consecutive 3×3 convolutional layers, a batch normalization layer, and a ReLU activation function.

[0082] The 2D physical feature extraction module, serving as the visual encoding front-end of the model, employs a topology of shared backbone and task-specific branches, aiming to simultaneously decouple the general semantic features and physical dynamic features of 2D surface data. First, the input data is fed into a shared feature encoder. The encoder uses an initial 3×3 convolutional layer to map the input to 32-channel shallow features, which are then passed consecutively through three residual convolutional blocks. As the network depth increases, the number of convolutional kernels is set to 64, 128, and 128 respectively. The stride is fixed at 1 to maintain the spatial resolution of the feature mapping, resulting in 128 channels of shared features rich in texture and geometric information. Second, a vortex prediction branch is established to extract dynamic information related to rotation and shear, providing physical information regularization. This branch contains three processing stages: the first two stages consist of 64-channel and 32-channel convolutional blocks, each followed by a 2D spatial attention module. The attention module generates a spatial weight map by calculating average pooling and max pooling features along the channel dimensions, guiding the model to focus on physically critical regions with strong vortex gradients. The third stage compresses the channels to 16 and outputs physical features for subsequent fusion. The 1×1 convolutional head at the end of the branch directly predicts the vortex map, which is used to calculate the physical gradient loss. Finally, to fuse semantic and physical information, the main path compresses the 128-channel shared features to 64 channels through a 1×1 convolution, and then concatenates them with the 16-channel physical features to form an 80-channel hybrid feature. The fused feature is then input into the Convolutional Block Attention (CBAM) module to adaptively recalibrate the feature weights, achieving deep fusion of multi-source information.

[0083] The 3D feature inversion module acts as a logical bridge between the 2D plane and the 3D volume. It uses a U-Net-like feature expander to achieve implicit size inversion. This module takes 80-channel fused features as input. The encoding path includes two downsampling stages, one for each convolutional block (160 and 320 channels) and 2×2 max pooling to capture large-scale context. The bottleneck is extended to 640 channels. The decoding path uses transposed convolutions to gradually restore spatial resolution and uses skip connections to fuse low-level features. The key innovation lies in the design of the output dimension. The final convolutional layer outputs 800 channels (10 for a predefined depth level × 80 for the basic 3D feature dimension). A shaping operation reassembles the 2D feature map H×W×800 into a 3D feature volume H×W×10×80, decoupling the depth information of the embedded channel dimension.

[0084] The 3D semantic segmentation module is built on a 3D U-Net architecture, enabling fine-grained parsing of vortex structures directly in 3D space. The encoder comprises two downsampling stages, using 3×3×3 3D convolutions to extract spatiotemporal features with channel counts of 80, 160, and 320. Anisotropic max pooling with a span of 2×2×1 is applied between stages to maintain vertical resolution while compressing the horizontal dimensions to preserve vertical structural integrity.

[0085] To mitigate excessive smoothing of deep details, the decoder incorporates a multi-scale adaptive fusion mechanism integrated with 3D CBAM. At each upsampling stage, the cascaded encoder and decoder features are first refined by a 3D CBAM module, which suppresses background noise and enhances the response at vortex boundaries. The refined features are then decoded by 3D convolutional blocks with 160 and 80 channels. Finally, a 1×1×1 convolution maps the output to three classes, and Softmax activation generates the probability for each voxel class, enabling high-precision 3D vortex reconstruction.

[0086] Step 3: Construct the total loss function of the mesoscale eddy detection model and determine the total loss value of the model.

[0087] The loss function is developed based on the concept of Physical Information Neural Networks (PINNs) and consists of two parts: segmentation loss and vortex-based physical loss, such as... Figure 4 As shown. The segmentation loss is calculated using Dice coefficients and supports the entire model fitting and training process. The physical loss is calculated by the vorticity prediction branch, where the predicted vorticity is compared to the vorticity label, and the vorticity loss is applied to impose physical constraints on the model training.

[0088] This design employs physical regularization for mesoscale eddy detection, enabling the model to learn more physically consistent features and improving the reliability of 3D eddy identification.

