A strong convective weather sample reconstruction oversampling and enhanced identification method and system

Abstract

The present application relates to the technical field of sample recognition, in particular to a strong convective weather sample reconstruction hypersampling and enhanced recognition method and system. The method comprises the following steps: acquiring weather sample data of a target area; performing data preprocessing based on the acquired weather sample data of the target area; performing self-adaptive sampling on the preprocessed data by using a multi-granularity manifold structure regularization strategy; performing feature optimization on the sampled data by using a progressive structured manifold embedding loss function; performing discriminative manifold reconstruction under a bending metric field by using a non-Euclidean holomorphic geodesic embedder according to the optimized data; and performing recognition on the reconstructed data by using a topology-aware heterogeneous feature aggregation network architecture.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of sample recognition, in particular to a strong convective weather sample reconstruction oversampling and enhanced recognition method and system. BACKGROUND

[0002] Although the high spatiotemporal resolution observation of Doppler weather radar provides core data support for the nowcasting of severe convective weather, and deep learning paradigms such as convolutional neural networks and recurrent neural networks have shown potential superior to traditional optical flow methods in precipitation extrapolation, in the task of precise prediction of extreme and disastrous weather such as hail and thunderstorm gale, the existing technology is still subject to the following two structural bottlenecks, which make it difficult to simultaneously meet the access standards in actual business:

[0003] First, the model "desensitization" and the physical failure of the sampling strategy caused by the extreme skewed data distribution. Severe convective events in real atmospheric environments belong to typical low-frequency long-tail distribution, and the pixel ratio of high-intensity echoes (such as >45dBZ) in the full spatiotemporal domain is usually less than 5%. This extreme class imbalance causes the model to be dominated by the gradient generated by the vast amount of background noise during training, gradually losing sensitivity to the key features of the minority class, and tending to output smooth and averaged predictions. The existing balancing strategies have serious theoretical defects in the meteorological scene:

[0004] Physical distortion of synthetic samples: Most oversampling algorithms are based on the linear interpolation assumption in feature space. However, there are highly nonlinear microphysical processes within strong convective systems, and simple linear mixing of samples often violates atmospheric physical conservation laws in texture structure and intensity gradient. These "artifacts" samples not only cannot enhance the generalization ability of the model, but also introduce misleading feature noise.

[0005] Environmental field information is fragmented: Although the undersampling method balances the proportion by discarding negative samples, it often destroys the spatial integrity of the weather system and cuts off the dynamic link between the strong convective cell and its surrounding environment, making it impossible for the model to learn the system's birth and evolution mechanism.

[0006] Second, the essential topological mismatch between the Euclidean space assumption and the atmospheric dynamical manifold structure. The state evolution of atmospheric dynamical systems is essentially a high-dimensional nonlinear process constrained by the Navier-Stokes equation set, and its effective characteristics are distributed on a low-dimensional curved manifold, which has complex intrinsic geometric properties. However, existing deep learning models are generally based on the assumption of flat Euclidean space, and use L2 norm or other Euclidean distance to measure the similarity between samples. This mismatch in geometric assumptions has two serious consequences: metric failure: two samples with similar distances in Euclidean space may be far apart in the geodesic distance on the manifold. For example, two storms with similar shapes but at different life stages are difficult to distinguish in Euclidean distance, making it difficult for the model to correctly judge the future intensity trend. Distortion of feature representation: traditional convolutional operators extract features by sliding windows on flat grids and cannot perceive the local curvature changes of the data manifold. This makes it difficult for the model to capture the intrinsic topological structure of the system when dealing with non-uniformly distributed meteorological data, especially when generating or transforming features of unbalanced data, which can easily cause feature points to deviate from the true data manifold surface, resulting in a significant decrease in representation ability.

[0007] Although deep learning technology has shown great potential in analyzing radar data to warn of severe convective weather, there are still two technical gaps that are difficult to overcome in the actual landing process:

[0008] 1. The problem of extreme skewness of sample distribution: In real-world meteorological scenarios, severe convective events are significantly scarce, resulting in a severe long-tail distribution characteristic of the data set. Although conventional random oversampling or synthetic minority class techniques can balance the samples in terms of quantity, they often lack physical consistency constraints and generate a large number of redundant or even meteorologically inconsistent pseudo-features, thereby weakening the model's generalization boundary.

[0009] 2. Representation mismatch of complex manifold geometry: Meteorological evolution is essentially a high-dimensional system subject to nonlinear dynamics, and its core features are usually embedded in a low-dimensional manifold structure. However, existing CNN or RNN architectures are mostly based on the inductive bias of Euclidean space and are difficult to adapt to the complex topological geometry of meteorological data, making the model inadequate in capturing weak but crucial disaster precursors. SUMMARY

[0010] To solve the above-mentioned problems, the present application provides a strong convective weather sample reconstruction oversampling and enhanced recognition method and system.

[0011] In a first aspect, the present application provides a strong convective weather sample reconstruction oversampling and enhanced recognition method, which adopts the following technical solution:

[0012] A strong convective weather sample reconstruction oversampling and enhancement identification method comprises the following steps:

[0013] Obtain weather sample data of a target area;

[0014] Perform data preprocessing based on the obtained weather sample data of the target area;

[0015] Adaptively sample the preprocessed data by using a multi-granularity manifold structure regularization strategy;

[0016] Optimize the features of the sampled data by using a progressive structured manifold embedding loss function;

[0017] Reconstruct a discriminative manifold under a curvature metric field by using a non-Euclidean holomorphic geodesic embedder according to the optimized data;

[0018] Identify the reconstructed data by using a topology-aware heterogeneous feature aggregation network architecture.

[0019] In a second aspect, a strong convective weather sample reconstruction oversampling and enhancement identification system comprises:

[0020] A data acquisition module configured to obtain weather sample data of a target area;

[0021] A preprocessing module configured to perform data preprocessing based on the obtained weather sample data of the target area;

[0022] A sampling module configured to adaptively sample the preprocessed data by using a multi-granularity manifold structure regularization strategy;

[0023] An optimization module configured to optimize the features of the sampled data by using a progressive structured manifold embedding loss function;

[0024] A reconstruction module configured to reconstruct a discriminative manifold under a curvature metric field by using a non-Euclidean holomorphic geodesic embedder according to the optimized data;

[0025] An identification module configured to identify the reconstructed data by using a topology-aware heterogeneous feature aggregation network architecture.

[0026] In a third aspect, the present application provides a computer-readable storage medium having a plurality of instructions stored therein, wherein the instructions are adapted to be loaded by a processor of a terminal device and to execute the strong convective weather sample reconstruction oversampling and enhancement identification method.

