Adaptive protection structure based multi-region collaborative computing method for physical scene

Abstract

This invention relates to the field of computer-aided solution technology for physical fields or mathematical equations, and discloses a multi-region collaborative computation method for physical scenes based on adaptive structure preservation. The method includes: firstly, dividing the global solution domain into multiple interconnected and partially overlapping subdomains through domain decomposition, and equipping each subdomain with an independent physical information neural network model; then, iteratively executing the following steps: extracting multi-dimensional features based on composite feature indices within each subdomain; constructing a probability function based on the feature indices, and implementing adaptive sampling to dynamically update the training set; at the end of each training round, dynamically optimizing the weights of the loss function according to the changing trends of different loss terms, and adding a physical structure preservation constraint term to the total loss function; and iteratively executing until the convergence condition is met, outputting the numerical solution of the physical field. This invention achieves accurate capture of local high-gradient regions in the physical field, improving computational accuracy and efficiency while ensuring the stability and physical conservation of the model.

Description

Technical Field

[0001] This invention relates to the field of computer-aided solution technology for physical fields or mathematical equations, and more specifically to a multi-region collaborative calculation method for physical scenes based on adaptive structure preservation. Background Technology

[0002] Currently, the simulation analysis of physical fields mainly relies on various traditional simulation software, such as commercial simulation platforms developed based on numerical methods like finite element, finite volume, or finite difference. While these traditional simulation software programs are highly mature in engineering design and scientific research applications, they still have significant shortcomings in complex scenarios.

[0003] When dealing with complex geometries or multi-scale coupled problems, traditional simulation software requires extensive manual intervention for model mesh generation, and the computational scale increases dramatically with the problem's dimensionality. To obtain sufficient accuracy, extremely fine meshes and high-order discretization schemes are often used, which leads to low efficiency in solving physics fields, with a single simulation taking hours or even days, and requiring high-performance computing resources, resulting in extremely high computational costs.

[0004] The simulation speed of traditional simulation software has a bottleneck, which directly restricts the product development and optimization cycle. For example, in fluid dynamics design, the configuration of airfoils, impellers and other structures often need to undergo hundreds of aerodynamic shape adjustments and performance verifications. If each calculation cycle is too long, it will seriously affect the design efficiency and the speed of scheme iteration, and delay the overall development process.

[0005] Meanwhile, traditional solution processes are highly sensitive to changes in geometry and boundary conditions; even slight modifications require remodeling and remeshing, further increasing the computational burden. Furthermore, in multiphysics coupling problems (such as fluid-structure interaction or thermal-fluid interaction), traditional simulation software often requires multi-module joint computation, resulting in unstable convergence processes, complex data interaction, long simulation cycles, and inconsistent results, making it difficult to meet the demands of modern engineering for efficiency, flexibility, and real-time performance.

[0006] To overcome the limitations of traditional simulation software in terms of computational efficiency and scalability, intelligent solution methods based on Physics-Informed Neural Networks (PINNs) have emerged in recent years, hereinafter referred to as PINN methods. These methods directly embed the physical constraints of partial differential equations into a deep learning framework, achieving meshless solutions through a data-driven approach that integrates physical laws, thereby reducing modeling complexity and grid dependence to some extent. Simultaneously, PINN methods can leverage the efficient parallel computing characteristics of neural networks to significantly shorten solution time while achieving similar accuracy, enabling rapid solutions to complex physical fields and providing a new approach to efficient solutions for physical fields. However, existing PINN methods still have significant shortcomings in engineering applications.

[0007] On the one hand, its training strategy of uniform sampling across the entire domain makes it difficult to effectively identify and capture local high-gradient regions in the physical field, such as shock waves, interfaces, or boundary layers, resulting in large local solution errors and insufficient overall accuracy.

[0008] On the other hand, its network structure is usually fixed and lacks the ability to adaptively adjust to the differences in physical complexity and physical characteristics of different regions. When dealing with multi-scale, complex boundaries or nonlinear equations, it is prone to problems such as oscillation or non-convergence, and its stability is poor.

