Variational resolution grid-oriented graph neural network ensemble prediction method and system

Abstract

The application provides a variational resolution grid-oriented graph neural network ensemble prediction method and system, relates to the cross technical field of meteorological prediction and artificial intelligence, and comprises the following steps: constructing a multi-scale hierarchical graph structure aligned with the unstructured variational resolution grid topology; mapping historical meteorological input to the graph through an encoder to generate a conditional prior distribution parameter of a latent variable; completing multi-round cross-scale information transmission on the graph through a decoder, sampling the latent variable based on the distribution, and decoding layer by layer to obtain the node representation of the finest layer and perform local feature enhancement; and finally, mapping the enhanced features back to the unstructured variational resolution grid to generate an ensemble prediction result. The method and system provided by the application realize efficient and high-accuracy ensemble prediction for unstructured variational resolution grids through hierarchical graph structure, cross-scale bidirectional interaction and local feature enhancement, and provide a feasible technical path for probability prediction under such a grid framework.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of weather forecasting and artificial intelligence, and in particular to a graph neural network ensemble forecasting method and system for variable resolution grids. Background Technology

[0002] With the continuous evolution of global weather forecasting technology, numerical weather prediction models are gradually shifting towards unstructured grid architectures. Compared to traditional regular latitude and longitude grids, unstructured variable resolution grids, such as numerical models based on spherical Voronoi grids, can effectively eliminate polar singularity problems and support local smoothing and densification of target areas within a single global physical framework. This theoretically achieves seamless cross-scale integration of global large-scale background circulation and regional high-impact weather.

[0003] However, running large-scale ensemble forecasts within such advanced variable-resolution frameworks faces a severe computational cost bottleneck. Because the high-resolution grids in locally dense regions impose extremely stringent stability constraints on the time integration steps of the physical equations, the denser the grid, the shorter the time step required to ensure computational stability, leading to a significant surge in the number of integration steps per forecast. Furthermore, ensemble forecasts typically require running dozens to hundreds of members simultaneously to quantify forecast uncertainties. These two factors combined cause the total computational cost of traditional numerical ensemble forecasts to increase linearly or even exponentially, severely limiting the widespread application of high-resolution ensemble forecasts in practical operations. In recent years, data-driven forecasting models based on Artificial Intelligence (AI) have provided a new approach to building low-cost meteorological simulators due to their extremely high inference efficiency. However, most existing mainstream AI meteorological forecasting models are designed based on spatially uniform regular grids. When attempting to directly migrate or simply adapt existing AI network architectures to unstructured variable-resolution grids with drastically varying node density spatial gradients, systematic biases and distortions often occur during the spatial aggregation and evolution of information, thus failing to truly leverage the underlying geometric advantages of unstructured variable-resolution grids.

[0004] Therefore, how to achieve efficient and high-precision probabilistic ensemble forecasting has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0005] This invention provides a graph neural network ensemble forecasting method and system for variable resolution grids, which solves the problems of high computational cost of traditional numerical models, inability of existing AI models to directly adapt to unstructured grids, lack of cross-scale bidirectional collaborative interaction, and distortion of variable resolution features in the prior art, and achieves efficient and high-precision probabilistic ensemble forecasting.

[0006] This invention provides a graph neural network ensemble prediction method for variable resolution grids, comprising: Obtain a multi-scale hierarchical graph structure that is topologically aligned with an unstructured variable resolution mesh; the multi-scale hierarchical graph structure contains multiple scale layers, nodes within the same scale layer are connected by adjacent edges, and adjacent scale layers are connected by up-line and down-line edges. Historical meteorological input data is transmitted across grids and mapped to the finest layer of the multi-scale hierarchical graph structure. It is then propagated upwards along the upper edge to the coarsest layer, where the parameters of the conditional prior distribution are output. The initial states of each layer of the hierarchical graph structure are initialized independently, and multiple round-trip scan operations are performed. After each round-trip scan operation, the downlink node representations obtained by downlink propagation and the uplink node representations obtained by uplink propagation within the same scale layer are adaptively gated and fused. The fused node representations are used as the initial states for the next round-trip scan. Each round-trip scan operation includes propagating from the coarsest layer down along the downlink edge to the finest layer, and propagating from the finest layer up along the uplink edge to the coarsest layer. After completing multiple rounds of round-trip scanning, latent variables are generated by sampling based on the parameters of the conditional prior distribution. The latent variables are then injected into the coarsest layer and propagated down the downlink edge to the finest layer to obtain the current node representation of the finest layer. Obtain the resolution prior and local encrypted region mask for each node of the finest layer. Generate feature increments based on the current node representation and the initial node representation of the finest layer. Generate node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask. Weight the feature increments based on the node-by-node gating coefficients and superimpose them onto the current node representation of the finest layer to obtain the enhanced node representation of the finest layer. The enhanced finest layer node representation is used for cross-grid information transfer and mapped back to the unstructured variable resolution grid to generate probability set prediction results.

[0007] In some embodiments, obtaining a multi-scale hierarchical graph structure aligned with the topology of an unstructured variable-resolution mesh includes: Based on the icosahedron as the basic model, a global spherical mesh containing multiple scale layers is constructed by progressively subdividing the model into four subdivisions. At the location of the local refinement region corresponding to the unstructured variable resolution mesh, an additional local subdivision operation is performed on the global spherical mesh to obtain the multi-scale hierarchical graph structure.

[0008] In some embodiments, the adaptive gating fusion of the downlink node representation obtained by downlink propagation and the uplink node representation obtained by uplink propagation within the same scale layer includes: The quality assessment scores of the downlink node representation and the uplink node representation are calculated respectively using a learnable quality assessment network. The quality assessment score is scaled and mapped using preset temperature parameters to obtain the downlink gating coefficient and the uplink gating coefficient, respectively. Linear feature transformations are performed on the downlink node representation and the uplink node representation respectively to obtain the transformed downlink representation and the transformed uplink representation. Based on the downlink gating coefficient and the uplink gating coefficient, the downlink representation and the uplink representation are weighted and fused to obtain the gated fused backbone representation; The downlink node representation and the uplink node representation are concatenated along the feature dimension to calculate the residual refinement term. The residual refinement term is superimposed onto the gated fusion backbone representation to obtain the fused node representation.

[0009] In some embodiments, the resolution prior is calculated based on the area of ​​the unstructured variable resolution mesh; The local encryption region mask is used to identify encrypted nodes within the target region.

[0010] In some embodiments, the step of generating feature increments based on the current node representation of the finest layer and the initial node representation of the finest layer, and generating node-by-node gating coefficients based on the current node representation of the finest layer, the initial node representation of the finest layer, static geometric embedding, the resolution prior, and the local encrypted region mask, weighting the feature increments based on the node-by-node gating coefficients, and superimposing them on the current node representation of the finest layer to obtain the enhanced node representation of the finest layer includes: Obtain the initial node representation of the finest layer; The initial node representation of the finest layer and the current node representation of the finest layer are concatenated along the feature dimension, and feature extraction is performed through an augmentation network to generate feature increments; wherein, the initial node representation of the finest layer is the node representation cached after the grid feature has completed cross-grid mapping and before the hierarchical up-scan starts; the current node representation of the finest layer is the node representation after full hierarchical propagation and latent variable injection; The finest layer current node representation, the finest layer initial node representation, the node's static geometric embedding, and the resolution prior are concatenated along the feature dimension, and then processed by a gating network for feature mapping and activation function processing to generate initial gating coefficients. The initial gating coefficient is masked based on the local encrypted region mask to obtain the node-by-node gating coefficient; wherein the value of the node-by-node gating coefficient in the encrypted region indicated by the local encrypted region mask is greater than its value in the unencrypted region. The node-by-node gating coefficient is multiplied element-by-element by the feature increment to obtain the spatially selectively weighted feature increment; The spatially selectively weighted feature increment is added to the current node representation of the finest layer to obtain the enhanced node representation of the finest layer.