[0027] In a fourth aspect, the present application provides a terminal device, comprising a processor and a computer readable storage medium, the processor is used to implement instructions; the computer readable storage medium is used to store a plurality of instructions, the instructions are suitable for being loaded by the processor and performing the strong convective weather sample reconstruction oversampling and enhanced identification method.

[0028] In summary, the present application has the following beneficial technical effects:

[0029] 1. Overcomes the problem of extreme skewness distribution of meteorological data, realizes the accurate capture of strong convective core and edge signs

[0030] The present application discards the traditional random oversampling or simple synthesis technology, and innovatively proposes a multi-granularity manifold structure regularization strategy (S2).

[0031] Topology reconstruction instead of simple replication: by constructing a hierarchical topological neighborhood set containing "core homogeneity", "in-class bridging", "in-class boundary" and "minimum interval heterogeneous" nodes, the present application explicitly reconstructs the distribution density of sparse samples in the feature space.

[0032] Decision boundary sharpening: combined with progressive structured manifold embedding loss (S3), through a three-stage cascade constraint mechanism, the model is forced to enlarge the geodesic distance of heterogeneous samples (such as strong convective and high intensity stratiform cloud) on the feature hypersphere.

[0033] Performance improvement: this sampling paradigm based on physical and geometric constraints effectively solves the problem of "partial performance" of the model on the long-tail distribution, significantly improves the recall rate of >50 dBZ extreme echo, while maintaining low false alarm rate, significantly enhances the recognition ability of subtle but fatal early signals of strong convection.

[0034] 2. Breaks the shackles of Euclidean space flatness assumption, and constructs an intrinsic geometric representation conforming to the nature of atmospheric dynamics

[0035] In view of the disadvantages of forcibly embedding the curved meteorological physical field into the flat Euclidean space by the traditional deep learning model, the present application introduces a non-Euclidean holomorphic geodesic embedder (S4).

[0036] Riemannian manifold mapping: using Grassmannian quotient space to model meteorological dynamic state, through adaptive trust region algorithm on tangent bundle, it ensures that the feature evolution is along the intrinsic geodesic line of the data. This method automatically removes the redundant variation caused by sensor perspective or coordinate system rotation (coordinate independence).

[0037] Physical isomorphism preservation: combined with the bilateral heterogeneous feature extraction subsystem (S5.2), the model not only captures the texture information on the surface, but also extracts the deep dynamic isomorphic features.

[0038] Discrimination leap: Experiments show that under the action of the composite discriminant kernel, the separation degree between classes in the feature space is significantly improved compared with traditional methods, so that the model shows strong robustness and physical consistency when dealing with nonlinear and non-stationary strong convective systems.

[0039] 3. Fusion of efficient index and heterogeneous parallel architecture, achieving perfect balance between complex manifold calculation and business-level real-time performance

[0040] Although complex Riemannian geometry calculation is introduced, the invention ensures the efficiency of online inference through system-level engineering optimization.

[0041] Dynamic latent space acceleration: In the sampling stage, the hybrid index strategy (S2.1) of orthogonal space partition tree and local sensitive hash is used to reduce the high-dimensional feature retrieval complexity to sublinear level, solving the calculation bottleneck in large-scale training.

[0042] Architecture decoupling and parallel inference: The topology-aware heterogeneous network (S5) adopts a parallel double-flow design to decouple the complex manifold evolution and the conventional shape coding. In the inference stage, the pre-training-inference separation architecture enables the system to perform only efficient matrix operations to complete the holomorphic geodesic projection.

[0043] Business adaptation: The system can meet the high-frequency update requirement of 6 minutes / time under the standard hardware environment, and can generate high-resolution probabilistic forecast products for 0-2 hours in the future within 1 minute, fully capable of supporting the real-time operation of national meteorological business. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a method flowchart of the invention;

[0045] Figure 2 is a schematic diagram of the multi-granularity manifold topology sampling strategy of the invention;

[0046] Figure 3 is a schematic diagram of the non-Euclidean holomorphic geodesic embedder of the invention;

[0047] Figure 4 is a comparison diagram of the results of the method of the invention and other models. DETAILED DESCRIPTION

[0048] The invention will be further described in detail below with reference to the accompanying drawings.

[0049] Embodiment 1

[0050] Referring to Figure 1 , the strong convective weather sample reconstruction oversampling and enhanced recognition method of the embodiment includes:

[0051] S1. Data source acquisition and preprocessing based on physical threshold

[0052] S1.1. Target area data retrieval

[0053] Acquire historical archive and real-time updated weather radar reflectivity factor (dBZ) data of the specified area. Data channels include but are not limited to the National Operational Radar Network and special test radar. Taking the East China region as an example, set the time resolution to 6 minutes, and the backtracking period to 3 years, thus establishing the spatio-temporal coverage of the data.

[0054] S1.2. 13-level physical interval division standard

[0055] According to the physical mechanism of severe convective occurrence and actual prediction criteria, the radar echo value is accurately divided into 13 specific physical intervals. The specific division logic is as follows:

[0056] Intensity classification based on Z-R theory: Different dBZ value ranges map different precipitation properties, setting 15-30 dBZ as stratiform precipitation area, 30-45 dBZ as ordinary convective area, and above 45 dBZ as strong convective area.

[0057] Characterization of cloud microphysical processes: Use the interval to reflect the category of hydrometeors and dynamic processes, such as intervals greater than 50 dBZ to indicate intense upward motion and potential hail disasters.

[0058] Business key node alignment: Introduce the commonly used strong convective recognition threshold in meteorological business as the division node.

[0059] S1.3. Sample multi-labeling processing

[0060] Scan the radar image frame or local block, and generate a multi-label vector describing the echo intensity composition of the sample according to the falling area of the pixel value in each physical interval. This step aims to establish a dataset that fully retains the coexistence characteristics of various echoes and objectively reflects the class imbalance properties of meteorological data.

[0061] S2. Adaptive sampling paradigm based on multi-granularity manifold topology preservation

[0062] In view of the nonlinear manifold distribution characteristics of meteorological severe convective targets in high-dimensional feature space, as well as the challenges of extreme class imbalance and high intra-class variance, this study proposes a multi-granularity manifold structure regularization strategy. This strategy aims to construct a hierarchical constrained sampling mechanism by mining the local and global topological relationships of samples on the feature manifold, thereby replacing traditional random sampling or simple difficult example mining methods.