[0089] Optionally, step 3 includes the following sub-steps:

[0090] Sub-step 301: Calculate the Dice coefficients for cyclones, antivortices, and non-vortices based on the predicted classification categories and sample labels;

[0091] The Dice coefficient is a parameter that measures the similarity between two datasets. The calculation formula is shown in (3) below:

[0092] (3)

[0093] in, Represents the prediction set, Represents a set of tags, and express and Pixels in the intersection as well as They represent and The total number of pixels in the segment. The Dice coefficient ranges from 0 to 1, with values ​​closer to 1 indicating better segmentation performance. In this work, the Dice coefficient is used as a loss function to optimize the segmentation model.

[0094] Sub-step 302: Take a weighted average of the Dice coefficients of cyclones, antivortices and non-vortices to obtain the weighted average Dice coefficient, and then subtract the weighted average Dice coefficient from 1 to obtain the Dice coefficient loss value.

[0095] Since this model addresses multi-class segmentation problems with class imbalance (cyclonic vortex, anticyclonic vortex, and background), we use weighted Dice coefficients instead of a simple average. The class weights are set to the reciprocal of the sample proportion for each class. The weighted Dice coefficients and the corresponding losses are defined in equations (4) and (5), respectively.

[0096] (4)

[0097] (5)

[0098] dice_cyc, dice_acyc, and dice_bg represent the Dice coefficients for classification into cyclonic vortices, anticyclonic vortices, and background regions, respectively. and These are the weights assigned to each region. `dice_weighted` represents the overall weighted Dice coefficients of the data. By minimizing the coefficient loss during model training, we can enhance its learning and optimization capabilities for image segmentation tasks.

[0099] Sub-step 303: Calculate the physical loss constraint between the sea surface eddy label and the physical eddy prediction result based on the eddy prediction branch;

[0100] For vorticity regression, the loss is a weighted combination of mean squared error (MSE) and gradient consistency loss. While MSE effectively measures pixel-level numerical differences, it tends to over-smooth dynamic flow fields and discard fine-scale structure. To preserve physical clarity and spatial gradients, gradient consistency loss is introduced as a physical constraint. It penalizes the gradients of the predicted and actual vorticity fields in both the horizontal and vertical directions.

[0101] (6)

[0102] in, Ensure the accuracy of the numerical values ​​defined in formula (7), and Force structural smoothness. Set the hyperparameter to 0.05 to balance fidelity and physical consistency.

[0103] (7)

[0104] Sub-step 304: Establish the total loss function based on the weighted Dice coefficient loss of 3D segmentation and the physical loss constraint of vorticity prediction, and determine the total loss value of the model according to the total loss function;

[0105] By combining the two loss results above, the total loss function of the mesoscale eddy detection model is obtained, as shown in Equation (8).

[0106] (8)

[0107] in, =0.1 prevents vorticity branching from dominating training. This joint loss embodies the spirit of multi-task learning: the auxiliary vorticity prediction task injects physical inductive bias, guiding the main 3D segmentation task to focus on dynamically meaningful features, thereby improving segmentation accuracy and physical consistency.

[0108] Step 4: Based on the total loss value of the model, adjust the model parameters of the mesoscale eddy detection model to obtain the target mesoscale eddy detection model.

[0109] The model parameters are those in the improved U-Net model, including learning rate, batch size, weight decay, etc.

[0110] To avoid overfitting, the total loss value of the model on the test set is monitored. If the loss on the validation set does not decrease significantly within 30 consecutive epochs, the training process is automatically terminated, and the model with the best performance on the test set is retained as the target mesoscale eddy detection model. Alternatively, if the number of model parameter adjustments is greater than or equal to the preset number of iterations, the model parameter adjustments are stopped, and the model obtained after the last parameter adjustment is used as the target mesoscale eddy detection model.

[0111] Simulation Case

[0112] To verify the effectiveness of the three-dimensional mesoscale eddy detection method based on surface-to-volume physical constraints constructed in this invention, the following ablation experiments were conducted.

[0113] 1) Validation of the model structure ablation experiment

[0114] We conducted ablation experiments to validate the proposed model and analyze key components, including multi-scale feature fusion, attention mechanism, and physical information constraints. A series of ablation experiments are shown in Table 2.

