Efficient physical simulation system and method based on manifold embedding

Abstract

The application discloses a kind of high-efficiency physical simulation system and method based on manifold embedding, belong to physical simulation technical field.Multiple-source condition acquisition unit, the information of simulation object is collected, and is arranged into node local feature and global working condition condition;Manifold embedding perception unit, all kinds of information are uniformly encoded alignment, according to physical direction topological perception sparse sampling is carried out, sparse graph is constructed and is converted to latent space;Graph operator deduction identification unit, multi-layer graph transformation is executed in latent space, local physical information transmission and global attention mechanism are fused, and high-order feature for physical field prediction is generated;Result display unit, steady state and transient task are distinguished respectively decoding, the result is modified with explicit boundary constraint, and finally output and show simulation result.The system and method proposed in the application are adapted to complex unstructured grid, efficient and high-precision, support steady state and transient multi-task, engineering deployment is convenient, and landing is strong.

Description

Technical Field

[0001] This invention relates to the field of physical simulation technology, and in particular to an efficient physical simulation system and method based on manifold embedding. Background Technology

[0002] Physical simulation technology is a core foundation for scientific computing, engineering design, and industrial optimization. It has evolved from a single solution tool into a critical infrastructure that runs through the entire process of digital twins, complex equipment development, and intelligent manufacturing. In fields such as aerospace, automotive aerodynamics, and energy equipment, engineering objects generally have characteristics such as complex boundaries, large scale spans, and variable operating conditions. Although traditional high-fidelity numerical solution methods are reliable in accuracy, they have long calculation cycles and consume a lot of computing power, making it difficult to meet engineering requirements such as batch parameter scanning and real-time feedback.

[0003] In recent years, data-driven physical simulation technology based on machine learning has developed rapidly, forming an accelerated path of "offline learning and online prediction." However, existing solutions still have obvious limitations: traditional numerical simulation technology is inefficient in scenarios with repeated multi-parameter solutions; physical information neural networks are difficult to optimize under complex coupling mechanisms; neural operator methods rely on regular grids and have poor adaptability to unstructured grids; the fusion architecture of graph neural networks and Transformers is not specifically optimized for physical field regression tasks, resulting in problems such as high attention complexity, insufficient expression of local physical directionality, unreliable boundary condition handling, and poor scalability for large-scale industrial scenarios.

[0004] In summary, existing technologies have not yet formed a comprehensive technical framework that can simultaneously unify the expression of multi-source conditions, preserve unstructured geometric topology, explicitly encode local directional transmission, establish global correlations with linear complexity, and reliably constrain boundary conditions. This makes it impossible to meet the needs of efficient and high-precision physical simulation in complex industrial scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide an efficient physical simulation system and method based on manifold embedding, thereby solving the aforementioned technical problems.

[0006] To achieve the above objectives, the present invention provides an efficient physical simulation system based on manifold embedding, including a multi-source condition acquisition unit, a manifold embedding sensing unit, a graph operator inference and recognition unit, and a result display unit; The multi-source condition acquisition unit is used to receive information from the object to be simulated and organize it into node-level local features and sample-level global operating conditions. Manifold embedded sensing units are used to conditionally align and uniformly encode information, perform topological sensing sparse sampling based on physical directionality, construct sparse graph representations and project them onto the latent space; The graph operator inference and recognition unit is used to perform multi-layer graph transformation processing in the latent space, integrate local flux direction message passing and projective global attention, and output a high-order representation of the physical field prediction. The results display unit is used to distinguish between steady-state and transient task execution decoding, perform explicit boundary constraint correction on the results, and output and display the target physical simulation results.

[0007] Preferably, the information received by the multi-source condition acquisition unit includes at least geometric information, boundary conditions, and parameter time series; the multi-source condition acquisition unit is compatible with data import from traditional numerical simulation software, mesh preprocessors, experimental inversion results, or industrial databases, and has functions for checking the legality of missing fields, normalization, and type encoding; and supports autoregressive rolling input in long-time domain scenarios.

[0008] Preferably, the manifold embedded sensing unit includes a conditional alignment submodule, a position encoding submodule, a topology sampling submodule, and a graph embedding submodule; the position encoding submodule uses multi-scale periodic encoding to enhance coordinate representation, and the topology sampling submodule samples differently according to the grid scale.