[0063] S2.1. Dynamic mapping of latent space and topological neighbor search

[0064] To capture the evolution of the feature manifold in real-time during online training, the system constructs a dynamic latent space mapping mechanism. This mechanism is not a simple static database, but a dynamic graph structure that is periodically reconstructed as the feature extraction network iterates.

[0065] Feature embedding and space partitioning

[0066] At the initialization stage of each training epoch, the training dataset is processed by a lightweight 3D convolutional encoder , which maps it to a set of -dimensional feature vectors . To address the curse of dimensionality in high-dimensional space and achieve -order retrieval efficiency, we adopt a hybrid space partitioning strategy based on the sparsity of feature dimensions:

[0067] Orthogonal space partitioning tree: When the feature manifold is relatively compact in a low-dimensional subspace, we use an improved balanced KD-Tree structure to accurately capture the -nearest neighbors in Euclidean space.

[0068] Locality-sensitive hashing projection: For high-dimensional unstructured features, we introduce a family of hash functions based on -stable distributions. This method ensures that neighboring points in the original space collide into the same hash bucket with a very high probability, thus achieving approximate nearest neighbor queries in sublinear time.

[0069] This index library serves as a "long-term memory module" during the training process, ensuring that the relationships mined by the samples truly reflect the feature distribution state under the current network parameters .

[0070] S2.2. Construction of hierarchical topological neighborhood set and meteorological dynamics mapping

[0071] Unlike traditional binary pair or triple sampling, this method focuses on reconstructing the fine geometric structure of intra-class manifolds. For any selected anchor sample , we define a hierarchical topological neighborhood set containing four key nodes.

[0072] The construction process of this set is an online retrieval process based on Riemannian geometric distance. The geodesic distance in the feature space is defined as the square of the Euclidean distance . For the anchor , we first lock its belonging label manifold region , and select key nodes according to the following dynamics criteria:

[0073] 1. Core Homogeneous Node

[0074] Sampling Logic: Retrieve the sample closest to the anchor in . . .

[0075] Physical Interpretation: This node represents a sample that is highly isomorphic to the anchor in meteorological morphology. For example, adjacent frames of the same supercell storm within consecutive radar scan cycles, or spatial neighbors of the core region of the same mesoscale convective system. The spatiotemporal continuity in the physical world maps to a high compactness in the feature space, which serves to anchor the "center of mass" of the intra-class distribution.

[0076] 2. Intra-Class Bridge Node

[0077] Sampling Logic: Select the sample whose distance to the anchor is around the median of the distribution. . .

[0078] Physical Interpretation: This node characterizes the general variability of the same meteorological target. For example, a storm cell in the developing stage and a mature stage, which have significant differences in echo top height or vertical integrated liquid water content, but still share core dynamical characteristics. The introduction of this node aims to maintain the extensibility of the manifold, preventing the collapse of features due to excessive pursuit of compactness.

[0079] 3. Intra-Class Boundary Node

[0080] Sampling Logic: Retrieve the "extreme positive sample" farthest from the anchor in . .

[0081] Physical Interpretation: This node defines the topological edge of the class in the feature space. For example, a scale-giant squall line system and a solitary strong thunderstorm cell, although both belong to the "severe convective" label, have significant differences in texture and geometric characteristics. Capturing such sample pairs forces the network to learn the high-dimensional manifold coverage of the class, significantly improving the model's recall ability for atypical samples.

[0082] 4. Minimum Separation Hetero-Class Node

[0083] Sampling Logic: Among all hetero-class sample sets , find the sample closest to the anchor, i.e. .

[0084] Physical Interpretation: This is a "confusion zone" sample near the decision boundary. Common meteorological examples include high-intensity stratiform precipitation or weak convection in the dissipation stage. Effectively distinguishing such samples is key to sharpening the model's decision boundary and reducing false positive rates.

[0085] S3. Progressive structured manifold embedding loss function

[0086] To explicitly encode the above sampled topology into the deep neural network, we propose a progressive structured manifold embedding loss. This loss function focuses not only on the absolute position of samples, but also on the relative distance order between samples, thus constructing a clear hierarchical distribution structure on the feature hypersphere.

[0087] S3.1. Unified definition of loss functional

[0088] We formalize the optimization objective as a soft-margin maximization problem with a series of inequality constraints. Introduce a non-negative relaxation variable vector , the overall regularized objective function is defined as:

[0089] ,

[0090] where is the batch size, is the Frobenius norm regularizer. The core topology loss is composed of three cascaded sub-energy terms:

[0091] ,

[0092] Here is the Hinge loss operator, represents the distance difference between different levels, is the adaptive geometric margin, is the balance coefficient.

[0093] S3.2. Three-level cascaded constraint mechanism

[0094] This mechanism forces the feature distribution to exhibit an ideal manifold morphology of “core tight aggregation -> internal order -> clear boundary” through three progressive constraints.

[0095] First level: Local compactness constraint

[0096] Aims to compress the density of the core region. We require the distance between anchor points and homogeneous nodes to be significantly smaller than the distance between anchor points and bridge nodes. The corresponding distance difference term is defined as:

[0097] ,

[0098] Mathematical and physical meaning: This constraint forces samples with high homogeneity to form a low-entropy "core cluster" in feature space, establishing a solid base for the representation learning of classes.

[0099] Second level: manifold continuity constraint

[0100] Aims to maintain the hierarchical sense of intra-class distribution. Requires the distance between anchor and bridge nodes to be smaller than that between anchor and boundary nodes. Distance difference term is defined as:

[0101] ,

[0102] Mathematical and physical meaning: This constraint prevents the disordered collapse of feature space, ensuring that the feature transition from typical samples to atypical samples is smooth and continuous, accurately reflecting the evolution manifold of meteorological targets from generation, development to dissipation.

[0103] Third level: global separability constraint

[0104] This is the most discriminative constraint, requiring the boundary node with the largest intra-class difference to maintain a sufficient safety distance from the nearest out-of-class node. Distance difference term is defined as:

[0105] ,

[0106] Mathematical and physical meaning: This term essentially maximizes the minimum inter-class interval by pushing away out-of-class samples located at the edge of the manifold, achieving "sharpening" of the decision boundary.

[0107] S3.3. Interval adaptive initialization based on hyperspherical geometry prior

[0108] Traditional metric learning often uses a fixed scalar as the interval, which ignores the geometric properties of high-dimensional space. This study assumes that the feature vector is normalized and projected onto the unit hypersphere Based on the spherical binning theory, we propose an adaptive interval initialization strategy:

[0109] Let be the number of effective classes, be the expected coverage rate of class distribution. We use geometric prior to derive the interval :

[0110] Core cluster radius constraint ( ) :

[0111] ,

[0112] where For the preset intra-class cluster density coefficient, it reflects the consistency degree of the convection core pattern.