[0115] Table 2 Ablation Experiment Design

[0116]

[0117] After removing all advanced modules, only the baseline model is retained, such as Figure 5 As shown, the baseline still consists of 2D feature extraction, 3D feature inversion, and 3D vortex segmentation modules. However, the vortex branch, the U-Net-based multi-scale structure, and the attention mechanism have been removed. The modules employ direct hard mapping: convolutional layers expand the channel dimension to form the feature volume later.

[0118] This experiment uses global accuracy, weighted Dice coefficient, and macroscopic average F1 score for evaluation, which together provide a comprehensive assessment under class imbalance. Global accuracy measures the overall prediction consistency across all pixels and is defined as:

[0119] (9)

[0120] TP, TN, FP, and FN represent true positive, true negative, false positive, and false negative, respectively.

[0121] To mitigate the bias caused by imbalanced classes, a weighted Dice coefficient (defined in equation (4)) is used. It weights the Dice score for each class based on the reciprocal of the sample frequency, making it more reliable for vortex segmentation.

[0122] The F1 score balances precision and recall and is robust to class imbalance in 3D vortex segmentation. Precision and recall are defined as follows:

[0123] (10)

[0124] (11)

[0125] The F1 score for a class is:

[0126] (12)

[0127] We use the macro-average F1 score, which is the arithmetic mean of the F1 scores for background, cyclonic eddies, and anticyclonic eddies, respectively, thus reducing the impact of imbalanced sample distribution. In summary, these three metrics evaluate the model from a complementary perspective: global accuracy reflects overall correctness, the weighted Dice coefficient indicates class imbalance, and the F1 score quantifies the reliability of segmenting small eddy regions. Together, they constitute a reliable and comprehensive evaluation framework.

[0128] Based on the baseline model and the settings in Table 2, the effectiveness of each component was validated by adding modules incrementally. The experimental results are summarized in Table 3.

[0129] As shown in Table 3, the full-module model achieves improvements in key metrics of 3D segmentation compared to the baseline model. Specifically, the global accuracy increases from 95.99% to 96.97%, the weighted Dice coefficient increases from 0.7976 to 0.8480, and the macro F1 score increases from 0.8592 to 0.8955. This improvement indicates that the proposed enhancement does not reflect overfitting to the background, but substantially strengthens the identification of vortex kernels and enables a more accurate representation of 3D vortex geometry.

[0130] Further ablation analysis revealed that the performance improvement stemmed from the synergistic integration of structural refinement and physical regularization. Firstly, the multi-scale inversion and 3D decoding stages confirmed that the multi-scale strategy forms the foundation for high-precision 3D reconstruction. After introducing a U-Net-based multi-scale feature expander (ablation model 1), the results verified that multi-scale context extraction via U-Net is more effective than simple linear channel expansion. Ablation model 2 further incorporated multi-scale feature fusion into the 3D decoder, with the weighted Dice coefficient steadily increasing to 0.8056, indicating that multi-scale fusion effectively recovered deeply lost high-frequency details, producing clearer 3D vortex boundaries and better matching the ground reality.

[0131] The introduction of physical constraints significantly improves distinguishability and physical consistency. By adding vorticity prediction branches and physical losses, the full model achieves the largest performance leap, demonstrating that the injection of physical prior knowledge provides crucial regularization. Purely data-driven models often produce distorted or discontinuous structures in complex flow fields. By forcing the model to learn consistent dynamic characteristics, this network can correct for non-physical artifacts and generate more continuous, geometrically coherent, and dynamically reasonable 3D vortex structures.

[0132] Table 3 Experimental results of each scheme

[0133]

[0134] A random sample was selected from the test set for visual comparison, and the results are as follows: Figure 6 As shown. Figure 6 (a) shows the reference labels for the three-dimensional structure of the mesoscale vortex sample. Figure 6 (b) Figure 6 (c) and Figure 6 (d) corresponds to the different schemes used in the ablation experiment. Figure 6 In section (e), the currently commonly used method is 3D U-Res-Net. Figure 6 Figure (f) presents the final model results (λ=0.1, σ=0.05).