[0011] In some embodiments, the cross-grid information transmission is achieved by weighted summation of message representations within the neighborhood node set based on inverse distance weights; The inverse distance weights are obtained through offline pre-computation and stored collaboratively with the multi-scale hierarchical graph structure. The offline pre-computation process for the inverse distance weights includes: Obtain the spherical distance between the sending node and the receiving node; The inverse distance weight between nodes is calculated based on the negative power of the spherical distance.

[0012] This invention provides a graph neural network ensemble prediction system for variable resolution grids, comprising: The graph construction module is used to obtain a multi-scale hierarchical graph structure that is topologically aligned with an unstructured variable resolution grid. The multi-scale hierarchical graph structure contains multiple scale layers, and nodes within the same scale layer are connected by adjacent edges. Adjacent scale layers are connected by up-line and down-line edges. The encoding module is used to transmit historical meteorological input data across grids, map it to the finest layer of the multi-scale hierarchical graph structure, propagate it upwards along the upper edge to the coarsest layer, and output the parameters of the conditional prior distribution at the coarsest layer. The scanning module is used to independently initialize the initial state of each layer node of the hierarchical graph structure, perform multiple rounds of round-trip scanning operations, and after each round of round-trip scanning operations, perform adaptive gating fusion on the downlink node representation obtained by downlink propagation and the uplink node representation obtained by uplink propagation within the same scale layer, and use the fused node representation as the initial state of the next round of round-trip scanning; each round of round-trip scanning operation includes propagating down from the coarsest layer along the downlink edge to the finest layer, and propagating up from the finest layer along the uplink edge to the coarsest layer; The decoding module is used to sample and generate latent variables based on the parameters of the conditional prior distribution after completing multiple rounds of round-trip scanning, inject the latent variables into the coarsest layer, and propagate them down layer by layer along the downlink edge to the finest layer to obtain the current node representation of the finest layer; An adaptive local enhancement module is used to obtain the resolution prior and local encrypted region mask for each node of the finest layer, generate feature increments based on the current node representation and the initial node representation of the finest layer, generate node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask, weight the feature increments based on the node-by-node gating coefficients, and superimpose them on the current node representation of the finest layer to obtain the enhanced node representation of the finest layer. The output module is used to perform the cross-grid information transmission on the enhanced finest layer node representation, map it back to the unstructured variable resolution grid, and generate probability set prediction results.

[0013] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the graph neural network ensemble prediction method for variable resolution grids.

[0014] The present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the graph neural network ensemble prediction method for variable resolution grids.

[0015] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the graph neural network ensemble prediction method for variable resolution grids.

[0016] The graph neural network ensemble forecasting method and system for variable resolution grids provided by this invention constructs a multi-scale hierarchical graph structure aligned with the topology of the unstructured variable resolution grid. Historical data is aggregated layer by layer along the uplink edge to the coarsest layer, and conditional prior distribution parameters are output, effectively extracting large-scale background features and providing a probabilistic benchmark for subsequent quantification of meteorological evolution uncertainties. By performing multiple rounds of back-and-forth scanning and adaptively gating the downlink and uplink node representations, a two-way collaborative interaction between large-scale background constraints and local features is achieved, thus balancing global circulation consistency with fine local structure. By sampling latent variables based on conditional prior distributions and propagating them down layer by layer, reasonable randomness is introduced at extremely low computational cost, avoiding the high cost of ensemble integration calculations in traditional models. Adaptive local feature enhancement effectively restores and strengthens the local high-frequency dynamic details of encrypted areas. By mapping the enhanced finest layer node representations back to the real physical variable resolution grid across grids, the latent spatial features after multi-scale fusion are transformed into the physical meteorological variables required for operational use, ultimately outputting high-precision probabilistic ensemble forecast results, achieving efficient and high-precision probabilistic ensemble forecasting. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0018] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the graph neural network ensemble prediction method for variable resolution grids provided by the present invention.

[0020] Figure 2 This is a block diagram of the overall architecture of the graph neural network ensemble prediction method for variable resolution grids provided by the present invention.

[0021] Figure 3 This is a schematic diagram of the hierarchical icosahedral graph structure of the graph neural network ensemble prediction method for variable resolution grids provided by the present invention.

[0022] Figure 4 This is a schematic diagram of the adaptive gating fusion mechanism of the graph neural network ensemble prediction method for variable resolution grids provided by the present invention.

[0023] Figure 5 This is a schematic diagram of the adaptive local feature enhancement module of the graph neural network ensemble prediction method for variable resolution grids provided by the present invention.

[0024] Figure 6 This is a schematic diagram of the structure of the graph neural network ensemble prediction system for variable resolution grids provided by the present invention.

[0025] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] It should be noted that the terms "first," "second," etc., used in this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps, units, or modules is not necessarily limited to those explicitly listed, but may include other steps, units, or modules not explicitly listed or inherent to such processes, methods, products, or devices.

[0028] Figure 1 This is a flowchart illustrating the graph neural network ensemble prediction method for variable resolution grids provided by the present invention, as shown below. Figure 1 As shown, the method includes steps 110, 120, 130, 140, 150 and 160.

[0029] Step 110: Obtain a multi-scale hierarchical graph structure that is topologically aligned with the unstructured variable resolution mesh; the multi-scale hierarchical graph structure contains multiple scale layers, nodes within the same scale layer are connected by adjacent edges, and adjacent scale layers are connected by up-line and down-line edges.

[0030] Specifically, the execution entity of the graph neural network ensemble prediction method for variable resolution grids provided in this embodiment of the invention is a graph neural network ensemble prediction device for variable resolution grids. This device can be implemented in software, such as a graph neural network ensemble prediction program for variable resolution grids running in a computer; or it can be implemented in hardware, such as a computer or server that executes the graph neural network ensemble prediction method for variable resolution grids.

[0031] Existing AI weather forecasting models based on regular grid designs rely on uniform neighborhood definitions and regular convolution or attention operations, making them unsuitable for direct transfer to unstructured grids. While graph neural networks (GNNs) are naturally adaptable to arbitrary topologies, providing a theoretical basis for handling unstructured grids, existing GNN forecasting methods still have several shortcomings in multi-scale information interaction and variable resolution adaptation: For message passing bias caused by drastic spatial gradients in node density within variable resolution grids, existing methods lack effective geometric constraint mechanisms, easily leading to systematic distortions during feature aggregation; the global-scale circulation background and local high-frequency weather processes in the atmospheric system exhibit complex bidirectional interactions, but existing methods primarily focus on unidirectional information transmission, i.e., from coarse to fine or from fine to coarse, making true cross-scale bidirectional collaboration difficult; the feature representation requirements of high-resolution densified regions differ fundamentally from those of low-resolution background regions, and existing methods employ a uniform processing strategy, failing to meet the differentiated needs of different resolution regions.