[0009] In addition, during training, there are phenomena such as unbalanced loss term ratios, vanishing gradients, and difficulty in explicitly maintaining the original conservation properties of the physical system, which further affect the accuracy and reliability of the model. Summary of the Invention

[0010] In view of this, this invention provides a multi-region collaborative computation method for physical scenes based on adaptive structure preservation, aiming to solve the technical problems in existing physical field solution methods based on Physical Information Neural Networks (PINNs). These problems include insufficient local region computational accuracy, limited model generalization ability, poor training process stability, and difficulty in maintaining physical conservation properties due to the use of fixed sampling strategies and unified network structures. This invention aims to achieve high-precision, high-efficiency, and stable and reliable numerical simulation of complex physical fields.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] In a first aspect, the present invention provides a method for multi-region collaborative computation of physical scenes based on adaptive structure preservation, comprising the following steps:

[0013] S1. Domain Decomposition and Subdomain Construction: The global solution domain is divided into multiple interconnected and partially overlapping subdomains through the domain decomposition method. Coverage regions are set between adjacent subdomains, and each subdomain is equipped with an independent physical information neural network PINN model.

[0014] S2. Feature extraction within subdomains: Within each subdomain, a feature extraction algorithm based on composite feature indices is used to extract multi-dimensional features from the data after one round of computation by the neural network.

[0015] S3. Adaptive Sampling and Training Set Update: Construct a probability function based on the feature indicators extracted in S2, and select samples and update the training set in a targeted manner according to the importance and structural deviation of data in different regions.

[0016] S4. Adaptive Weight Adjustment and Model Convergence: At the end of each round of model training, the weights of the loss function are dynamically optimized according to the changing trends of different loss terms. At the same time, physical structure preservation constraints are explicitly added to the total loss function. Steps S2-S4 are executed iteratively until the convergence condition is met, and the numerical solution of the physical field is output.

[0017] In a specific implementation scheme, the domain decomposition in S1 is based on the geometric characteristics of the physical problem to be solved, the expected distribution of physical fields, or simple spatial partitioning rules; the covered area is used to exchange boundary information during training to ensure the continuity of the final solution at the subdomain boundary and the global conservation of physical quantities.

[0018] In a specific implementation scheme, the independent physical information neural network PINN model for each subdomain in S1 is used to train the local data training set of the subdomain to achieve personalized learning of features within the subdomain, and to transmit the training results to adjacent subdomains to achieve dynamic coordination of information between regions.

[0019] In a specific feasible implementation, the calculation formula for the composite feature index in S2 is as follows:

[0020] ;

[0021] Where α, β, and γ represent hyperparameters, all with a default value of 1. Represents the gradient operator. Represents the Laplace operator, This represents the prediction result of the neural network.

[0022] In a specific implementation scheme, the multi-dimensional features in S2 include residual distribution features and gradient rate of change, wherein the residual distribution features are the predicted solutions of the current physical information neural network PINN model. The degree to which the control partial differential equation is satisfied at sampling points within the subdomain, wherein the gradient change rate is the gradient magnitude or the rate of change of the physical field variable under the current solution.

[0023] In a specific feasible implementation, the formula for calculating the probability function in S3 is:

[0024] ;

[0025] Where x is the physical field coordinate. , For spatial coordinates, ω is the time coordinate, ω is the composite feature index described in S2, and k is the structure preservation weight coefficient, with a default value of 1.

[0026] In a specific implementation scheme, the adaptive sampling strategy in S3 is as follows: add new sampling points with a higher probability in regions with high eigenvalues, and maintain or reduce sampling points in regions with low eigenvalues. The regions with high eigenvalues ​​are regions where the physical field changes drastically or where the current solution error is large.

[0027] In a specific feasible implementation, the formula for calculating the total loss function in S4 is:

[0028] ;

[0029] in, Represents the number of neural networks. For residual loss, For boundary loss, For initial value loss, θ Represents the internal parameters of the neural network. , , This is a hyperparameter with a default value of 0, which is updated during training.

[0030] In one specific implementation, the physical structure preservation constraints described in S4 include weak-form constraints of global mass conservation and momentum conservation.

[0031] In a specific implementation scheme, the convergence condition described in S4 is that the verification error and structural constraint residual of all subdomains are lower than a preset threshold.