[0135] like Figure 6 As shown, from the tag ( Figure 6 The vortex structure in (a) does not present a regular, vertical cylinder. Instead, it exhibits a pronounced axial tilt, with a finely serrated texture along its boundaries. Figure 6 (b) produces an almost upright cylindrical shape, fails to capture depth-dependent tilt patterns, and produces substantially offset layer-by-layer boundaries compared to ground reality. (Ablation Model 1, Figure 6 In (c), the depiction of the horizontal contour is improved, but the realistic spatial tilt remains unresolved. (Ablation Model 2) Figure 6 In the middle (d), the reconstructed vortex axis gradually aligns with the physical configuration, and high-frequency edge details are better preserved. The complete model with embedded physical constraint branches ( Figure 6 The middle (f) achieves the highest reconstruction fidelity, accurately recovers the 3D tilt characteristics, and closely matches the fine edge geometry of the reference.

[0136] Besides architecture comparison Figure 6 In (e), a 3D U-Res-Net model was used. We can see that the overall tilt features and subtle jagged edge patterns in the labels are over-smoothed, indicating significant overfitting. This observation highlights the necessity of introducing physical constraints.

[0137] To further verify that the model effectively reconstructs the vortex boundaries at different depths... Figure 7 The difference between the prediction results and the labeling results for each layer is shown.

[0138] Figure 7 The reconstruction of the two-dimensional boundary details of the vortex at different depth layers is shown, and from... Figure 7 (a)-(f) follow Figure 6 The configuration order is shown in the diagram. Inconsistent pixels are marked in gray, and overlapping areas are highlighted in orange. Overall, for all models, the gray area gradually increases with depth, indicating a moderate degradation in fitting performance at deeper layers.

[0139] For different model architectures, the visualization results are consistent with the quantitative metrics listed in Table 3. The baseline model produces the lowest evaluation scores and shows more gray mismatched regions, and the improvement in quantitative performance is also visually reflected in Figs. 8(c) and 8(d) with fewer errors. Figure 7 Figs. 8(c) and 8(d) also visually reflect with fewer errors. Figure 7 Fig. 8(f) represents the complete model, which achieves the highest metric and the smallest gray-scale region, demonstrating the most accurate detection of 3D vortex structures.

[0140] Figure 7 In Fig. 8(e), the 3D U-Res-Net method is adopted, and the overfitting phenomenon becomes more obvious. As shown in Fig. 8(e), the deep learning training over-smooths the fine sawtooth features of the ground truth, and the predictions of layers 8 to 10 cannot recover the prominent structures in the labels. In contrast, our model (Fig. 8(f)) introduces appropriate vorticity-based physical constraints, enhances multi-scale initial feature extraction, effectively suppresses the over-smoothing inherent in the deep learning method, thus achieving the best quantitative performance in Table 5 and providing more accurate predictions for the prominent boundary features of layers 8 - 10. The visualization results strongly support the results in Section 5. Figure 6 As shown in Fig. 8(e), the deep learning training over-smooths the fine sawtooth features of the ground truth, where the predictions of layers 8 to 10 cannot recover the prominent structures in the labels. In contrast, our model (Fig. 8(f)) introduces appropriate vorticity-based physical constraints, enhances multi-scale initial feature extraction, effectively suppresses the over-smoothing inherent in the deep learning method, thus achieving the best quantitative performance in Table 5 and providing more accurate predictions for the prominent boundary features of layers 8 - 10. The visualization results strongly support the results in Section 5. Figure 7 In Fig. 8(f), our model introduces appropriate vorticity-based physical constraints, enhances multi-scale initial feature extraction, effectively suppresses the over-smoothing inherent in the deep learning method, thus achieving the best quantitative performance in Table 5 and providing more accurate predictions for the prominent boundary features of layers 8 - 10. The visualization results strongly support the results in Section 5.

[0141] 2) Validation of data input combinations

[0142] To validate the effectiveness of multi-source data, five experiments with different data inputs were designed to systematically evaluate the contribution of each data source to the mesoscale vortex detection performance. All experiments follow the principle of controlling variables: the model structure, sensitive parameters (λ = 0.05, σ = 0.1), vorticity calculation, training settings, and evaluation metrics remain consistent, while different data sources are gradually incorporated to study their impact on the detection performance.