[0032] Figure 2 This is a block diagram of the overall architecture of the graph neural network ensemble prediction method for variable resolution grids provided by the present invention, as follows: Figure 2 As shown, this invention provides a graph neural network ensemble forecasting method and system for variable resolution grids, aiming to solve technical problems such as unstructured grid adaptation, message propagation bias caused by drastic spatial gradients in node density under variable resolution grid frameworks, insufficient cross-scale bidirectional information interaction, and lack of differentiated representation capabilities for different resolution regions. It achieves efficient probabilistic ensemble forecasting with a computational cost far lower than traditional numerical integration. The hierarchical graph structure, cross-scale bidirectional interaction mechanism, and adaptive local feature enhancement design concepts proposed in this invention do not rely on specific unstructured grid configurations and can be extended to other unstructured grid models such as the Model for Prediction Across Scales (MPAS) and the ICOsahedral Non-hydrostatic model (ICON) based on unstructured triangular grids, providing a general technical solution for the construction of next-generation ensemble forecasting systems.

[0033] Unstructured variable-resolution grids refer to irregular grids, such as those based on spherical Voronoi diagrams, used in numerical weather prediction models, such as the Global-Regional Integrated Forecast System (GRIST) and the Model for Prediction Across Scales (MPAS). Compared to traditional regular latitude and longitude grids, they avoid the singularity problem in polar regions. The "variable resolution" attribute allows for smooth grid refinement in local high-impact weather areas within the same global grid framework, thus balancing the simulation of global background circulation and detailed local weather with limited computational resources.

[0034] Multi-scale hierarchical graph structures refer to graph neural network computational skeletons specifically constructed to adapt to the aforementioned unstructured physical grids. Since traditional artificial intelligence convolutional models cannot directly process unstructured data, embodiments of this invention convert it into a graph form containing multiple resolution levels (i.e., multiple scale layers).

[0035] Adjacent edges are located within the same scale layer and are used to connect spatially adjacent graph nodes. They are mainly responsible for message passing and aggregation of local spatial features at the same resolution scale.

[0036] The uplink and downlink edges are located between different scale layers. The uplink edge is used to unidirectionally transmit node information from the fine-scale layer (i.e., high resolution) to the coarse-scale layer (i.e., low resolution), thereby achieving upward aggregation of features. The downlink edge is used to unidirectionally transmit node information from the coarse-scale layer to the fine-scale layer, thereby achieving downward constraint of large-scale background features.

[0037] In this embodiment of the invention, firstly, a hierarchical icosahedral graph structure aligned with the topology of an unstructured Voronoi grid is constructed; the hierarchical graph structure contains multiple scale layers, nodes within the same scale layer are connected by adjacent edges for local information transmission, and adjacent scale layers support cross-scale information flow through up and down edges.

[0038] Step 120: Transfer historical meteorological input data across grids and map it to the finest layer of the multi-scale hierarchical graph structure. Propagate it layer by layer along the upward edge to the coarsest layer and output the parameters of the conditional prior distribution at the coarsest layer.

[0039] Specifically, historical meteorological input data refers to the initial field and boundary condition data used to drive the model for forecasting. It typically includes atmospheric physical state variables over one or more past time steps, such as three-dimensional meteorological field elements like temperature, wind field, and humidity, as well as external forcing field data, such as topographic height, sea surface temperature, and solar radiation.

[0040] The conditional prior distribution refers to the probability distribution used to characterize the uncertainty of future weather system evolution within the variational autoencoder forecasting framework constructed in this embodiment of the invention. This distribution is a latent stochastic probability model of global large-scale meteorological states derived "conditionally based on historical inputs".

[0041] In this embodiment of the invention, historical meteorological data and external forcing fields are mapped to the finest layer of a hierarchical graph structure. The encoder propagates the data layer by layer along the upper edge, and the node representations of each layer are aggregated to the coarsest layer. The parameters of the conditional prior distribution are output at the coarsest layer.

[0042] The encoder is responsible for mapping historical weather conditions and external forcing fields into conditional prior distributions of latent variables.

[0043] Historical states, external forcing fields, and static grid features are concatenated and embedded using a Multi-Layer Perceptron (MLP) to obtain grid node representations. These representations are then propagated to the finest layer via a Grid-to-Mesh (G2M) mapping, and subsequently spread upwards layer by layer along the uplink edges. Each layer uses a graph neural network for message passing, while simultaneously updating local information through adjacent edges within the same layer. At the coarsest layer, the MLP maps the node representations to conditional prior distribution parameters of latent variables.

[0044] It should be noted that during the training phase, the encoder also receives the ground truth state at the target time as additional input to parameterize the variational posterior distribution. The KL divergence (KL) between the variational posterior distribution and the conditional prior distribution participates in model optimization as a regularization term. During the inference phase, only the conditional prior distribution is used to generate latent variables.

[0045] Step 130: Independently initialize the initial state of each layer node of the hierarchical graph structure, perform multiple rounds of round-trip scanning operations, and after each round of round-trip scanning operations, perform adaptive gating fusion on the downlink node representation obtained by downlink propagation and the uplink node representation obtained by uplink propagation within the same scale layer, and use the fused node representation as the initial state of the next round of round-trip scanning; each round of round-trip scanning operations includes propagating down from the coarsest layer along the downlink edge to the finest layer, and propagating up from the finest layer along the uplink edge to the coarsest layer.

[0046] Specifically, independent initialization refers to the process in the decoding stage where, instead of directly using the intermediate states aggregated layer by layer by the encoder, each node in the hierarchical graph structure is reassigned initial feature values, such as zero vectors or specific prior embeddings. This decoupled design helps the model to perform multi-scale feature reconstruction more flexibly during the decoding stage.

[0047] Round-trip scanning refers to the process of information flowing bidirectionally across scales within a hierarchical graph structure, including sequential or alternating downlink and uplink propagation. In this embodiment of the invention, the decoder performs multiple round-trip scans. Each scan includes: downlink propagation, transmitting large-scale background constraint information layer by layer downwards from the coarsest layer along the downlink edges; and uplink propagation, feeding back local correction information layer by layer upwards from the finest layer along the uplink edges. After each scan, adaptive gating fusion is performed on the downlink and uplink representations within the same scale layer.

[0048] Downward propagation refers to the process by which information is transmitted from the coarsest layer down the descending edge to the finest layer; its physical significance lies in transmitting information about the evolution trend of the atmospheric background on a large scale and global dynamic constraints.

[0049] Upward propagation refers to the process by which information is transmitted from the finest layer to the coarsest layer along the upward edge; its physical significance lies in the upward feedback of local small-scale high-frequency meteorological characteristics and local correction information caused by topography.

[0050] Adaptive gating fusion is a data-driven feature combination mechanism that can dynamically calculate fusion weights based on the degree of dependence of different spatial locations and scale layers on large-scale background and local correction, thereby organically combining the two types of information.

[0051] In this embodiment of the invention, the initial state of each layer of the hierarchical graph structure is independently initialized in the decoder, and then multiple rounds of round-trip scanning are performed. Each round-trip scanning includes: downlink propagation from the coarsest layer to the finest layer, progressively transmitting large-scale background constraint information; and uplink propagation from the finest layer to the coarsest layer, progressively feeding back local correction information. After each round-trip scanning, the node representations obtained by downlink propagation and the node representations obtained by uplink propagation within the same scale layer are adaptively gated and fused. The fused node representation is used as the initial state of the next round-trip scanning.