[0113] Manifold extension constraint ( ) :

[0114] ,

[0115] For the manifold inflation factor, it is used to tolerate the natural variation of the same class samples in the pattern.

[0116] Inter-class safety barrier ( ): Based on the Tammes problem, the theoretical lower limit of inter-class separation is related to . We set:

[0117] ,

[0118] The initial value ensures that in the worst case, there is still a minimum physical separation between different class manifolds based on statistical rules. During the training process, these parameters will be learned as variables, and the clustering index on the validation set will be fine-tuned.

[0119] S4. Non-Euclidean holomorphic geodesic embedder: discriminative manifold reconstruction under curved metric field

[0120] S4.1. Geometric failure of Euclidean flatness assumption and intrinsic metric redefinition

[0121] In the feature expression of geosciences and meteorological big data, a fundamental problem that has been long neglected is the topological mismatch between the geometric properties of the observation space and the metric assumptions of the feature space. Meteorological physical fields are essentially continuous sections defined on Riemannian manifolds with non-zero curvature. The existing linear dimensionality reduction paradigm usually forces these data to be embedded into a zero-curvature Euclidean space, and relies on norm for similarity measurement.

[0122] This "forced flattening" operation is actually a differential homeomorphism distortion of the intrinsic geometric structure of the data, resulting in physical adjacent dynamic states being stretched or torn in the feature space. In order to correct this systematic bias introduced by the difference in geometric properties of the environment space, this study proposes a non-Euclidean holomorphic geodesic embedder. This method discards the flatness constraint of the external coordinate system, and redefines the feature learning process on a Riemannian manifold with constant curvature, to ensure that the feature evolution trajectory follows the intrinsic geodesic line of the data, thereby realizing effective compression of high-dimensional information while preserving the physical topological structure.

[0123] S4.2. Modeling of dynamic equivalence classes in Grassmannian quotient space

[0124] To disentangle the interference of observation coordinate system and extract pure dynamic modes in dimension reduction, we choose Grassmannian quotient manifold as the target topology space for feature embedding.

[0125] S4.2.1. Subspace isomorphism and quotient topology

[0126] Let the feature space after semantic tensor extraction with pre-topology association be , and the embedding dimension of the low-dimensional manifold we want to construct be ( ). We model the target space as Grassmann manifold , i.e. the set of all -dimensional linear subspaces in -dimensional vector space.

[0127] In the perspective of differential geometry, can be regarded as the quotient space of orthogonal group . Each "point" on the manifold actually represents an equivalence class generated by a set of orthogonal basis matrices :

[0128] ,

[0129] where denotes the -dimensional orthogonal rotation group, is the identity matrix. This definition shows that the point on the manifold corresponds to the subspace itself, while the specific rotation posture of the basis vectors that span the subspace has a normative invariance.

[0130] S4.2.2. Coordinate independence of physical state

[0131] The core motivation of introducing Grassmannian geometry lies in the "basis independence" of meteorological dynamic systems. For example, the evolving state of a mesoscale convective system can be perfectly described by the space spanned by a set of state variables. Different sensors or feature extraction operators may produce numerically completely different feature vectors, but as long as they span the same subspace, the atmospheric physical state they represent is isomorphic. By conducting geodesic discriminative learning on , the model can automatically filter out the redundant variations caused by observation angles or coordinate system rotations and focus on capturing the subspace structure that can represent the essence of the physical process.

[0132] S4.3. Compound discriminative kernel and maximum manifold divergence field

[0133] To achieve the "intra-class cohesion, inter-class repulsion" of features on curved manifolds, we reformulate the discriminative criterion based on spectral graph theory, and propose a strategy of maximizing the composite discriminative kernel.

[0134] S4.3.1. Construction of the Riemannian divergence tensor

[0135] To avoid the metric error caused by directly using the Euclidean distance, we construct a divergence matrix based on the manifold geometry. Let the dataset be divided into physical modal categories, the -th category contains samples.

[0136] Define the local cohesion divergence as the second moment of the intra-class samples relative to the class center:

[0137] ,

[0138] Define the global separation divergence as the weighted divergence of the sub-class centers relative to the global center:

[0139] ,

[0140] where is the class index set, and are the local and global centroids, respectively.

[0141] S4.3.2. Trace gain functional

[0142] Unlike the traditional trace ratio form, we transform the optimization objective into a maximum energy functional problem in the form of convex combination. Define the composite discriminative kernel matrix as:

[0143] ,

[0144] where is a regularization hyperparameter that controls the discriminative degree. Our goal is to find a mapping such that the projected subspace can maximize the energy of this kernel matrix:

[0145] ,

[0146] The physical meaning of this formula is: find a geodesic subspace on the manifold, so that in this space, the physical states of different categories are as orthogonal as possible, while the states of the same category are as coincident as possible.

[0147] S4.4. Adaptive curvature trust region evolution on the tangent bundle

[0148] To solve the manifold optimization problem defined in S4.3, we implement a geodesic discriminative learning strategy. The core idea is not to perform a straight line search on the curved manifold, but to exploit the local linearization property of Riemannian geometry to transform the non-linear optimization problem into an unconstrained sub-problem on the tangent space, and then "unwrap" the solution back to the manifold surface via exponential mapping or retraction operator. The detailed implementation steps are as follows:

[0149] The optimization problem above is subject to the non-linear geometric constraint of the manifold . Direct application of Euclidean gradient method will destroy the manifold structure. Therefore, we design a tangent bundle adaptive trust region algorithm to perform second-order optimization on the tangent space of the manifold.

[0150] S4.4.1. Tangential projection of Riemannian gradient

[0151] First, calculate the Euclidean gradient of the energy functional in ambient space :

[0152] ,

[0153] Since the gradient direction may point outside the manifold, it must be orthogonally projected to the tangent space at the current point . Using the orthogonal projection operator , we get the Riemannian gradient :

[0154] ,

[0155] This gradient vector field is strictly defined on the tangent plane, indicating the fastest path of energy growth along the geodesic direction.

[0156] S4.4.2. Riemannian Hessian operator and second-order approximation

[0157] To accelerate convergence using curvature information, we introduce the Riemannian Hessian operator . For any tangent vector , the Riemannian Hessian is defined as the covariant derivative of the Riemannian gradient. In Grassmann geometry, its analytical form contains the tangential component of the Euclidean Hessian and the curvature correction term:

[0158] ,

[0159] In the th iteration, we construct a local quadratic model to approximate the objective function in the tangent space:

[0160] ,

[0161] and solve the sub-problem in the trust region radius to get the optimal tangent update .