[0009] Preferably, the graph operator inference and recognition unit includes a flux transfer submodule, a projection attention submodule, a residual normalization submodule, and a hierarchical stacking submodule; the residual normalization submodule is used to prevent instability in deep stacking training, and the hierarchical stacking submodule extracts the physical patterns from local to global layer by layer.

[0010] Preferably, when the flux transfer submodule performs local message propagation on directed edges, it first performs a joint update on the edge representation and the associated source node and target node representation, and then splits each edge into outflow direction and inflow direction orientation information and aggregates the average values ​​on the nodes respectively; the system supports subgraph segmentation and overlapping region result aggregation of ultra-large-scale grids.

[0011] A method for an efficient physical simulation system based on manifold embedding includes the following steps: S1. Collect the geometric coordinates, mesh node attributes, boundary conditions, initial state, physical parameters and time step information of the object to be simulated, and organize them into node-level local features and sample-level global working conditions. S2. Perform conditional alignment and unified encoding on heterogeneous features, topologically aware sparse sampling based on physical flux direction, construct a sparse graph and project it onto the latent space. S3. Perform multi-level graph transformation in the latent space, preserve local transport relationships through directed message passing, and combine projective global attention to model global dependencies to generate higher-order representations. S4. Steady-state tasks directly decode high-order representations, while transient tasks use incremental temporal extrapolation decoding. Explicit boundary constraint corrections are applied to the decoding results, and the simulation results are output and displayed.

[0012] Preferably, in S2, the sparse sampling strategy is as follows: small and medium-sized grids retain directional constraint edge sets, large-scale grids use random edge sampling, and ultra-large-scale grids use consistent point-edge sampling and block processing.

[0013] Preferably, in S3, projective global attention projects a large number of nodes onto a low-dimensional global subspace for refinement and backpropagation using a set of learnable query vectors that are far fewer than the number of nodes, thus restoring long-range dependencies with linear complexity.

[0014] Preferably, in S4, incremental temporal extrapolation decodes the current latent representation into the state increment of the next time step, which is combined with the state of the previous time step to form a continuous time progression result, supporting long-term prediction.

[0015] Preferably, in S4, the explicit boundary constraint correction includes setting the velocity of the solid wall no-slip boundary to zero, and the rule adaptation correction for the periodic boundary, flux boundary, and specified gradient boundary.

[0016] Therefore, the present invention employs the above-mentioned efficient physical simulation system and method based on manifold embedding, which has the following beneficial effects: 1. Enhance the adaptability to complex geometries and unstructured meshes: By using a unified multi-source condition acquisition and manifold embedding perception mechanism, coordinates, field values, node types, physical parameters, and time information are incorporated into the same representation system. Combined with a topology-fidelity directed sampling strategy, the system maintains stable modeling capabilities on curved surfaces, irregular boundaries, and multi-scale meshes, supports transfer reasoning when geometry, boundaries, and operating conditions change, and broadens the applicability of the proxy simulation system.

[0017] 2. Balancing computational efficiency and scalability: The topology-aware sampling mechanism compresses the number of edges while preserving physical directionality and the connection skeleton, reducing graph propagation overhead; projective global attention constructs a low-dimensional global subspace through learnable query vectors, transforming global dependency modeling into linear complexity computation. This scheme achieves an average relative error reduction of approximately 26.70%, while reducing the number of parameters by approximately 55.32% and floating-point computation by approximately 50.60%, achieving a balanced optimization between accuracy, parameter size, and computational power consumption.

[0018] 3. Enhance long-term prediction stability: By combining incremental temporal extrapolation with graph operator hierarchical inference, short-range evolutionary relationships are preserved through local flux transfer, and long-distance coupling information is supplemented through projection-based global attention, effectively reducing the risk of error amplification during the rolling prediction process.

[0019] 4. Possesses unified multi-task modeling capabilities: Through a unified input representation, graph embedding method, and graph operator backbone, it simultaneously supports steady-state forward and transient evolution tasks, taking into account both field distribution prediction and coefficient-type index prediction. There is no need to redesign the backbone network for different tasks, significantly reducing development and maintenance costs.

[0020] 5. Improve physical consistency and engineering feasibility: Introduce an explicit boundary correction mechanism to ensure that key boundary nodes meet the constraint rules without increasing model complexity, avoiding the instability of implicitly learned boundary rules; support subgraph partitioning, batch inference and overlapping region aggregation of ultra-large-scale grids, which is convenient for deployment to industrial software and digital prototype platforms.