[0032] Compared with existing technologies, the adaptive structure-preserving multi-region collaborative computation method for physical scenes described in this invention is used for efficient and high-precision numerical simulation and solution of complex physical fields. This method decomposes the overall solution domain into multiple "physical feature-driven" subdomains and combines them with independent neural networks for parallel processing. Within each subdomain, adaptive sampling based on physical features and dynamic updates of the training set are implemented. An adaptive weight adjustment mechanism is used in the global training to maintain the consistency of the physical structure. This achieves accurate capture of local high-gradient regions, stable generalization of multi-physics problems, and preservation of overall physical conservation laws, effectively improving the computational accuracy, efficiency, and stability of numerical solutions for complex physical scenes. It has the following beneficial effects:

[0033] 1. Significantly Improved Computational Accuracy: This invention utilizes intelligent feature extraction technology combined with adaptive methods to automatically increase the density of sampling points in regions of drastic physical change, such as high gradients, interfaces, or boundary layers. This enables the model to automatically identify key features in the physical field across different decomposition regions, deeply mining the core features of physical information while preserving the structural information of the physical system, thereby fundamentally improving computational accuracy and physical consistency. Compared to similar intelligent algorithms, the relative L2 error of this invention can be reduced by at least one order of magnitude in calculations across different physical fields (Table 1), achieving a more accurate reconstruction of physical phenomena and meeting the high-precision computational requirements under domain decomposition conditions.

[0034]

[0035] Where N represents the size of the training set data, ( ) represents the physical field coordinates, where denoted by , where u represents the model's predicted solution and u represents the exact solution.

[0036] 2. Breakthrough Enhancement of Model Extensibility: The physics field solution model constructed in this invention introduces an adaptive feature extraction and structure preservation constraint strategy, which can maintain the physical structure stability and conservation properties of the equations under different physics fields and complex boundary conditions (Table 1). The model can automatically adjust the sampling density and network structure according to the physical complexity of different regions, thereby achieving robust transfer and generalization in multiphysics scenarios, greatly expanding the application scope and scalability of the model.

[0037] 3. Effectively Improves Model Stability: In the joint training process of adaptive sampling and domain decomposition networks, this invention combines adaptive weight adjustment and structural constraint consistency optimization mechanisms. This allows for the dynamic and automatic balancing of the weight distribution of each loss term during training, maintaining the model's focus on gradient continuity during optimization and preventing the training process from getting trapped in local optima or experiencing numerical oscillations. This mechanism significantly improves the model's convergence stability and global consistency, ensuring continuous, reliable, and efficient operation in solving complex physical fields.

[0038] 4. Improved computational efficiency and resource utilization, and shortened overall solution time: This invention supports parallel computing of multiple subdomains through modular decomposition and independent processing of solution subdomains; each subdomain can carry out numerical calculations and model training simultaneously without waiting for the overall domain to advance, which greatly shortens the solution cycle of complex engineering physics problems; at the same time, task decomposition reduces the computational resource consumption of a single module, enabling the method to achieve efficient solutions on conventional computing devices, which significantly improves the efficiency of engineering implementation of the technology.

[0039] 5. Enhanced versatility and adaptability to different engineering scenarios: Relying on a dynamic sampling and weight adjustment mechanism driven by physical features, this invention can achieve cross-scenario adaptation; for physical problems in different engineering fields such as water conservancy, aerospace, and energy, there is no need to reconstruct the model framework. By simply dynamically adjusting the sampling strategy and loss function weights, it can accurately match the physical features and solution requirements in different scenarios; at the same time, this mechanism can automatically adapt to complex situations such as differences in data distribution and changes in boundary conditions, which greatly reduces the secondary development cost of the model in different engineering scenarios and improves the versatility and applicability of the technology.

[0040] 6. Achieves high-precision and stable output results while ensuring the controllability of the solution process: This invention ensures the overall solution coherence through collaborative interaction of solution subdomains, improves the quality of training data by combining dynamic data optimization, and avoids local optima through adaptive weight adjustment, thus constructing a precision guarantee mechanism for the entire "data-training-solution" process; it can accurately capture the core laws and key features of engineering physics problems, and the output numerical calculation results have a high degree of consistency with actual engineering scenarios; at the same time, by monitoring the training status in real time and dynamically adjusting parameters, the solution error can be effectively controlled within the preset range, ensuring the stability and reliability of the model output results.