[0162] S4.4.3. Polar decomposition retraction mapping

[0163] Since the tangent vector is located in the linear space, in order to map it back to the curved manifold surface, it is necessary to introduce the retraction operator. This method uses the retraction mapping based on polar decomposition , which has better numerical stability than the traditional QR decomposition:

[0164] ,

[0165] This operation is geometrically equivalent to "wrapping" the tangent vector along the geodesic back to the manifold surface, thereby realizing the iterative evolution of the discriminant subspace while ensuring that the orthogonal constraint is strictly met. Through this curvature-aware optimization mechanism, the algorithm can efficiently converge to the global optimum or a high-quality local optimum.

[0166] S5. Topology-aware heterogeneous feature aggregation network architecture

[0167] S5.1 Architecture evolution and core paradigm

[0168] In view of the inherent nonlinear manifold distribution characteristics of strong convective weather systems in feature space, as well as the complex situation of extreme class imbalance and high intra-class dispersion coexisting, this study constructs a multi-element cascading fusion framework that preserves the topological structure.

[0169] This framework not only improves the structure of the traditional encoder-decoder model, but also is a deep physical implementation of the "adaptive sampling paradigm" described in S2 and the "manifold embedding constraint" in S3. Its design follows the evolution principles of the following three orthogonal dimensions:

[0170] Geometric decoupling: Abandoning the flatness assumption of single Euclidean metric, we utilize the holomorphic metric projection technique to peel off the observation coordinate redundancy in the Grassmannian quotient space and extract the intrinsic isomorphism of the dynamic state. Specifically, we deploy the Euclidean space feature extractor and the intrinsic manifold subspace projector in parallel, the former handles the regular image transformation, and the latter maps the weather state to a subspace point on the Grassmann manifold. For example, when a radar monitors a supercell storm that is rotating, although the radar echo map at consecutive times changes dramatically due to rotation or tilting, the traditional network is prone to misjudgment as different objects. However, our architecture can calculate the coincidence of the subspaces spanned by these two moments using the basis independence of Grassmann geometry, thus automatically filtering out the rotation interference and locking the "isomorphic" identity that remains unchanged in its physical essence.

[0171] Closed-loop topology-driven: The update of network parameters is not a static process, but is explicitly driven by the dynamic neighborhood graph structure defined by S2, forming a co-evolution mechanism of "sampling-feature reconstruction". Under this mechanism, the network no longer randomly reads data, but the sampler dynamically generates an "five-tuple" input stream containing anchor points, homogeneous points and boundary points according to the current model's discrimination difficulty. For example, when facing the "confusion area" samples of high-intensity stratiform cloud and weak convective cell with similar echo intensity (such as 35-40 dBZ), S2 sampler will identify them as difficult examples and force them to be paired, cooperating with the manifold embedding loss of S3 to generate high-penalty gradient, forcing the network to dig out the subtle differences between the two in texture gradient or vertical structure, thus pushing them away in the feature space, and realizing the adaptive sharpening of the decision boundary.

[0172] Dual-flow complementarity: High-frequency spatial texture and low-frequency dynamic manifold features are captured through heterogeneous dual channels respectively, and unified through a nonlinear gating mechanism. When constructing, the multi-field hollow perception module of gradient-sensitive morphological encoder (MSEB) captures the jagged high-frequency details of cloud edges, while the manifold projector extracts the low-frequency dynamic modes such as evolution trend, and finally the compression-excitation (SE) gating unit is used for weighted fusion. For example, when predicting a fast-moving squall line, the MSEB channel can accurately lock the "bow echo" boundary position of the squall line, preventing image blurring; while the manifold channel can accurately analyze that the squall line is in the "development and enhancement period" rather than the "dissipation period", and the combined features contain both accurate geographical location information and correct intensity evolution trend, ensuring the dual precision of the prediction result in time and space dimensions.

[0173] S5.2 Dual-heterogeneous feature extraction subsystem

[0174] To address the challenge of multi-scale physical process representation, the system deploys two branches of feature extraction with distinct mathematical properties in parallel. The input data stream is defined as a four-dimensional tensor , which is processed and converged into a consistent dimension of hidden layer representation.

[0175] S5.2.1 Gradient-sensitive morphological encoder

[0176] Construction motivation: Aim to overcome the non-rigid deformation challenge of strong convective echoes on the Euclidean projection plane, and strengthen the response accuracy of the model to irregular strong gradient edges.

[0177] Key components: Variants based on the U-Net backbone, integrating adaptive geometric offset perception and multi-receptive field fusion modules.

[0178] Geometric adaptive convolution operator: Replace the traditional grid sampling convolution with a learnable offset field . This operator allows the sampling grid to be dynamically twisted according to the local gradient distribution of the input feature map, thereby achieving "fitting" feature extraction of the unstructured convective cloud boundary at the pixel level.

[0179] Multi-field cavity perception module: In the shallow feature extraction stage, stack the dilated convolution layers with cascading dilation rates in parallel. This design maintains the resolution of the feature map while constructing multi-scale concentric receptive fields, effectively capturing multi-level spatial gradient information from the stratiform cloud background to the convective core area.

[0180] Output stream: MSEB generates a set of multi-resolution spatial feature pyramids , where indicates the down-sampling level, focusing on carrying high-frequency texture and geometric boundary information.

[0181] S5.2.2 Intrinsic manifold subspace projector

[0182] Construction motivation: In response to the "Euclidean flatness assumption failure" problem pointed out in S4, reconstruct the low-dimensional discriminative embedding of meteorological dynamics on the Grassmannian quotient manifold.

[0183] Key components: Consists of three stages: tensor mapping, geodesic manifold evolution, and tangent space linearization.

[0184] Tensor space initialization: Use the lightweight 3D convolution front-end to map the original input sequence to a high-dimensional feature cluster , which is still subject to the geometric constraints of the observation coordinate system at this stage.

[0185] Grassmannian orthogonal group mapping: reformulate the feature learning task as a subspace optimization problem on the Grassmann manifold .

[0186] quotient topology definition: model the physical state as an equivalence class in the quotient space of the orthogonal group .

[0187] discriminative kernel maximization: introduce the hybrid separation energy functional proposed in S4.3, force the subspaces of the same dynamic mode to coincide as much as possible on the manifold by maximizing the composite kernel .

[0188] trust region second-order optimization: adopt the adaptive trust region algorithm on the tangent bundle, iteratively update the projection matrix along the geodesic direction, and eliminate the coordinate system rotation interference caused by the sensor viewing angle.