[0052] Step 140: After completing multiple rounds of round-trip scanning, latent variables are generated by sampling based on the parameters of the conditional prior distribution. The latent variables are injected into the coarsest layer and propagated down the downlink edge to the finest layer to obtain the current node representation of the finest layer.

[0053] Specifically, the conditional prior distribution refers to the probability distribution output at the coarsest layer of the multi-scale hierarchical graph structure after the encoder extracts features from historical meteorological data and external forcing fields. This distribution characterizes the macroscopic evolution trend and uncertainty of future atmospheric conditions under given historical observation conditions.

[0054] Latent variables are implicit feature vectors randomly sampled from the aforementioned conditional prior distributions. In ensemble forecasting scenarios, different latent variables represent different possibilities for the evolution of future weather systems, i.e., different ensemble members.

[0055] The coarsest layer corresponds to the layer with the fewest nodes and the lowest spatial resolution in the hierarchical graph structure, and is used to capture the large-scale circulation background on a global scale; the finest layer corresponds to the layer with the most nodes and the highest resolution, and is used to characterize complex local weather processes.

[0056] In this embodiment of the invention, after completing multiple rounds of round-trip scanning, latent variables are sampled from the conditional prior distribution, the latent variables are injected into the coarsest layer, and the final downlink propagation is performed to pass randomness to each scale layer step by step; the propagation is carried out layer by layer down the downlink edge to the finest layer to obtain the current node representation of the finest layer.

[0057] By generating set members through random sampling in the latent variable space, the probability distribution evolution of atmospheric state is modeled in an autoregressive manner. The inference speed is improved by about two orders of magnitude compared with traditional numerical set integration, while reducing computational costs while maintaining forecast accuracy.

[0058] During the training phase, a variational inference framework is used to optimize the model parameters. At each time step, latent variables are sampled from the variational posterior, and gradient backpropagation is ensured through reparameterization techniques. The total loss function includes a negative log-likelihood term and a KL divergence regularization term.

[0059] In the inference phase, ensemble members are generated by running the autoregressive forecasting process independently multiple times. In each run, a latent variable is independently sampled from the conditional prior distribution at each forecast time. This sample is then decoded to generate the forecast state for the current time step, which is used as the historical input for the next time step. This process is repeated autoregressively over time until the forecast ends, forming a complete forecast trajectory. This process is repeated several times, with latent variable sampling independent between runs, and the trajectory gradually diverges over time, generating multiple complete forecast trajectories. The ensemble mean of these trajectories serves as the deterministic forecast, and the ensemble standard deviation serves as the uncertainty measure, constituting the final probabilistic ensemble forecast.

[0060] Step 150: Obtain the resolution prior and local encryption region mask for each node of the finest layer; generate feature increments based on the current node representation and the initial node representation of the finest layer; generate node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encryption region mask; weight the feature increments based on the node-by-node gating coefficients and superimpose them onto the current node representation of the finest layer to obtain the enhanced node representation of the finest layer.

[0061] Specifically, resolution priors refer to prior information that reflects the resolution attribute of the physical space where the nodes of the graph structure are located.

[0062] A local encryption region mask is a spatial identifier matrix or vector used to distinguish whether the current grid node is located within a pre-defined high-resolution encryption region.

[0063] In this embodiment of the invention, after downlink propagation to the finest layer, node-by-node gating coefficients are generated on the finest layer based on the current dynamic representation of the node, the initial node representation of the finest layer, static geometric embedding, resolution prior, and local encrypted region mask. Feature increments are jointly generated by the enhancement network based on the current dynamic representation of the node and the initial node representation of the finest layer. The gating coefficients and feature increments are multiplied element-by-element and then superimposed on the current node representation of the finest layer to perform resolution-aware local enhancement on the node representation of the finest layer, resulting in the enhanced node representation.

[0064] Step 160: Perform the cross-grid information transfer on the enhanced finest layer node representation, map it back to the unstructured variable resolution grid, and generate probability set prediction results.

[0065] Specifically, probabilistic ensemble forecast results mean that the forecast output is no longer a single deterministic meteorological value, but an estimate of the conditional probability distribution of the target meteorological state in order to quantify the uncertainty in the atmospheric evolution process.

[0066] In this embodiment of the invention, the finest layer node representation after local enhancement is mapped back to the original Voronoi grid, and the mean and standard deviation of the predicted distribution are output to generate a probability ensemble forecast.

[0067] The enhanced finest layer representation is back-projected onto the original Voronoi grid through a mesh-to-grid (M2G) mapping. The mean and standard deviation of the predicted distribution are then output by the MLP to obtain the conditional probability distribution parameters for the current time step.

[0068] The graph neural network ensemble forecasting method for variable resolution grids provided in this invention constructs a multi-scale hierarchical graph structure aligned with the topology of the unstructured variable resolution grid. Historical data is aggregated layer by layer along the uplink edge to the coarsest layer, and conditional prior distribution parameters are output. This effectively extracts large-scale background features and provides a probabilistic benchmark for quantifying the uncertainty of meteorological evolution. By performing multiple rounds of back-and-forth scanning and adaptively gating the downlink and uplink node representations, a bidirectional collaborative interaction between large-scale background constraints and local features is achieved, thus balancing global circulation consistency with fine local structure. By sampling latent variables based on conditional prior distributions and propagating them down layer by layer, reasonable randomness is introduced at extremely low computational cost, avoiding the high cost of ensemble integration calculations in traditional models. Adaptive local feature enhancement effectively restores and strengthens the local high-frequency dynamic details of encrypted areas. By mapping the enhanced finest layer node representations back to the real physical variable resolution grid across the grid, the latent space features after multi-scale fusion are transformed into the physical meteorological variables required for operational purposes, ultimately outputting high-precision probabilistic ensemble forecast results, achieving efficient and high-precision probabilistic ensemble forecasting.

[0069] In some embodiments, obtaining a multi-scale hierarchical graph structure aligned with the topology of an unstructured variable-resolution mesh includes: Based on the icosahedron as the basic model, a global spherical mesh containing multiple scale layers is constructed by progressively subdividing the model into four subdivisions. At the location of the local refinement region corresponding to the unstructured variable resolution mesh, an additional local subdivision operation is performed on the global spherical mesh to obtain the multi-scale hierarchical graph structure.

[0070] Specifically, a regular icosahedron is a convex regular polyhedron composed of 20 congruent equilateral triangular faces.

[0071] Stepwise subdivision into four smaller triangles is a classic spherical grid encryption algorithm. Its operation involves taking the midpoints of each side of the original triangle and connecting these midpoints pairwise, thus dividing a large triangle into four congruent smaller triangles. Each time this operation is performed, the grid depth increases by one level, thereby improving the resolution.

[0072] In practical meteorological operations, to focus on high-impact weather-prone areas with limited computing power, such as the topographically complex East Asian region or typhoon-prone sea areas, a higher-resolution grid with a denser mesh than the global background grid is set within the specific geographical boundaries. This area is known as the local densification zone.

[0073] This invention relates to a global numerical weather prediction model employing an unstructured, variable-resolution Voronoi grid. First, a hierarchical graph structure aligned with the physical Voronoi grid topology is constructed.

[0074] In this embodiment of the invention, the hierarchical graph structure is constructed based on a regular icosahedron through progressively subdivided 4 subdivisions, and additional local subdivisions are performed in the encrypted regions corresponding to the original physical grid, so that the node resolution of the finest layer in the local encrypted regions matches the resolution of the physical Voronoi grid; the hierarchical graph structure remains fixed during training and inference.