[0143] Table 4 summarizes the performance comparison under five input combinations. The results show that there are significant differences in the vortex detection performance of different data source inputs.

[0144] This paper first uses single data sources such as SSH, SST, and sea surface current as inputs. When using only SSH as input, the model already demonstrates strong eddy current detection capability, achieving an accuracy of 96.92%, indicating that SSH is a key physical quantity characterizing sea surface anomalies caused by eddy currents. When using only SST or SSU+SSV as input variables, all evaluation metrics decrease, especially SST input, which results in the lowest performance metrics, indicating that SST is far less effective than the other two single input variables. When using SSH and SST as inputs, the model performance falls between that of single SSH input and single SST input. This implies potential information redundancy or noise interference between SSH and SST. Direct fusion fails to produce complementary feature gains, instead introducing irrelevant or conflicting signals, leading the model to learn suboptimal feature representations.

[0145] The most comprehensive multi-source input combination (SSH+SST+SSU+SSV) achieved the best performance across all metrics in all experiments. This result confirms the advantages of multi-source data: the model can more completely and robustly describe the morphology and dynamic characteristics of vortices, avoiding the limitation of a single data source reflecting only partial features. Multi-source fusion effectively reduces uncertainty and noise, thereby achieving higher detection accuracy and better physical consistency.

[0146] Table 4 Comparison of Model Data Input

[0147]

[0148] Figure 8 The visualization of the 3D vortex structure is shown, obtained using different input combinations according to the data configuration order listed in Table 4.

[0149] Figure 8 The visualization results are consistent with the conclusions drawn in Section 5.3. When using only SSH ( Figure 8 In (b), the model retains the overall sloping structure, although the fine jagged edge features are weakened. When only SST is used as input ( Figure 8 In (c), exaggerated edge patterns appear at the bottom of the vortex, while the inherent tilt characteristics are distorted, resulting in poor reconstruction performance. Figure 8 (d) and SSH+SST Figure 8 (e) exhibits intermediate quality between the SSH-only and SST-only cases. The complete multi-source input combination (SSH + SST + surface velocity) produces the best visual results. Figure 8 (f)). This scheme preserves the overall structural geometry and detailed jagged boundaries, effectively mitigating the oversmoothing and loss of detail common in deep learning methods.

[0150] 3) Verify the effectiveness of fusion physical loss.

[0151] To further verify the effectiveness of the hybrid loss function in improving model performance, especially the contribution of vortex-based physical loss, we conducted comparative experiments by adjusting the sensitivity parameter λ and σ with the hybrid loss, as shown in Table 5. As described in Section 4.5, σ represents the weight of gradient loss in vortex physical loss, while λ represents the weight of vortex physical loss in the overall model loss.

[0152] Table 5 Comparison of Weightlessness Parameters

[0153]

[0154] Experimental results show that, under appropriate weighting parameters, the hybrid loss of physical constraints can significantly improve vortex detection performance. When λ=0, no physical loss is introduced during training, therefore, changes in σ have no effect on the results. In this case, the model performance is relatively low, representing the lowest value among all combinations of test parameters. When λ≠0, physical loss is introduced, and the accuracy is significantly improved. This demonstrates the obvious benefits of the vortex-based physical constraint term. The model performs best when λ=0.1, achieving an accuracy exceeding 96.9% for all cases where σ<0.2. As λ further increases, the model still converges, but both training and validation classification accuracies decrease, indicating the onset of overfitting.

[0155] For the parameter σ, which balances the MSE loss and gradient consistency loss in the physical vorticity term, performance continuously improves when σ≠0. The best global accuracy, weighted Dice coefficient, and macroscopic average F1 score are achieved at λ=0.1 and σ=0.05, reflecting excellent segmentation and overall model behavior. As σ increases, the model leads to a performance decline, indicating overfitting and an imbalance in the proportions of λ and σ.

[0156] A visual comparison of vorticity prediction results, as follows: Figure 9 As shown in the diagram, although the vorticity fields predicted by the two loss functions are generally close to the actual vorticity, the error plots show significant differences. The prediction error using only the mean squared error loss is significantly greater than the prediction error using the hybrid loss with gradient consistency constraints, fully validating the effectiveness of the proposed hybrid loss function that combines mean squared error and gradient consistency loss.