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 This is a block diagram illustrating the principle of a high-efficiency physical simulation system based on manifold embedding according to the present invention. Figure 2 This is a block diagram illustrating the principle of the multi-source condition acquisition unit of the present invention. Figure 3 This is a block diagram illustrating the principle of the manifold embedded sensing unit of the present invention; Figure 4 This is a block diagram illustrating the principle of the graph operator deduction and recognition unit of the present invention. Figure 5 This is a block diagram of the result display unit of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0024] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0025] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0026] like Figure 1As shown, this invention provides a high-efficiency physical simulation system based on manifold embedding, comprising a multi-source condition acquisition unit, a manifold embedding sensing unit, a graph operator inference and recognition unit, and a result display unit. The core process involves first aggregating three types of inputs—geometric information, boundary conditions, and parameter time series—to the multi-source condition acquisition unit. These inputs then pass through two core processing stages: the manifold embedding sensing unit and the graph operator inference and recognition unit. Finally, the result display unit outputs two types of simulation results: field distribution and coefficient values. This overall architecture can be used for both forward steady-state simulation and transient rolling prediction. It is suitable for small- to medium-scale unstructured meshes and can be extended to large-scale 3D industrial scenes through subgraph partitioning and result aggregation. Compared to existing single graph networks or single attention schemes, this system achieves a complete technical closed loop of "unified expression of multi-source conditions—topology-fidelity compression—local-global collaborative reasoning—boundary constraint output," which is beneficial for truly transforming high-precision physical proxy models into a general-purpose simulation system that can be deployed in engineering.

[0027] like Figure 2 As shown, the multi-source condition acquisition unit receives the geometric coordinates, mesh node attributes, boundary conditions, initial state, physical parameters, and time step information of the object to be simulated, and organizes them into node-level local features and sample-level global operating conditions. This unit includes a coordinate input submodule, a field value input submodule, a parameter timing submodule, and a data processing submodule: the coordinate input submodule acquires the node position, mesh structure index, and relative position description information of the object to be simulated in physical space; the field value input submodule acquires one or more physical field values ​​such as velocity, pressure, temperature, density, and electron concentration at the current or initial time, as well as discrete identifiers such as boundary node type, solid wall / inlet / outlet; the parameter timing submodule acquires global operating condition information such as Reynolds number, material parameters, source term strength, control variables, and discrete time steps; the data processing submodule organizes the aforementioned local and global inputs hierarchically, retaining local information at the node level and broadcasting global information as condition vectors to the entire sample or the entire time step.

[0028] By adopting the above-described data acquisition method, the problems of fragmented information sources and inconsistent input formats in existing technologies are avoided, enabling the same system to simultaneously handle steady-state, transient, and multi-physical quantity output problems. This unit is compatible with importing data from traditional numerical simulation software, grid preprocessors, experimental inversion results, or industrial databases. It features missing field validity checks, normalization, and type encoding. In long-time domain scenarios, it supports receiving the previous step's prediction results and combining them with the control quantity at the next moment to form a new input, achieving autoregressive rolling calls. Therefore, the multi-source conditional acquisition unit effectively acts as a bridge from the original simulation description to the unified learning input, providing a standardized and highly compatible basic data interface for subsequent manifold embedding and efficient inference.

[0029] like Figure 3As shown, the manifold embedding sensing unit is used for conditional alignment and unified encoding of heterogeneous information. It performs topological sensing sparse sampling based on physical directionality, constructs a sparse graph, and projects it onto the latent space. This unit includes a conditional alignment submodule, a position encoding submodule, a topological sampling submodule, and a graph embedding submodule. The conditional alignment submodule addresses the heterogeneous features of node-level local information and sample-level global conditions. It encodes local variables such as coordinates, relative positions, node attributes, and historical physics fields, along with global conditions such as physical parameters and time steps, through independent mapping paths before fusing them, enabling each node to perceive overall condition changes. The position encoding submodule uses a multi-scale periodic encoding method to enhance coordinate representation, ensuring stable spatial perception capabilities even on complex surfaces, sparse non-uniform grids, and at different resolutions. The topological sampling submodule constructs directed edges based on local flux directions and samples differently according to grid size. The graph embedding submodule constructs edge features based on the sampled connection relationships, extracts displacement vectors, reverse displacements, and distance magnitudes between nodes, and projects the node representations and edge representations together onto a unified latent space.