[0189] tangent space linearization reconstruction: in order to adapt to the subsequent euclidean network layer, the optimal subspace point on the curved manifold needs to be mapped back to the tangent plane. By logarithmic mapping or tangent space parameterization, the manifold feature is generated .

[0190] This feature implicitly contains the topological prior of "core tight clustering - clear boundary" in S3, and has strong inter-class discriminability.

[0191] S5.2.3 cross-domain representation adaptive synthesis module

[0192] For the local detail features of MSEB and the global topological features of IMSP, this unit designs a cascade fusion mechanism based on saliency re-labeling.

[0193] Multi-modal tensor concatenation: at a certain resolution level , the euclidean space feature is concatenated with the manifold feature upsampled to align along the channel dimension:

[0194] ,

[0195] spatio-temporal saliency re-labeling:

[0196] Channel dimension gating: adopt the compression-excitation topology structure. Through the nonlinear mapping of global statistics, the redundant channels are adaptively suppressed, and the feature response weight containing the core convection information is enhanced.

[0197] Spatial dimension focusing: Based on the channel weighting results, further generate a spatial attention map. This mechanism uses a combination of max-pooling and average-pooling descriptors to dynamically lock the focus area of high echo intensity and filter background noise interference.

[0198] Synthetic output: Final fused representation Via Convolutional layers for cross-channel information integration:

[0199] ,

[0200] This process realizes the organic unification of "micro texture" and "macro physical modalities".

[0201] S5.3 Fine-grained random field restoration decoder

[0202] The decoding subsystem is responsible for gradually mapping the highly abstract fused features back to the reflectivity factor field in physical space and quantifying the uncertainty of the prediction.

[0203] S5.3.1 Non-local perception upsampling unit

[0204] Each decoding level consists of two parts: spatial reconstruction and correlation modeling:

[0205] Transposed convolution reconstruction: receives the decoding features from the previous level And the same level encoder fusion features , restore the spatial resolution through transposed convolution operation.

[0206] Global correlation modeling: Introduce multi-head self-attention mechanism instead of standard convolution. This module captures the long-range spatial dependence of large-scale weather systems by calculating the affinity between global pixels in the feature map, effectively compensating for the limitations of the local receptive field of the convolution operator.

[0207] S5.3.2 Spatial position embedding

[0208] In order to give the model absolute geographical coordinate perception ability, coordinate convolution layer is introduced at the end.

[0209] Mechanism: Explicitly inject normalized grid coordinates into feature channels .

[0210] Effect: Breaks the translational invariance limit of convolutional networks, allowing the model to dynamically adjust the prediction distribution based on the absolute position of the meteorological target and correct spatial geometric distortion.

[0211] S5.3.3 Distributed inference output layer

[0212] Based on the attention mechanism to fuse multi-scale features, the time series prediction network outputs the probability prediction of the physical constraint within 0-2 hours. For each output time node, the end output head performs double-mode mapping. In order to output the probabilistic prediction product containing confidence information, the output head is specifically designed as a multinomial distribution mapper:

[0213] Category probability projection: the end convolution layer maps the channel dimension to .

[0214] Normalized likelihood vector: for any spatial coordinate , the Softmax function is applied to generate a probability distribution vector , satisfying the normalization constraint .

[0215] Dual-mode product generation:

[0216] Deterministic field: select the reflectivity median corresponding to the probability maximum index: .

[0217] Entropy weight uncertainty map: calculate the information entropy of the distribution, which directly corresponds to the "minimum interval heterogeneous node" region defined in S2.2, used to identify the confusion zone with low prediction confidence.

[0218] Experimental verification

[0219] In order to verify the effectiveness of the strong convective weather prediction method based on manifold reconstruction in solving the problems of extreme sample scarcity and nonlinear dynamic modeling, this embodiment constructs a strict time series generalization experiment in a high-performance computing cluster environment. The experimental data selects the radar echo observation records with typical strong convective characteristics in the main flood period of 2016. According to the time sequence, the continuous observation sequence from July 1st to 21st is divided into a training set, which is used for the construction of manifold space and the iteration of network parameters; the data immediately following from July 22nd to 23rd is selected as a validation set to monitor the convergence state of the loss function; and the independent meteorological process from July 24th to 31st containing multiple squall line and thunderstorm wind processes is selected as a test set to evaluate the generalization boundary of the model on non-stationary manifold. The computing environment relies on the PyTorch deep learning framework and NVIDIA GPU accelerated cluster to meet the complex Riemannian geometry operations in the Grassmannian manifold space and the high-concurrency tensor throughput requirements of the double-flow heterogeneous network.

[0220] In the comparative experiment session, the model of the application and TrajGRU, UNet, SiMVP, Cuboid_transformer and FourcastNet and other mainstream spatiotemporal prediction models are horizontally evaluated on the test set, focusing on the critical success index (CSI), hit rate (POD) and other meteorological statistical indicators, and the structural similarity (SSIM) and other image quality indicators. The experimental results show that in the general precipitation interval, the prediction performance of each model is in the same order of magnitude, but in the critical high reflectivity threshold interval involving severe convective warning, the model of the application shows a significant performance advantage. Especially in the task of capturing extreme echo cores, compared with the comparative model which tends to smooth out the sparse high-intensity pixels, the model can greatly improve the hit rate of disastrous weather while maintaining a low false alarm rate, effectively improving the "desensitization" phenomenon of traditional methods under long-tail distribution data. In the long-time deduction aspect, the radar echo predicted by the model can still maintain a compact physical form and clear texture structure after a long time span, and its SSIM decay curve is significantly better than the linear decay trend of traditional methods, proving the superiority of the model in maintaining the consistency of meteorological system dynamics.

[0221] Further module ablation studies confirm the indispensability of each core innovation. When removing the adaptive sampling paradigm based on multi-granularity manifold topology preservation described in S2, and instead of using random sampling, the model becomes blurred in distinguishing the boundaries between strong convective and strong stratiform clouds in complex flow regions, leading to a rebound in false alarm rate in the high threshold interval, proving the key role of the topology constraint mechanism in sharpening the decision boundary. If the non-Euclidean holomorphic geodesic embedder of S4 is replaced by a standard Euclidean convolution layer, the prediction path deviates from the actual observation gradually increases when dealing with rotating supercells or rapidly deforming squall line processes, and the rotational invariance of meteorological targets cannot be effectively maintained, verifying the necessity of intrinsic dynamics modeling in the Grassmannian quotient space. In addition, if the gradient-sensitive branch in the bilateral heterogeneous feature extraction subsystem of S5 is removed, the edge details of the predicted image will be smoothed, lacking the jagged edges characteristic of convective clouds, confirming the unique value of the dual-flow complementary mechanism in balancing dynamic evolution and micro-texture recovery. In summary, the application realizes the dual improvement of accuracy and physical consistency in severe convective nowcasting tasks through the deep combination of manifold geometry and topological sampling.