[0075] Figure 3 This is a schematic diagram of the hierarchical icosahedral graph structure of the graph neural network ensemble prediction method for variable resolution grids provided by this invention, as shown below. Figure 3 As shown, this structure is based on a regular icosahedron and obtains multi-layered spherical triangulation from global to local scales through successive 4-level subdivision. Additional local subdivision is performed in the target region to match the node resolution of the finest layer within the target region to the physical Voronoi grid. Nodes in the same layer are connected by adjacent edges, and information flow across scales is supported between adjacent layers through up and down edges. This hierarchical graph structure remains constant during training and inference.

[0076] It should be noted that, to bridge the gap between the original physical space and the multi-scale latent space, G2M and M2G mappings are constructed. The G2M module maps Voronoi grid nodes to the finest layer, while the M2G module maps the finest layer representations back to the Voronoi grid. An inverse distance weight constraint based on spherical distance is introduced in the cross-grid mapping, allowing neighboring nodes to receive a higher message contribution and suppressing feature shifts caused by drastic changes in node density. This weight depends only on static geometric relationships and can be pre-computed offline before training.

[0077] The graph neural network ensemble forecasting method for variable resolution grids provided in this invention obtains a multi-scale hierarchical graph structure that is topologically aligned with the unstructured variable resolution grid. This ensures that the node resolution of the finest layer of the AI ​​hierarchical graph structure in the local densified region matches the resolution of the unstructured Voronoi grid output by the physical model, guaranteeing the accurate transmission of atmospheric dynamic characteristics in the subsequent cross-grid mapping stage and providing underlying grid structure support for climate forecasting in local high-resolution regions.

[0078] In some embodiments, the adaptive gating fusion of the downlink node representation obtained by downlink propagation and the uplink node representation obtained by uplink propagation within the same scale layer includes: The quality assessment scores of the downlink node representation and the uplink node representation are calculated respectively using a learnable quality assessment network. The quality assessment score is scaled and mapped using preset temperature parameters to obtain the downlink gating coefficient and the uplink gating coefficient, respectively. Linear feature transformations are performed on the downlink node representation and the uplink node representation respectively to obtain the transformed downlink representation and the transformed uplink representation. Based on the downlink gating coefficient and the uplink gating coefficient, the downlink representation and the uplink representation are weighted and fused to obtain the gated fused backbone representation; The downlink node representation and the uplink node representation are concatenated along the feature dimension to calculate the residual refinement term. The residual refinement term is superimposed onto the gated fusion backbone representation to obtain the fused node representation.

[0079] Specifically, a quality assessment network is a learnable neural network component, such as a multilayer perceptron (MLP), embedded in the overall model. Its function is to output one or a set of values, namely a quality assessment score, based on the input node features. This score is used to characterize the relative importance or information confidence of the feature in the current forecast task and the current spatial location.

[0080] Temperature is a commonly used hyperparameter or learnable parameter in deep learning, especially in attention or gating mechanisms. Its main function is to smooth or sharpen the probability distribution of the output. Introducing a temperature parameter can effectively prevent the network from becoming overconfident in the early stages of training, i.e., preventing the gating coefficients from approaching 0 or 1 too early, thereby maintaining stable gradient propagation.

[0081] The residual refinement term is a supplementary feature introduced to prevent the loss of effective implicit information in the original features during the gating weighting process. It is calculated through another network bypass and added to the backbone output in an additive manner, which helps to improve the deep expressive power of the network.

[0082] In this embodiment of the invention, adaptive gating fusion includes: performing layer normalization on the downlink node representation and the uplink node representation within the same scale layer, and calculating their respective quality scores through a shared-weight quality assessment MLP; dividing the quality score by a temperature parameter and mapping it through a Sigmoid function to obtain downlink gating coefficients and uplink gating coefficients; performing linear transformation on the downlink node representation and the uplink node representation to obtain the transformed representation; obtaining a gating fusion backbone through gating weighted fusion; concatenating the downlink node representation and the uplink node representation along the feature dimension and inputting them into the fusion MLP, weighting them with learnable scaling coefficients as a residual term (i.e., a residual refinement term), and adding them to the gating fusion backbone to obtain the fused node representation.

[0083] Figure 4 This is a schematic diagram of the adaptive gating fusion mechanism of the graph neural network ensemble prediction method for variable resolution grids provided by this invention, as shown below. Figure 4As shown, the adaptive gating fusion mechanism fuses two representations in the following steps: calculate the quality scores of the downlink and uplink representations respectively, and map them to gating coefficients after scaling by temperature parameters; perform linear transformation on the two representations and then weight fusion by gating coefficients; and then superimpose the residual refinement term based on the splicing features of the two representations to obtain the fused representation as the initial state for the next round of scanning.

[0084] The graph neural network ensemble prediction method for variable resolution grids provided in this invention, by designing a multi-round round-trip scanning mechanism that alternates between downlink and uplink propagation, enables full bidirectional interaction between large-scale background constraints and local correction information in a hierarchical graph structure. At the same time, it introduces an adaptive gating fusion mechanism to dynamically adjust the fusion ratio according to the degree of dependence of different spatial locations on the two types of information, thus solving the limitation of unidirectional information transmission in existing methods. Based on multi-round round-trip scanning and adaptive gating fusion, it achieves cross-scale bidirectional collaboration.

[0085] In some embodiments, the resolution prior is calculated based on the area of ​​the unstructured variable resolution mesh; The local encryption region mask is used to identify encrypted nodes within the target region.

[0086] Specifically, in this embodiment of the invention, the resolution prior is calculated based on the area of ​​an unstructured variable resolution grid, and the smaller the grid area, the higher the resolution.

[0087] The local encryption region mask is used to identify the encryption nodes within the target region; the modified gating coefficient has a higher value within the local encryption region and a lower value outside the local encryption region to achieve differentiated local enhancement.

[0088] The graph neural network ensemble prediction method for variable resolution grids provided in this invention introduces an adaptive local feature enhancement module in the finest layer. Using the current dynamic representation of a node and the initial node representation in the finest layer as joint input, the enhancement network generates feature increments that compensate for information suppressed by global aggregation. Simultaneously, a gating network integrates the current dynamic representation, the initial node representation in the finest layer, static geometric embedding, resolution priors, and local encrypted region masks to generate node-by-node gating coefficients. Sufficient feature correction is applied in high-resolution encrypted regions, while the correction magnitude is suppressed in low-resolution background regions. This achieves differentiated enhancement for different resolution regions, effectively recovering the local high-frequency dynamic information attenuated during global propagation.

[0089] In some embodiments, the step of generating feature increments based on the current node representation of the finest layer and the initial node representation of the finest layer, and generating node-by-node gating coefficients based on the current node representation of the finest layer, the initial node representation of the finest layer, static geometric embedding, the resolution prior, and the local encrypted region mask, weighting the feature increments based on the node-by-node gating coefficients, and superimposing them on the current node representation of the finest layer to obtain the enhanced node representation of the finest layer includes: Obtain the initial node representation of the finest layer; The initial node representation of the finest layer and the current node representation of the finest layer are concatenated along the feature dimension, and feature extraction is performed through an augmentation network to generate feature increments; wherein, the initial node representation of the finest layer is the node representation cached after the grid feature has completed cross-grid mapping and before the hierarchical up-scan starts; the current node representation of the finest layer is the node representation after full hierarchical propagation and latent variable injection; The finest layer current node representation, the finest layer initial node representation, the node's static geometric embedding, and the resolution prior are concatenated along the feature dimension, and then processed by a gating network for feature mapping and activation function processing to generate initial gating coefficients. The initial gating coefficient is masked based on the local encrypted region mask to obtain the node-by-node gating coefficient; wherein the value of the node-by-node gating coefficient in the encrypted region indicated by the local encrypted region mask is greater than its value in the unencrypted region. The node-by-node gating coefficient is multiplied element-by-element by the feature increment to obtain the spatially selectively weighted feature increment; The spatially selectively weighted feature increment is added to the current node representation of the finest layer to obtain the enhanced node representation of the finest layer.