[0030] Specifically, the discrete physical domain adopts a mesh diagram. Expression, among which, for A set of grid nodes, The set of edges connecting the original mesh; for any adjacent nodes i and j, based on the dominant physical vector at node i. With edge vectors The inner product determines the local transport direction, and the local projected flux is defined as... ,when When the directed edge from node i to node j is retained; when Retain the reverse side; for fluid, heat transfer, electromagnetic, or solid mechanics tasks, The local velocity, heat flux density, field gradient, or principal stress direction can be chosen respectively, so that the sparse connection is consistent with the main propagation direction of the physical quantity to be predicted. The relevant formula is: ; In the formula, It is the transpose symbol. This is the set of directed edges retained after filtering. The specific method for conditional alignment and latent spatial projection is as follows: The local features of the nodes are denoted as... ,in, Represents coordinates, Indicates relative position or boundary type encoding, The dominant physical vector represents one or more physical field values; the sample-level global operating conditions are denoted as... ,in, Represents a vector of physical parameters. Indicates a time step.

[0031] Local node features and global operating conditions are processed by independent multilayer perceptrons. and After mapping to the C-dimensional latent space, the elements are added together to align conditions from different sources and dimensions at the node level. The representation of node i in the C-dimensional latent space... for: ; The position encoding submodule performs multi-scale sinusoidal encoding on the normalized coordinate matrix X. Its formula is: ; Where r is the index of the real physical field. A positive integer, used to control the scale range from the lowest to the highest frequency, for the sampled directed edges. Take displacement Reverse displacement and distance modulus Edge mapping network Obtain the C-dimensional edge representation .

[0032] The core value of manifold-embedded sensing units lies in transforming the original complex physical domain into a sparse graph representation that "knows the operating conditions, understands the topology, and can control the scale," providing a stable and efficient input foundation for subsequent graph transformation operators. Especially in industrial scenarios with frequent geometric changes, inconsistent boundary conditions, and large data scales, this unit can significantly improve the geometric adaptability and training and inference efficiency of the system.

[0033] like Figure 4As shown, the graph operator inference and recognition unit is used to perform multi-layer graph transformation processing in the latent space, integrate local flux direction message passing and projective global attention, and output a high-order representation of the physical field prediction. This unit includes a flux transfer submodule, a projection attention submodule, a residual normalization submodule, and a hierarchical stacking submodule. The flux transfer submodule, when performing local message propagation on directed edges, first jointly updates the edge representation with the associated source and target node representations. Then, it splits each edge into outflow and inflow direction orientation information and aggregates the averages on the nodes, preserving the local transport direction and distinguishing between the outflow and inflow effects of nodes. The projection attention submodule introduces a set of learnable query vectors far fewer than the number of nodes. In the latent space, it first projects a large set of nodes onto a low-dimensional global subspace, then performs relation refinement in this subspace, and finally propagates the refined global information back to the original node space, efficiently restoring long-distance associations and cross-regional couplings. The residual normalization submodule is used for normalization and residual connection after each layer of processing to prevent training instability and information degradation during deep stacking. The hierarchical stacking submodule allows several graph operator layers to be connected sequentially, enabling the model to extract physical correlation patterns layer by layer from local to global and from low-order to high-order.