[0222] Figure 4 The schematic diagram for comparing the prediction results of the method of the application and other models. Among them, Figure 4The (a), (b), (c) and (d) correspond to the prediction results of the future 30 minutes, 60 minutes, 90 minutes and 120 minutes respectively; in each group of predictions, the prediction maps of the true value, the method, TrajGRU, UNet, SiMVP, Cuboid_transformer and FourcastNet are sequentially shown from left to right.

[0223] Embodiment 2

[0224] The embodiment provides a strong convective weather sample reconstruction super sampling and enhanced recognition system, comprising:

[0225] The data acquisition module is configured to:

[0226] A computer readable storage medium, wherein a plurality of instructions are stored, the instructions are suitable for being loaded and executed by a processor of a terminal device.

[0227] A terminal device, comprising a processor and a computer readable storage medium, the processor is used to implement instructions; the computer readable storage medium is used to store a plurality of instructions, the instructions are suitable for being loaded and executed by the processor to execute the strong convective weather sample reconstruction super sampling and enhanced recognition method.

[0228] The above are preferred embodiments of the present application, not limited to the protection scope of the present application, therefore: all equivalent changes made according to the structure, shape, principle of the present application should be covered in the protection scope of the present application.

Claims

1. A method for oversampling and enhancement identification of severe convective weather samples, characterized in that, include: Obtain weather sample data for the target area; Data preprocessing is performed based on the acquired weather sample data of the target area; Adaptive sampling of preprocessed data is performed using a multi-granularity manifold structure regularization strategy. Feature optimization of the sampled data is performed using a progressive structured manifold embedding loss function; Based on the optimized data, discriminative manifold reconstruction under the curvature metric field is performed using a non-Euclidean holomorphic geodesic embedding. A topology-aware heterogeneous feature aggregation network architecture identifies reconstructed data; This includes constructing a topology-preserving multi-level cascaded fusion framework for structurally improving encoder-decoder models. It abandons the flattening assumption of a single Euclidean metric, utilizing holomorphic geodesic projection to strip observation coordinate redundancy in the Grassmannian quotient space and extract the intrinsic isomorphism of dynamic states. A dynamic neighborhood graph structure explicitly drives network parameter updates, forming a sampling-feature reconstruction co-evolutionary mechanism. Heterogeneous dual channels capture high-frequency spatial texture and low-frequency dynamic manifold features respectively, and a nonlinear gating mechanism achieves unified cross-domain representation. The method of adaptively sampling the preprocessed data using a multi-granularity manifold structure regularization strategy includes first constructing a dynamic latent space mapping mechanism, including following the feature extraction network. The dynamic graph structure is reconstructed periodically through parameter iteration. During the initialization phase of each training epoch, a lightweight 3D convolutional encoder is used to process the entire training set. Map it to 3D feature vector set To solve the curse of dimensionality in high-dimensional space and achieve To achieve high retrieval efficiency, a hybrid space partitioning strategy is employed based on the sparsity of feature dimensions. This includes utilizing orthogonal space partitioning trees and, when the feature manifold is projected compactly into the low-dimensional subspace, using an improved balanced KD-Tree structure to capture the Euclidean space. -Nearest neighbor; and employing locality-sensitive hash projection, for high-dimensional unstructured features, introducing a system based on... - A stable distributed family of hash functions enables sublinear time approximate nearest neighbor queries; then, an online retrieval process based on Riemannian geometric distance constructs a hierarchical topological neighborhood set containing key nodes. By defining the geodesic distance in the feature space as approximately equal to the square of the Euclidean distance, For anchor points Lock the label manifold region to which it belongs. And select key nodes according to dynamic criteria, among which, through Search and The nearest sample, i.e. Obtain core homogeneous nodes; by selecting nodes whose distance distribution is in the range of... Samples near the median serve as intra-class bridging nodes; by sampling in The search term is the extreme positive sample that is furthest away from the target. Obtain the intra-class boundary node; through all heterogeneous sample sets. In the process, find the sample closest to the anchor point, i.e. Find the minimum-interval heterogeneous node; The method of using a progressive structured manifold embedding loss function to optimize the features of the sampled data includes formalizing the optimization objective into a soft-margin maximization problem with inequality constraints, and introducing a non-negative relaxation variable vector. The overall regularization objective function Defined as: in For batch size, The core topological loss is represented by the Frobenius norm regularization term. It consists of three cascaded sub-energy terms: ,in, For Hinge loss operator, Represents the distance difference between different levels. For adaptive geometric interval, The balance coefficient is used; then a three-level cascaded constraint mechanism is constructed to make the feature distribution present an ideal manifold shape. The first level uses local compactness constraints to limit the distance between the anchor point and homogeneous nodes to be less than the distance between the anchor point and bridging nodes, corresponding to the distance difference term. Defined as: The second level utilizes manifold continuity constraints to limit the distance between the anchor point and the bridging node to be less than its distance from the boundary node; the distance difference term... Defined as: The third level utilizes global separability constraints to maintain a set safe distance between the boundary node with the greatest intra-class difference and the nearest out-of-class node; the distance difference term... Defined as: Finally, an adaptive initialization based on hyperspherical geometric priors is performed, assuming... The number of valid categories, To calculate the expected coverage of the category distribution, the margins at each level are derived using geometric priors. ; The process involves reconstructing a discriminative manifold under a curvature metric field using a non-Euclidean holomorphic geodesic embedder based on the optimized data. This includes removing interference from the observation coordinate system and extracting pure dynamic modes during dimensionality reduction, selecting the Grassmannian quotient manifold as the target topological space for feature embedding, and assuming the feature space after semantic tensor extraction via preorder topological association is... The desired low-dimensional manifold embedding dimension is ( The target space is modeled as a Grassmann manifold. ,Right now All in the dimensional vector space A set of linear subspaces; in the perspective of differential geometry, Quotient space as an orthogonal group Each point on the manifold represents an equivalence class. , consisting of a set of orthogonal basis matrices generate: in Denotes the orthogonal rotation group. The identity matrix is ​​then introduced; the core motivation for introducing Grassmannian geometry lies in the basis independence of meteorological dynamic systems, through... Geodesic discrimination learning is performed on the surface to filter out redundant variations caused by observation angles or coordinate system rotation, focusing on capturing subspace structures that can characterize the essence of physical processes.