[0157] Example 2

[0158] This embodiment provides a mesoscale eddy identification method, which may include:

[0159] Step 1: Acquire the image to be detected;

[0160] The image to be detected refers to the reanalysis image;

[0161] Step 2: Input the image to be detected into the target mesoscale eddy detection model and output the mesoscale eddy classification category; the target mesoscale eddy detection model is obtained according to the model training method described above;

[0162] Step 3: Based on the mesoscale vortex classification category, determine the three-dimensional mesoscale vortex mask in the image to be detected.

[0163] In embodiments of this application, the mesoscale eddy classification can be displayed in the output image of the target mesoscale eddy detection model. The location of the mesoscale eddy can be identified using bright colors, and different numbers or colors can be used to identify the first classification category corresponding to the mesoscale eddy. For example, 1 can represent an anticyclonic eddy, and 2 can represent a cyclonic eddy. Based on this, the mesoscale eddy category in the image to be detected can be determined according to the first classification category.

[0164] Example 3

[0165] This application provides a multi-source, multi-scale fusion surface-volume physical information-guided training device for a three-dimensional mesoscale eddy detection model. The device may include:

[0166] The data acquisition module is used to acquire multi-source sample data and preprocess the multi-source sample data to obtain the sample mesoscale eddy dataset.

[0167] The input / output module is used to input the sample mesoscale eddy dataset into the 3D mesoscale eddy detection model and output a 3D mesoscale eddy mask.

[0168] The loss determination module is used to construct the total loss function of the mesoscale eddy detection model and determine the total loss value of the model.

[0169] The parameter adjustment module is used to adjust the model parameters of the mesoscale eddy detection model based on the total model loss value, so as to obtain the target mesoscale eddy detection model.

[0170] The device in this application embodiment can be an electronic device or a component within an electronic device, such as an integrated circuit or a chip. The electronic device can be a terminal or other devices besides a terminal. For example, the electronic device can be a GPU BOX, mobile phone, tablet computer, laptop computer, PDA, in-vehicle electronic device, mobile internet device (MID), augmented reality (AR) / virtual reality (VR) device, robot, wearable device, ultra-mobile personal computer (UMPC), netbook, or personal digital assistant (PDA), etc. It can also be a server, network attached storage (NAS), personal computer (PC), television (TV), ATM, or self-service machine, etc. This application embodiment does not specifically limit the device.

[0171] The device in this application embodiment can be a device with an operating system. The operating system can be Android, Linux, Windows, or other possible operating systems; this application embodiment does not specifically limit it.

[0172] This application also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps in the mesoscale eddy identification method or model training method disclosed in this application.

[0173] This application also provides a computer program product that, when run on an electronic device, enables the processor to execute the steps in the mesoscale eddy identification method or model training method disclosed in this application.

[0174] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the model training method or the mesoscale eddy recognition method as described above.