[0090] Specifically, the initial node representation of the finest layer is a cached node representation after the grid features have completed cross-grid mapping and before the hierarchical upscan starts, preserving the original structure of the local information before it is processed by hierarchical aggregation.

[0091] The current node in the finest layer is represented as a node after propagation through the complete hierarchy and injection of latent variables.

[0092] The static geometric embedding of a node refers to the feature vector that characterizes the inherent spatial properties of an unstructured mesh node. It typically includes geometric and topological information that does not change over time, such as the node's three-dimensional spherical coordinates, relative distance to neighboring nodes, and relative angle.

[0093] Both augmented networks and gated networks are feature extraction modules whose weights can be updated through deep learning training. For example, they can be implemented using multilayer perceptron (MLP) or graph convolutional network layers, respectively, for nonlinear feature purification and dynamic weight mapping generation.

[0094] In this embodiment of the invention, adaptive local feature enhancement includes: inputting the current dynamic representation, initial reference representation, static geometric embedding, resolution prior, and encrypted region mask of a node into an adaptive local feature enhancement module; generating a local feature increment through an enhancement network using the current dynamic representation and initial reference representation as joint inputs; generating node-by-node gating coefficients through a gating network using the current dynamic representation, initial reference representation, static geometric embedding, resolution prior, and encrypted region mask as joint inputs; and multiplying the gating coefficients element-wise with the local feature increment and then adding them to the current dynamic representation to obtain the enhanced node representation.

[0095] Specifically, the following steps are performed: First, obtain the initial node representation of the finest layer. Second, concatenate the initial node representation and the current node representation of the finest layer along the feature dimension, and perform feature extraction via an augmentation network to generate feature increments. Third, concatenate the current node representation, the initial node representation, the static geometric embedding of the node, and the resolution prior along the feature dimension, and perform feature mapping and Sigmoid activation function processing via a gating network to generate initial gating coefficients. Fourth, perform mask modulation on the initial gating coefficients based on a local encrypted region mask to obtain per-node gating coefficients. The per-node gating coefficients have higher values ​​within the encrypted region indicated by the local encrypted region mask than within the unencrypted region. Fifth, multiply the per-node gating coefficients element-wise with the feature increments to obtain spatially selectively weighted feature increments. Sixth, add the spatially selectively weighted feature increments to the current node representation of the finest layer to obtain the finest layer node representation after local high-frequency detail compensation.

[0096] After the downlink propagation reaches the finest layer, local high-frequency detail compensation is performed at the finest layer through an adaptive local feature enhancement module.

[0097] Figure 5 This is a schematic diagram of the adaptive local feature enhancement module of the graph neural network ensemble prediction method for variable resolution grids provided by the present invention, as shown below. Figure 5 As shown, this module consists of two collaborative components: a gating network and an augmentation network. The augmentation network takes the current dynamic representation h and the initial representation h0 of a node as joint inputs to generate a feature increment Δh. h0 is the initial Level-1 node representation cached after the grid features have undergone G2M projection and before the hierarchical upsweep begins, preserving the original structure of local information before hierarchical aggregation. h, on the other hand, is the current representation after complete hierarchical propagation and latent variable injection, carrying the top-down global multi-scale semantics. The joint input of these two components enables the augmentation network to model the representation changes before and after hierarchical processing, thereby generating a feature increment Δh that compensates for the information suppressed by global aggregation.

[0098] The gating network integrates the current dynamic representation h, the initial reference representation h0, the static geometric embedding s, the resolution prior p, and the encryption region mask m to learn the node-wise gating coefficients. ∈(0,1), adaptively determining the enhancement strength of each node. The two work together to apply gated residual enhancement to the node representation:

[0099]

[0100]

[0101] Where [·] represents concatenation along the feature dimension, and ⊙ represents element-wise multiplication. The resolution prior p is calculated from the area of ​​the original unstructured prior resolution grid; the smaller the grid area, the higher the resolution, and the larger the p value. The encryption region mask m identifies the nodes within the ROI range. The initial reference representation h0 is naturally generated during the forward propagation g2m stage and can be cached at low cost. None of the above three introduce additional runtime overhead. Under the joint constraint of the resolution prior and the encryption region mask, the gating coefficients... In high-resolution encrypted regions, a greater enhancement is adaptively activated, while in low-resolution background regions, active suppression is employed to increase the weighted feature increment. ⊙Δh is spatially concentrated in the encrypted region, achieving spatially selective feature compensation. This design enables the model to selectively recover local weather details in the encrypted region that are suppressed by global aggregation, improving the ability of ensemble members to characterize weather processes in the encrypted region.

[0102] The graph neural network ensemble prediction method for variable resolution grids provided in this invention introduces an enhancement network and a gated network in the finest layer. It uses node dynamic representation, initial node representation in the finest layer, static geometric embedding, resolution prior, and local encrypted region masking to jointly drive node-by-node adaptive feature refinement. This balances the relationship between the background field and the local high-frequency field, injecting rich fine structure into the target encrypted region while avoiding the introduction of unnecessary noise in the sparse background region. This effectively improves the overall ensemble prediction performance under the unstructured variable resolution grid mode.

[0103] In some embodiments, the cross-grid information transmission is achieved by weighted summation of message representations within the neighborhood node set based on inverse distance weights; The inverse distance weights are obtained through offline pre-computation and stored collaboratively with the multi-scale hierarchical graph structure. The offline pre-computation process for the inverse distance weights includes: Obtain the spherical distance between the sending node and the receiving node; The inverse distance weight between nodes is calculated based on the negative power of the spherical distance.

[0104] Specifically, in this embodiment of the invention, cross-grid information transmission is achieved by weighted summation of message representations within the neighboring node set based on inverse distance weights.

[0105] Since the spatial topological relationship between the unstructured physical grid and the multi-scale hierarchical graph structure in this embodiment of the invention is relatively fixed, meaning that the geographical coordinates of each grid node do not change during the prediction time integration process, the inverse distance weights are pre-calculated offline and stored in conjunction with the multi-scale hierarchical graph structure to reduce the computational overhead of the model during the inference phase. This means that before model training or formal business inference begins, the system has already pre-calculated the inter-grid mapping weights using computing resources and stored them as static graph attribute data in memory or on disk, which can be directly called during online runtime, thereby significantly improving the computational efficiency of model inference.

[0106] In the cross-grid information transfer process of mapping the original Voronoi grid nodes to the finest layer of the hierarchical graph structure, and in the cross-grid information transfer process of mapping the finest layer node representation back to the original Voronoi grid, an inverse distance weight constraint based on spherical distance is introduced: the message contribution between nodes is proportional to the negative power of the spherical distance, and the inverse distance weight is pre-computed offline before training and stored together with the graph structure.