2. The method for oversampling and enhancement identification of severe convective weather samples according to claim 1, characterized in that, The process of reconstructing a discriminative manifold under a curved metric field using a non-Euclidean holomorphic geodesic embedding device based on optimized data also includes reconstructing a discriminant criterion based on spectral theory to achieve intra-class cohesion and inter-class repulsion of features on the curved manifold. To avoid metric errors caused by directly using Euclidean distance, a divergence matrix based on manifold geometry is constructed. The dataset is divided into... The physical mode category, the first Class contains Given a sample, define the local cohesive divergence. The second moment of the in-class sample with respect to the class center: Define global separation divergence The weighted dispersion of each subclass center relative to the global center: in For class index set, and The local and global centroids are respectively identified, and by distinguishing from the traditional trace ratio form, the optimization objective is transformed into an energy functional maximization problem of convex combinatorial form, and a composite discriminant kernel matrix is ​​defined. for: ,in It is a regularization hyperparameter that controls the discrimination strength and is used to find a mapping. To maximize the energy of the kernel matrix in the projected subspace: .

3. The method for oversampling and enhancement identification of severe convective weather samples according to claim 2, characterized in that, The process of reconstructing a discriminative manifold under a curvature metric field using a non-Euclidean holomorphic geodesic embedding device based on optimized data also includes constructing a tangent bundle adaptive trust region algorithm to perform second-order optimization on the tangent space of the manifold. Specifically, this involves calculating the tangential projection of the Riemann gradient, first by calculating the energy functional... Euclidean gradient in environmental space : Project orthogonally onto the current point tangent space Using orthogonal projection operators The Riemann gradient is obtained. : The Riemann gradient vector field, defined on the tangent plane, indicates the path of the fastest energy growth along the geodesic direction. Then, the Riemann-Hessian operator and second-order approximation are calculated, where the Riemann-Hessian operator is introduced to accelerate convergence by utilizing curvature information. For any tangent vector The Riemann Hessian is defined as the covariant derivative of the Riemann gradient. In Grassmann geometry, its analytical form includes the tangential component of the Euclidean Hessian and a curvature correction term. In the In each iteration, a local quadratic model is constructed within the tangent space. To approximate the objective function: and within the trust region radius Solve the subproblem internally to obtain the optimal tangential update amount. Finally, due to the tangent vector To map this back to a curved manifold surface in a linear space, a retraction mapping based on pole decomposition is employed. Introducing a shrinkage operator, This is used to geometrically equate to wrapping the tangent vector back around the manifold surface along the geodesic, thereby achieving the iterative evolution of the discriminative subspace.

4. The method for oversampling and enhancement identification of severe convective weather samples according to claim 3, characterized in that, The topology-aware heterogeneous feature aggregation network architecture identifies the reconstructed data and also utilizes a bilateral heterogeneous feature extraction subsystem to enhance the model's response accuracy to irregular strong gradient edges. The input data stream is defined as a four-dimensional tensor. After processing, the data converges into a hidden layer representation with consistent dimensions. Based on a variant of the U-Net backbone, it integrates an adaptive geometric offset awareness and multi-receptive field fusion module, and uses a geometrically adaptive convolution operator to replace the traditional grid sampling convolution, introducing a learnable offset field. By employing operators that allow the sampling grid to be dynamically distorted according to the local gradient distribution of the input feature map, a fitting feature extraction of the boundaries of unstructured convective clouds is achieved. In the shallow feature extraction stage, dilated convolutional layers with cascading dilation rates are stacked in parallel to construct multi-scale concentric receptive fields while maintaining the feature map resolution, thereby capturing multi-level spatial gradient information from the layered cloud background to the convective core region. The output stream is generated by MSEB into a set of multi-resolution spatial feature pyramids. ,in The sampling level is identified; simultaneously, to address the failure of the Euclidean flatness assumption, a low-dimensional discriminative embedding of meteorological dynamics is reconstructed on the Grassmannian quotient manifold, consisting of three stages: tensor mapping, geodesic manifold evolution, and tangent space linearization; finally, for the local detail features of MSEB and the global topological features of IMSP, a cascaded fusion mechanism based on saliency recalibration is designed, wherein, at a specific resolution level... Features of Euclidean space manifold features aligned with upsampling Tensor splicing along the channel dimension: A compression-excitation topology is adopted, and redundant channels are adaptively suppressed through nonlinear mapping of global statistics; a spatial attention map is further generated based on the channel weighting results; and the final fusion representation is then used. via Convolutional layers integrate information across channels: .

5. The method for oversampling and enhancement identification of severe convective weather samples according to claim 4, characterized in that, The topology-aware heterogeneous feature aggregation network architecture identifies the reconstructed data and also uses a random field restoration decoder to map the fused features back to the reflectivity factor field of physical space and quantify the uncertainty of the forecast. Each decoding level consists of two parts: spatial reconstruction and correlation modeling. The spatial reconstruction includes transposed convolutional reconstruction, which is used to receive the decoded features from the previous level. Features fused with peer encoders Spatial resolution is restored through transposed convolution; the correlation modeling includes global correlation modeling, which introduces a multi-head self-attention mechanism to replace standard convolution; to give the model absolute geographic coordinate awareness, a coordinate convolutional layer is introduced at the end; to output a probabilistic forecast product containing confidence information, the end output head is designed as a multinomial distribution mapper, wherein the end convolutional layer maps the channel dimension to... and for any spatial coordinates The Softmax function is applied to generate the probability distribution vector. Satisfying normalization constraints Finally, the median reflectance corresponding to the index with the highest probability is selected: Calculate the information entropy of the distribution This indicator directly corresponds to the minimum interval heterogeneous node region and is used to identify confusing areas with low forecast reliability.

6. A severe convective weather sample reconstruction oversampling and enhancement identification system, executing the severe convective weather sample reconstruction oversampling and enhancement identification method as described in claim 1, characterized in that, include: The data acquisition module is configured to acquire weather sample data for the target area; The preprocessing module is configured to perform data preprocessing based on the acquired weather sample data of the target area; The sampling module is configured to adaptively sample the preprocessed data using a multi-granularity manifold structure regularization strategy. The optimization module is configured to perform feature optimization on the sampled data using a progressive structured manifold embedding loss function; The reconstruction module is configured to perform discriminative manifold reconstruction under a curvature metric field using a non-Euclidean holomorphic geodesic embedding device based on the optimized data. The identification module is configured to identify the reconstructed data using a topology-aware heterogeneous feature aggregation network architecture.

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