[0175] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0176] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, apparatuses, electronic devices, and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0177] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0178] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0179] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended technical solutions are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0180] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0181] The above provides a detailed description of a three-dimensional mesoscale eddy detection method and apparatus based on surface-to-volume physical constraints provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for training a three-dimensional mesoscale vortex detection model based on surface-to-volume physical constraints, characterized in that, The method includes: Acquire multi-source sample data and preprocess the multi-source sample data to obtain a mesoscale eddy dataset. Input the sample mesoscale eddy dataset into the mesoscale eddy detection model to output the mesoscale eddy vortex of the three-dimensional structure; Construct the total loss function of the mesoscale eddy detection model, and determine the total loss value of the model based on the mesoscale eddy in the three-dimensional structure; Based on the total loss value of the model, the model parameters of the mesoscale eddy detection model are adjusted to obtain a three-dimensional mesoscale eddy detection model of the target based on surface-to-volume physical constraints. The three-dimensional mesoscale eddy detection model based on surface-to-volume physical constraints includes interconnected two-dimensional physical feature extraction modules, three-dimensional feature inversion modules, and three-dimensional semantic segmentation modules; wherein: The two-dimensional physical feature extraction module is used to extract multi-scale spatial features from multi-source sea surface observation data; The 3D feature inversion module is used to establish a correlation mapping from sea surface features to deep volume features, thereby enhancing the spatial dimension. The 3D semantic segmentation module adopts a U-Net-like architecture that includes spatial attention and channel attention mechanisms, and outputs 3D pixel-level vortex boundary depictions. The two-dimensional physical feature extraction module adopts a topology structure of a shared backbone and a task-specific branch. The shared backbone is a shared feature encoder, which maps the input data into 128-channel shared features containing texture and geometric information. The task-specific branch is a vortex prediction branch, which extracts dynamic information and provides physical information regularization, outputting 16-channel physical features. The two-dimensional physical feature extraction module compresses the shared features through 1×1 convolution, splices the physical features, and then completes the deep fusion of multi-source information through a convolutional block attention module (CBAM). At the end of the vortex prediction branch, a 1×1 convolution head is used to predict the vortex map used to calculate the physical gradient loss. The three-dimensional feature inversion module uses a U-Net-like feature expander to achieve implicit size inversion. It takes 80-channel fused features as input, captures large-scale context through the encoding path, restores spatial resolution through the decoding path, and finally outputs 800-channel features through the convolutional layer. These features are then recombined into a three-dimensional feature volume through a shaping operation, thus decoupling the depth information of the embedded channel dimension. The 3D semantic segmentation module is based on the 3D U-Net architecture. The encoder extracts spatiotemporal features and maintains the integrity of the vertical structure through 3D convolution and anisotropic max pooling. The decoder refines the features by combining the 3D CBAM module and a multi-scale adaptive fusion mechanism. Finally, the class probability of each voxel is generated through convolutional mapping and Softmax activation to achieve high-precision 3D vortex reconstruction.

2. The training method for a three-dimensional mesoscale eddy detection model based on surface-to-volume physical constraints according to claim 1, characterized in that, The construction of the total loss function for the mesoscale eddy detection model and the determination of the total model loss value include: Based on the predicted classification category and sample labels, the Dice coefficients for cyclonic vortices, antivortices, and non-vortices are determined respectively. The weighted average Dice coefficient is obtained by taking the weighted average Dice coefficient of cyclone vortex, anti-vortex and non-vortex. Then, the weighted average Dice coefficient is subtracted from 1 to obtain the Dice coefficient loss value. Determine the physical loss constraint between the sample labels and the predicted classification category; The physical loss of the vortex branch is a weighted combination of mean squared error (MSE) and gradient consistency loss: The hyperparameter was set to 0.05 to balance fidelity and physical consistency. A total loss function is established based on the Dice coefficient loss and physical loss constraints, and the total loss value of the model is determined according to the total loss function: Among them, σ=0.1 prevents vorticity branch from dominating the training.

3. A method for detecting mesoscale vortices in three dimensions based on surface-to-volume physical constraints, characterized in that, The method includes: Acquire the image to be detected; The image to be detected is input into the target mesoscale eddy detection model to identify the mesoscale eddy classification category; wherein, the target mesoscale eddy detection model is obtained by the method of any one of claims 1-2; Based on the mesoscale vortex classification category, the three-dimensional mesoscale vortex mask in the image to be detected is determined.

4. A three-dimensional mesoscale vortex identification apparatus, characterized by, The device includes: The acquisition module is used to acquire the image to be detected; The recognition module is used to input the image to be detected into the target mesoscale eddy detection model and identify the mesoscale eddy classification category; wherein, the target mesoscale eddy detection model is obtained by the model training method according to any one of claims 1-2; The output module is used to determine the 3D mesoscale vortex mask of the image to be detected based on the mesoscale vortex classification category.

5. An electronic device, comprising: The device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the model training method according to any one of claims 1-2, or the three-dimensional mesoscale eddy detection method according to claim 3.

6. A readable storage medium characterized by, The readable storage medium stores a program or instructions that, when executed by a processor, implement the model training method as described in any one of claims 1-2, or the three-dimensional mesoscale eddy detection method as described in claim 3.

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