[0107] Furthermore, in this embodiment of the invention, the formula for calculating the inverse distance weight is:

[0108] in, For nodes With nodes The spherical distance between them This is the distance attenuation coefficient. For nodes The set of neighboring nodes.

[0109] It should be noted that, It performs local normalization on the weights of all sending nodes in the neighborhood to ensure that the magnitude of the feature values ​​of the target node remains stable after the weighted summation is completed, thus avoiding feature explosion or gradient vanishing.

[0110] The graph neural network ensemble prediction method for variable resolution grids provided in this invention introduces an inverse distance weight constraint based on spherical distance in the cross-grid information transmission between the original Voronoi grid and the finest layer of the hierarchical graph structure. This allows neighboring nodes to obtain higher message contributions, thereby suppressing the feature averaging bias and information dilution problems caused by the drastic spatial gradient of node density and ensuring the spatial continuity of the atmospheric physical field.

[0111] Furthermore, this embodiment validates the effectiveness of the proposed method on encrypted simulation data of East Asia from the Global-Regional Integrated Forecast System (GRIST). Experimental results show that, compared to conventional graph neural network benchmarks, the method provided in this embodiment significantly improves the Continuous Ranked Probability Score (CRPS) and Spread-Skill Ratio (SSR) for key variables, and the inference speed is improved by approximately two orders of magnitude compared to traditional numerical ensemble integration.

[0112] The apparatus provided in the embodiments of the present invention will be described below. The apparatus described below can be referred to in correspondence with the method described above.

[0113] Figure 6 This is a schematic diagram of the structure of the graph neural network ensemble prediction system for variable resolution grids provided by the present invention, as shown below. Figure 6 As shown, the device includes a graph construction module 610, an encoding module 620, a scanning module 630, a decoding module 640, an adaptive local enhancement module 650, and an output module 660 connected in sequence.

[0114] Graph construction module 610 is used to obtain a multi-scale hierarchical graph structure that is topologically aligned with an unstructured variable resolution grid; the multi-scale hierarchical graph structure contains multiple scale layers, nodes within the same scale layer are connected by adjacent edges, and adjacent scale layers are connected by up-line and down-line edges. Encoding module 620 is used to transmit historical meteorological input data across grids, map it to the finest layer of the multi-scale hierarchical graph structure, propagate it upwards along the upper edge to the coarsest layer, and output the parameters of the conditional prior distribution at the coarsest layer. The scanning module 630 is used to independently initialize the initial state of each layer node of the hierarchical graph structure, perform multiple round-trip scanning operations, and after each round-trip scanning operation, perform adaptive gating fusion on the downlink node representation obtained by downlink propagation and the uplink node representation obtained by uplink propagation within the same scale layer, and use the fused node representation as the initial state of the next round-trip scanning operation; each round-trip scanning operation includes propagating down from the coarsest layer along the downlink edge to the finest layer, and propagating up from the finest layer along the uplink edge to the coarsest layer; The decoding module 640 is used to sample and generate latent variables based on the parameters of the conditional prior distribution after completing multiple rounds of round-trip scanning, inject the latent variables into the coarsest layer, and propagate them down layer by layer along the downlink edge to the finest layer to obtain the current node representation of the finest layer. The adaptive local enhancement module 650 is used to obtain the resolution prior and local encrypted region mask for each node of the finest layer, generate feature increments based on the current node representation and the initial node representation of the finest layer, generate node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask, weight the feature increments based on the node-by-node gating coefficients, and superimpose them on the current node representation of the finest layer to obtain the enhanced node representation of the finest layer. The output module 660 is used to perform the cross-grid information transmission on the enhanced finest layer node representation, map it back to the unstructured variable resolution grid, and generate probability set prediction results.

[0115] The graph neural network ensemble forecasting system for variable resolution grids provided in this invention constructs a multi-scale hierarchical graph structure aligned with the topology of the unstructured variable resolution grid. Historical data is aggregated layer by layer along the uplink edge to the coarsest layer, and conditional prior distribution parameters are output. This effectively extracts large-scale background features and provides a probabilistic benchmark for quantifying the uncertainty of meteorological evolution. By performing multiple rounds of back-and-forth scanning and adaptively gating the downlink and uplink node representations, a bidirectional collaborative interaction between large-scale background constraints and local features is achieved, thus balancing global circulation consistency with fine local structure. By sampling latent variables based on conditional prior distributions and propagating them down layer by layer, reasonable randomness is introduced at extremely low computational cost, avoiding the high cost of ensemble integration calculations in traditional models. Adaptive local feature enhancement effectively restores and strengthens the local high-frequency dynamic details of encrypted areas. By mapping the enhanced finest layer node representations back to the real physical variable resolution grid across grids, the latent spatial features after multi-scale fusion are transformed into the physical meteorological variables required for operational use, ultimately outputting high-precision probabilistic ensemble forecast results, achieving efficient and high-precision probabilistic ensemble forecasting.

[0116] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 7 As shown, the electronic device may include a processor 710, a communications interface 720, a memory 730, and a communications bus 740, wherein the processor 710, communications interface 720, and memory 730 communicate with each other via the communications bus 740. The processor 710 can call logical commands stored in the memory 730 to execute the methods described in the above embodiments, for example: A multi-scale hierarchical graph structure aligned with the topology of an unstructured variable-resolution grid is obtained. This structure comprises multiple scale layers, with nodes within the same scale layer connected by adjacent edges, and adjacent scale layers connected by up and down edges. Historical meteorological input data is transferred across grids and mapped to the finest layer of the multi-scale hierarchical graph structure, then propagated upwards along the up edge to the coarsest layer. Parameters of the conditional prior distribution are output at the coarsest layer. The initial states of nodes in each layer of the hierarchical graph structure are independently initialized, and multiple round-trip scan operations are performed. After each round-trip scan, the down-propagation node representations obtained from down-propagation within the same scale layer are adaptively gated and fused with the up-propagation node representations obtained from up-propagation. The fused node representation is used as the initial state for the next round-trip scan. Each round-trip scan includes propagating downwards from the coarsest layer along the down edge to the finest layer, and propagating downwards from the finest layer along the up edge. The row edges propagate upwards layer by layer to the coarsest layer. After multiple round-trip scans, latent variables are generated by sampling based on the parameters of the conditional prior distribution. These latent variables are injected into the coarsest layer and propagated downwards layer by layer along the down-row edges to the finest layer, resulting in the current node representation of the finest layer. The resolution prior and local encrypted region mask for each node in the finest layer are obtained. Feature increments are generated based on the current node representation and the initial node representation of the finest layer. Node-by-node gating coefficients are generated based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask. The feature increments are weighted based on the node-by-node gating coefficients and superimposed on the current node representation of the finest layer to obtain the enhanced node representation of the finest layer. The enhanced node representation of the finest layer is then subjected to cross-grid information transfer and mapped back to the unstructured variable resolution grid to generate a probability set prediction result.

[0117] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0118] The processor in the electronic device provided in this embodiment of the invention can call logical instructions in the memory to implement the above method. Its specific implementation method is the same as the aforementioned method implementation method and can achieve the same beneficial effects, which will not be repeated here.

[0119] This invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the methods provided in the above embodiments.

[0120] The specific implementation method is the same as the aforementioned method implementation method and can achieve the same beneficial effects, so it will not be repeated here.