[0034] Specifically, in the l-th layer graph operator, the flux transfer submodule first utilizes the edge mapping network. The residual update is performed on the current edge representation, and the formula is as follows: ; in, This represents the edge representation after message passing. and Let C represent the sending node and the receiving node respectively. For edge mapping networks, the updated edge representation Divided into two Subvectors and These characters represent the positive and negative local physical effects, respectively, thus preserving bidirectional interaction information without recovering the paired bidirectional edges. For any node k, consider its outflow neighborhood. and the inflow neighborhood Perform mean aggregation to obtain flux messages. Subsequently, the node mapping network... The current node representation is merged with the throughput message, and the node is updated using a residual method, with the following formula: ; In the formula, and These represent the number of outflowing neighbors and the number of inflowing neighbors, respectively, where m is the index in the corresponding neighborhood. This indicates that node k is in the current graph operator layer (layer l); in the projection attention submodule, let For a local representation of N nodes, Let be the set of real numbers, and let The learnable space is a consistent query matrix, and M is much smaller than N; utilizing Compress N nodes into M global potential labels. Subsequently, inter-label relations are formed in the M-dimensional global subspace. Finally, the global information is transmitted back to N nodes to obtain... Specifically: ; ; ; In the above formula, the softmax values ​​are all normalized according to the last dimension. A Gaussian distribution with zero mean and unit variance is used for initialization and optimized together with the system parameters. Global backhaul results are updated using a pre-normalized residual structure, the formula of which is: ; in, This represents the intermediate node after merging. Let LN represent the final node output of the graph operator layer, where LN represents layer normalization and FFN represents the feedforward network. Stacking the above processes into L layers allows for the sequential extraction of local topological patterns and global cross-regional associations. The computational complexity of flux transfer is O(n log n). The computational complexity of projection attention is ,in, To maximize graph degree, Where M is the sampling ratio, C is the number of potential labels, and M is the dimension of potential features. When M is much smaller than N, the overall complexity increases approximately linearly with the number of nodes N. By using graph operator inference and identification units, this invention can maintain the linear complexity trend while taking into account local physical transport and global structural dependencies, making it suitable for field regression and long-term evolution tasks on unstructured grids.

[0035] like Figure 5As shown, the results display unit is used to distinguish between steady-state and transient tasks for decoding, perform explicit boundary constraint corrections on the results, and output and display the target physical simulation results. This unit includes a steady-state decoding submodule, a time-series extrapolation submodule, a boundary correction submodule, and a results display submodule. The steady-state decoding submodule, for steady-state tasks such as drag coefficient estimation and surface pressure reconstruction, feeds the latent node representation processed by the graph operator and the global operating condition encoding into the decoding network to directly obtain the target physical quantity. The time-series extrapolation submodule, for transient tasks such as velocity fields and temperature fields, uses an incremental prediction method to decode the current latent representation into the state increment for the next time step, and then combines it with the state of the previous time step to form a continuously rolling time-progressing result. The boundary correction submodule performs explicit physical constraints on the decoding results. The results display submodule is responsible for converting the prediction results into visual cloud maps, coefficient curves, node value lists, or interface-returned data, serving design optimization, scheme selection, digital prototypes, and online monitoring. Therefore, the results display unit can more naturally adapt to the needs of different industrial tasks, improving the feasibility and reliability of the entire system.

[0036] Furthermore, the decoding result of the steady-state task can be expressed as: , in, For decoding networks Encoding of global operating conditions. Let be the target steady-state physical quantity at node i. The transient task adopts a first-order incremental propagation approach, using the decoder network output as the state increment between adjacent time steps to reduce the cumulative offset when directly predicting the absolute field value. The formula is as follows: ; In the formula, and These represent the physical field states of node i at time t and time t-1, respectively. The boundary correction submodule applies hard constraints using boundary masks, and its correction results... The formula is: ; In the formula, let Represents a node Does it belong to the boundary of a given value? =1 indicates that the node belongs to the boundary of the given value. =0 indicates that the node does not belong to the given value boundary. This indicates the boundary value specified for this node. This represents the initial output of the decoding network.

[0037] For solid, no-slip boundaries, the velocity is specified as zero; for periodic boundaries, paired nodes are mapped to the same periodic equivalence class and then uniformization is performed; for flux boundaries or specified gradient boundaries, the outputs of adjacent internal nodes are projected and corrected based on the boundary normal vector and the given flux.

[0038] Based on the above system, a specific implementation scenario of an efficient physical simulation method based on manifold embedding is illustrated by taking transient prediction of flow around a cylinder on an unstructured mesh as an example. The simulation region is discretized by an irregular triangular mesh. The inlet is given a velocity condition that varies with the operating conditions. The cylinder surface and solid wall are set with no-slip boundaries, and the outlet is set with pressure boundaries. The node states include two-dimensional coordinates, mesh connection, boundary type, current velocity component and pressure. The sample-level conditions include Reynolds number, inlet control quantity and discrete time step.