[0121] This invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0122] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0123] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A graph neural network ensemble prediction method for variable resolution grids, characterized in that, include: Obtain a multi-scale hierarchical graph structure that is topologically aligned with an unstructured variable-resolution mesh; The multi-scale hierarchical graph structure contains multiple scale layers. Nodes within the same scale layer are connected by adjacent edges, and adjacent scale layers are connected by up-line and down-line edges. Historical meteorological input data is transmitted across grids and mapped to the finest layer of the multi-scale hierarchical graph structure. It is then propagated upwards along the upper edge to the coarsest layer, where the parameters of the conditional prior distribution are output. The initial states of each layer of the hierarchical graph structure are initialized independently, and multiple round-trip scan operations are performed. After each round-trip scan operation, the downlink node representations obtained by downlink propagation and the uplink node representations obtained by uplink propagation within the same scale layer are adaptively gated and fused. The fused node representations are used as the initial states for the next round-trip scan. Each round-trip scan operation includes propagating from the coarsest layer down along the downlink edge to the finest layer, and propagating from the finest layer up along the uplink edge to the coarsest layer. After completing multiple rounds of round-trip scanning, latent variables are generated by sampling based on the parameters of the conditional prior distribution. The latent variables are then injected into the coarsest layer and propagated down the downlink edge to the finest layer to obtain the current node representation of the finest layer. Obtain the resolution prior and local encrypted region mask for each node of the finest layer. Generate feature increments based on the current node representation and the initial node representation of the finest layer. Generate node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask. Weight the feature increments based on the node-by-node gating coefficients and superimpose them onto the current node representation of the finest layer to obtain the enhanced node representation of the finest layer. The enhanced finest layer node representation is used for cross-grid information transfer and mapped back to the unstructured variable resolution grid to generate probability set prediction results.

2. The graph neural network ensemble prediction method for variable resolution grids according to claim 1, characterized in that, The acquisition of a multi-scale hierarchical graph structure aligned with the topology of an unstructured variable-resolution grid includes: Based on the icosahedron as the basic model, a global spherical mesh containing multiple scale layers is constructed by progressively subdividing the model into four subdivisions. At the location of the local refinement region corresponding to the unstructured variable resolution mesh, an additional local subdivision operation is performed on the global spherical mesh to obtain the multi-scale hierarchical graph structure.

3. The graph neural network ensemble prediction method for variable resolution grids according to claim 1, characterized in that, The adaptive gating fusion of the downlink node representation obtained from downlink propagation and the uplink node representation obtained from uplink propagation within the same scale layer includes: The quality assessment scores of the downlink node representation and the uplink node representation are calculated respectively using a learnable quality assessment network. The quality assessment score is scaled and mapped using preset temperature parameters to obtain the downlink gating coefficient and the uplink gating coefficient, respectively. Linear feature transformations are performed on the downlink node representation and the uplink node representation respectively to obtain the transformed downlink representation and the transformed uplink representation. Based on the downlink gating coefficient and the uplink gating coefficient, the downlink representation and the uplink representation are weighted and fused to obtain the gated fused backbone representation; The downlink node representation and the uplink node representation are concatenated along the feature dimension to calculate the residual refinement term. The residual refinement term is superimposed onto the gated fusion backbone representation to obtain the fused node representation.

4. The graph neural network ensemble prediction method for variable resolution grids according to claim 1, characterized in that, The resolution prior is calculated based on the area of ​​the unstructured variable resolution mesh; The local encryption region mask is used to identify encrypted nodes within the target region.

5. The graph neural network ensemble prediction method for variable resolution grids according to claim 1, characterized in that, The process involves generating feature increments based on the current node representation and the initial node representation of the finest layer, and generating node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask. The feature increments are then weighted based on these node-by-node gating coefficients and superimposed onto the current node representation of the finest layer to obtain the enhanced finest layer node representation. This process includes: Obtain the initial node representation of the finest layer; The initial node representation of the finest layer and the current node representation of the finest layer are concatenated along the feature dimension, and feature extraction is performed through an augmentation network to generate feature increments; wherein, the initial node representation of the finest layer is the node representation cached after the grid feature has completed cross-grid mapping and before the hierarchical up-scan starts; the current node representation of the finest layer is the node representation after full hierarchical propagation and latent variable injection; The finest layer current node representation, the finest layer initial node representation, the node's static geometric embedding, and the resolution prior are concatenated along the feature dimension, and then processed by a gating network for feature mapping and activation function processing to generate initial gating coefficients. The initial gating coefficient is masked based on the local encrypted region mask to obtain the node-by-node gating coefficient; wherein the value of the node-by-node gating coefficient in the encrypted region indicated by the local encrypted region mask is greater than its value in the unencrypted region. The node-by-node gating coefficient is multiplied element-by-element by the feature increment to obtain the spatially selectively weighted feature increment; The spatially selectively weighted feature increment is added to the current node representation of the finest layer to obtain the enhanced node representation of the finest layer.

6. The graph neural network ensemble prediction method for variable resolution grids according to claim 1, characterized in that, The cross-grid information transmission is achieved by weighted summation of message representations within the neighborhood node set based on inverse distance weights; The inverse distance weights are obtained through offline pre-computation and stored collaboratively with the multi-scale hierarchical graph structure. The offline pre-computation process for the inverse distance weights includes: Obtain the spherical distance between the sending node and the receiving node; The inverse distance weight between nodes is calculated based on the negative power of the spherical distance.

7. A graph neural network ensemble prediction system for variable resolution grids, characterized in that, include: The graph construction module is used to obtain a multi-scale hierarchical graph structure that is topologically aligned with an unstructured variable-resolution mesh. The multi-scale hierarchical graph structure contains multiple scale layers. Nodes within the same scale layer are connected by adjacent edges, and adjacent scale layers are connected by up-line and down-line edges. The encoding module is used to transmit historical meteorological input data across grids, map it to the finest layer of the multi-scale hierarchical graph structure, propagate it upwards along the upper edge to the coarsest layer, and output the parameters of the conditional prior distribution at the coarsest layer. The scanning module is used to independently initialize the initial state of each layer node of the hierarchical graph structure, perform multiple round-trip scanning operations, and after each round-trip scanning operation, perform adaptive gating fusion on the downlink node representation obtained by downlink propagation and the uplink node representation obtained by uplink propagation within the same scale layer, and use the fused node representation as the initial state of the next round-trip scanning operation; each round-trip scanning operation includes propagating down from the coarsest layer along the downlink edge to the finest layer, and propagating up from the finest layer along the uplink edge to the coarsest layer; The decoding module is used to sample and generate latent variables based on the parameters of the conditional prior distribution after completing multiple rounds of round-trip scanning, inject the latent variables into the coarsest layer, and propagate them down layer by layer along the downlink edge to the finest layer to obtain the current node representation of the finest layer; An adaptive local enhancement module is used to obtain the resolution prior and local encrypted region mask for each node of the finest layer, generate feature increments based on the current node representation and the initial node representation of the finest layer, generate node-by-node gating coefficients based on the current node representation, the initial node representation, static geometric embedding, the resolution prior, and the local encrypted region mask, weight the feature increments based on the node-by-node gating coefficients, and superimpose them on the current node representation of the finest layer to obtain the enhanced node representation of the finest layer. The output module is used to perform the cross-grid information transmission on the enhanced finest layer node representation, map it back to the unstructured variable resolution grid, and generate probability set prediction results.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the graph neural network ensemble prediction method for variable resolution grids as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the graph neural network ensemble prediction method for variable resolution grids as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the graph neural network ensemble prediction method for variable resolution grids as described in any one of claims 1 to 6.

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