[0039] The system is trained using short sequences of five consecutive time steps and then predicts the next five, 50, or 250 time steps during the inference phase to simultaneously test short-term accuracy and long-term stability. This scenario is only used to explain the execution process of each step and does not constitute a limitation on the applicable physical type and geometry. Specifically, it includes the following steps: S1. Through the coordinate input submodule, field value input submodule, and parameter timing submodule of the multi-source condition acquisition unit, the geometric coordinates, mesh node attributes, boundary conditions, initial state, physical parameters, and time step information of the object to be simulated are collected respectively. The data processing submodule then organizes these information into node-level local features and sample-level global operating conditions. In the cylinder flow scenario, the node-level local features include at least... velocity components , Including inlet / solid wall / outlet markings, the sample-level global operating conditions should at least include the Reynolds number Re, inlet velocity, and time step. .

[0040] S2. Heterogeneous features are conditionally aligned and uniformly encoded by the conditional alignment submodule of the manifold embedding sensing unit. The coordinate representation is then enhanced by multi-scale periodic encoding via the position encoding submodule. Next, the topology sampling submodule performs topology-aware sparse sampling based on the physical flux direction. Finally, a sparse graph is constructed by the graph embedding submodule and projected onto the latent space. In the above-mentioned cylinder flow scenario, directed edges are determined by the inner product of the local velocity vector and the mesh edge vector. The original mesh connections corresponding to the solid wall and inlet / outlet boundary nodes are preferentially preserved to avoid sparsification disrupting the boundary geometry. Furthermore, the sparse sampling strategy is adaptively selected according to the mesh size. When the number of nodes When, replace each pair of bidirectional edges with the one that satisfies A single flux-oriented edge is used to reduce the number of edges to about half of the original bidirectional edge set while maintaining physical directionality; when At that time, in the directional edge set According to the retention ratio Perform uniform random edge sampling, where each edge corresponds to a random variable. Follow the interval The uniform distribution on the surface satisfies The edges are preserved; when First, edges that maintain the topological skeleton and their covered nodes are sampled. Then, nodes are sampled in uncovered areas to form a training subgraph with consistent points and edges, thus taking into account both connectivity and spatial coverage. Furthermore, during large-scale full-size inference, the original mesh is divided into K spatially uniform subgraphs with overlapping regions. Independent inference is performed on each subgraph in batches, and the multiple predictions of overlapping nodes are averaged to reconstruct the complete physical field. Information gaps across subgraphs caused by sparse sampling or block partitioning are compensated by the projection attention submodule establishing global interactions within the shared potential subspace and transmitting them back to the node space, rather than relying on local message passing to recover them automatically.

[0041] S3. The graph operator inference and identification unit performs multi-layer graph transformations in the latent space. The flux transfer submodule preserves local transport relationships through directional message passing. The projection attention submodule, combined with projection-based global attention, models global dependencies. The residual normalization submodule performs normalization and residual connection. The hierarchical stacking submodule extracts physical patterns layer by layer, ultimately generating a high-order representation of the predicted physical field. In the cylinder flow scenario, the query number M and the latent dimension C can be set to be the same and significantly smaller than the number of nodes N, allowing long-distance coupling in the wake region to be propagated back to each grid node through the global subspace. Furthermore, the query number M used in the projection-based global attention is no greater than the latent feature dimension C, and is preferably set to... To achieve a balance between query matrix rank, representational power, and computational overhead.

[0042] S4. The result display unit distinguishes task types and performs decoding: steady-state tasks are directly decoded by the steady-state decoding submodule, while transient tasks are decoded by the temporal extrapolation submodule using incremental temporal extrapolation; then, the boundary correction submodule performs explicit boundary constraint correction on the decoding results, and finally, the result display submodule outputs and displays the simulation results; in the cylinder flow scenario, the predicted velocity of the solid wall nodes is forcibly corrected to zero, and the velocity field, pressure field, velocity modulus cloud map, and drag coefficient curve obtained based on the surface pressure integral are output for each time step; further, the incremental temporal extrapolation decodes the current latent representation into the state increment of the next time step, which is combined with the state of the previous time step to form a continuous time progression result; explicit boundary constraint correction includes rule adaptation correction for solid wall no-slip boundaries, periodic boundaries, flux boundaries, and specified gradient boundaries.

[0043] To verify the prediction accuracy, computational efficiency, and cross-scale adaptability of this invention, 11 physical simulation tasks across three categories were set up in an experimental embodiment. The first category consists of unstructured mesh tasks, including five tasks: irregular Darcy flow, turbulence in pipes, heat transfer, composite workpiece deformation, and hemodynamics. The second category consists of complex transient flow tasks, including four tasks: flow around a cylinder, complex two-dimensional flow, industrial heat flow, and inductively coupled plasma. The third category consists of large-scale three-dimensional geometry tasks, including two tasks: parameterized vehicle body and real vehicle shape prediction for surface pressure and aerodynamic coefficients. Each task covers different scales from two-dimensional to three-dimensional, steady-state to transient, single-physics to multi-physics, and approximately 3,000 to over 300,000 mesh nodes or 100,000 to 500,000 mesh faces.

[0044] The experiment compared the present invention with existing models of deep operators, Fourier operators, graph neural networks, and graph Transformers using the same data partitioning and training budget. Representative comparison models included DeepONet, FNO, Geo-FNO, GraphSAGE, NORM, MeshGraphNet, GraphViT, GNOT, Translator, and GINO. The test sample counts for the unstructured mesh task were 200, 100, 100, 100, and 100, respectively; the test sample counts for the four transient tasks were 100, 118, 97, and 98, respectively, using a short-sequence training long-time rolling protocol with 5 training steps and subsequent 5, 50, and 250 testing steps; the test sample counts for the two large-scale 3D tasks were 51 and 595, respectively. The parameterized vehicle body data contained 551 samples, and the real vehicle shape data contained over 4000 3D samples, with Reynolds number coverage... to .

[0045] The evaluation metric is the L2 relative error across datasets, time steps, and physical field averages. At the same time, the number of trainable parameters is counted. The formula for the number of floating-point operations (FLOPs) in a single forward inference is: ; In the formula, D is the range of the dataset or test sample index, and T is the number of prediction time steps. and Let r be the actual physics field and the predicted physics field of the k-th sample at time step t, respectively. This represents the Euclidean norm.

[0046] Comparative results show that, compared to the best-performing existing control model across all tasks, this invention reduces the average L2 relative error by 26.70%, the average number of trainable parameters by 55.32%, and the average number of FLOPs by 50.60% on the aforementioned 11 tasks. In the tasks of parameterized vehicle body and real vehicle shape, the coefficient of determination between the predicted drag coefficient and the true value... The accuracy values ​​reached 0.9250 and 0.9595 respectively. In long-term rolling tests, the present invention remained stable within the prediction range of 50 and 250 steps, while some existing models showed error divergence at 250 steps. The comparison between the predicted field cloud map and the ground truth cloud map also showed that the present invention has lower point-level absolute error on curved surfaces, composite boundaries, and areas with large local gradients.

[0047] Further module ablation experiments were conducted: After removing the projected attention submodule, the L2 relative errors of the cylindrical flow and inductively coupled plasma missions were respectively reduced by , Increase to , This corresponds to increases of approximately 58% and 111%; after removing the throughput submodule, the errors for the two tasks increased to [missing information]. and This corresponds to an increase of approximately 451% and 206%. Compared to pairwise bidirectional message passing, flux-oriented lightweight passing reduces FLOPs by 32.7% and 33.1% in both tasks, respectively, demonstrating that the synergy between local flux passing and global projection attention can achieve a stable balance between accuracy and efficiency.

[0048] In summary, the system of this invention comprises four core units. Through techniques such as multi-condition unified embedding, flux-oriented topology sampling, linear complexity local-global cooperative graph operators, incremental temporal extrapolation, and explicit boundary constraints, it reduces the average L2 relative error by 26.70%, while decreasing the number of trainable parameters by 55.32% and the computational load by 50.60%. It is adaptable to complex unstructured meshes and large-scale 3D geometry, supports steady-state and transient multi-tasking, and can be applied to rapid simulation and design optimization in fields such as aerospace, automotive, energy, biofluidics, and industrial equipment.

[0049] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A high-efficiency physical simulation system based on manifold embedding, characterized in that: It includes a multi-source condition acquisition unit, a manifold embedding sensing unit, a graph operator inference and recognition unit, and a result display unit; The multi-source condition acquisition unit is used to receive information from the object to be simulated and organize it into node-level local features and sample-level global operating conditions. Manifold embedded sensing units are used to conditionally align and uniformly encode information, perform topological sensing sparse sampling based on physical directionality, construct sparse graph representations and project them onto the latent space; The graph operator inference and recognition unit is used to perform multi-layer graph transformation processing in the latent space, integrate local flux direction message passing and projective global attention, and output a high-order representation of the physical field prediction. The results display unit is used to distinguish between steady-state and transient task execution decoding, perform explicit boundary constraint correction on the results, and output and display the target physical simulation results.

2. The efficient physical simulation system based on manifold embedding according to claim 1, characterized in that: The information received by the multi-source condition acquisition unit includes at least geometric information, boundary conditions, and parameter time series. The multi-source condition acquisition unit is compatible with data import from traditional numerical simulation software, mesh preprocessors, experimental inversion results, or industrial databases. It has functions for checking the legality of missing fields, normalization, and type encoding. It supports autoregressive rolling input in long-time domain scenarios.

3. The efficient physical simulation system based on manifold embedding according to claim 1, characterized in that: The manifold embedding sensing unit includes a conditional alignment submodule, a position encoding submodule, a topology sampling submodule, and a graph embedding submodule; The location encoding submodule uses multi-scale periodic encoding to enhance coordinate representation, and the topology sampling submodule performs differential sampling according to the grid scale. Differential sampling refers to sampling when the number of nodes is less than 10. 5 Preserve the directional constraint edge set when the number of nodes is 10. 5 Up to 10 6 Random edge sampling is performed between nodes when the number of nodes is greater than 10. 6 Point-edge consistency sampling and block processing are performed in real time.

4. The efficient physical simulation system based on manifold embedding according to claim 1, characterized in that: The graph operator inference and recognition unit includes a flux transfer submodule, a projection attention submodule, a residual normalization submodule, and a hierarchical stacking submodule. The residual normalization submodule is used to prevent instability during deep stacking training, and the hierarchical stacking submodule extracts the physical patterns from local to global layers.

5. The efficient physical simulation system based on manifold embedding according to claim 4, characterized in that: When the flux transfer submodule performs local message propagation on directed edges, it first performs a joint update on the edge representation and the associated source and target node representations, and then splits each edge into outflow and inflow direction orientation information and aggregates the average values ​​on the nodes respectively; the system supports subgraph partitioning and overlapping region result aggregation for ultra-large-scale grids.

6. A method for a high-efficiency physical simulation system based on manifold embedding according to any one of claims 1-5, characterized in that, Includes the following steps: S1. Collect the geometric coordinates, mesh node attributes, boundary conditions, initial state, physical parameters and time step information of the object to be simulated, and organize them into node-level local features and sample-level global working conditions. S2. Perform conditional alignment and unified encoding on heterogeneous features, topologically aware sparse sampling based on physical flux direction, construct a sparse graph and project it onto the latent space. S3. Perform multi-level graph transformation in the latent space, preserve local transport relationships through directed message passing, and combine projective global attention to model global dependencies to generate higher-order representations. S4. Steady-state tasks directly decode high-order representations, while transient tasks use incremental temporal extrapolation decoding. Explicit boundary constraint corrections are applied to the decoding results, and the simulation results are output and displayed.

7. The method for a high-efficiency physical simulation system based on manifold embedding according to claim 6, characterized in that, In S2, the sparse sampling strategy is as follows: small and medium-sized grids retain directional constraint edge sets, large-scale grids use random edge sampling, and ultra-large-scale grids use consistent point-edge sampling and block processing.

8. The method for a high-efficiency physical simulation system based on manifold embedding according to claim 6, characterized in that: In S3, projective global attention uses a set of learnable query vectors that are far fewer than the number of nodes to project a large number of nodes onto a low-dimensional global subspace for refinement and backpropagation, restoring long-range dependencies with linear complexity.

9. The method for a high-efficiency physical simulation system based on manifold embedding according to claim 6, characterized in that: In S4, incremental temporal extrapolation decodes the current latent representation into the state increment of the next time step, which is combined with the state of the previous time step to form a continuous time progression result, supporting long-term prediction.

10. The method for a high-efficiency physical simulation system based on manifold embedding according to claim 6, characterized in that: In S4, explicit boundary constraint corrections include zeroing the velocity of solid wall no-slip boundaries, and rule adaptation corrections for periodic boundaries, flux boundaries, and specified gradient boundaries.

Images