[0041] Table 1. Comparison of the errors of this invention in solving different physical fields with those of other intelligent algorithms.

[0042]

[0043] Table 1 shows the solutions for the same physical field model using different methods under the same experimental conditions. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present 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 only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0045] Figure 1This is an overall flowchart of the adaptive structure-preserving physical scene multi-region collaborative computing method described in this invention.

[0046] Figure 2 This is a schematic diagram of modular domain decomposition and collaborative interaction structure.

[0047] Figure 3 This is a schematic diagram of a feature-driven dynamic data optimization process.

[0048] Figure 4 This is a schematic diagram illustrating the adaptive weight adjustment principle during the training process.

[0049] Figure 5 This is a schematic diagram of the region division in the domain decomposition and subdomain construction described in this invention.

[0050] Figure 6 The diagrams are schematic diagrams of the model prediction results for application examples. (a) is a schematic diagram of the exact solution of the physical field, (b) is a schematic diagram of the solution of the physical field predicted by the model of the present invention, and (c) is a schematic diagram of the absolute error between the predicted solution and the exact solution of the model of the present invention.

[0051] Figure 7 The diagram shows a comparison of the distribution of adaptive sampling points and different sampling point strategies in the application example. (a) represents uniform sampling, (b) represents residual resampling, and (c) represents the probability density resampling of the present invention. Detailed Implementation

[0052] The technical solutions in the embodiments of the present invention will be clearly and completely described below. 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 are within the scope of protection of the present invention.

[0053] One of the objectives of this invention is to overcome the inherent shortcomings of traditional numerical simulation software based on mesh methods such as finite element and finite volume. These methods suffer from massive computational scales, lengthy simulation times, and heavy reliance on high-performance computing resources and manual mesh generation when dealing with complex geometries, multi-scale coupling, and high-dimensional physical problems. This limits product development and optimization cycles, making it difficult to meet the demands of modern engineering for efficiency and flexibility.

[0054] Another objective of this invention is to overcome the application bottlenecks of existing intelligent solution methods based on Physical Information Neural Networks (PINNs). While these methods can achieve meshless solutions and accelerate computation through parallel processing, their global uniform sampling strategy struggles to accurately capture local high-gradient regions in the physical field, resulting in insufficient accuracy in critical regions. Furthermore, their fixed network structure lacks adaptability to differences in regional characteristics, affecting the model's stability and generalization when handling multi-scale, nonlinear problems. Simultaneously, issues such as imbalanced loss terms and difficulty in explicitly preserving physical conservation properties during training also limit the physical credibility and reliability of their solution results.

[0055] The adaptive, structure-preserving, multi-region collaborative computation method for physical scenes described in this invention intelligently decomposes the complex global physical solution domain into multiple physical feature-driven subdomains, and performs parallel solutions based on Physical Information Neural Networks (PINNs) within each subdomain. Simultaneously, this method introduces an adaptive sampling strategy driven by local physical features and a dynamic weight adjustment mechanism aimed at maintaining the consistency of the global physical structure, thereby synergistically achieving a comprehensive improvement in the accuracy, efficiency, and stability of the physical field solution.

[0056] like Figure 1 As shown, this invention begins with the definition of the physical problem and the setting of the solution domain. Its core process sequentially includes: S1 domain decomposition and subdomain construction, S2 feature extraction within the subdomain, S3 adaptive sampling and training set update, and S4 adaptive weight adjustment and model convergence. Finally, when the convergence condition is met, a high-fidelity numerical solution of the physical field is output. Each step is tightly coupled through data flow and constraints, forming a closed-loop optimization process. Specifically, it includes the following steps:

[0057] S1. Domain Decomposition and Subdomain Construction: This step divides the global solution domain into multiple computationally parallelizable units. The entire solution domain is divided into interconnected subdomains using a domain decomposition method, with overlapping regions between adjacent subdomains to ensure data continuity and transmission. Each subdomain is equipped with an independent Physical Information Neural Network (PINN) model trained on its local training set. This network can perform personalized learning based on the features within the subdomain and transmit the training results to adjacent subdomains, achieving dynamic coordination of information between regions. This step not only provides the basic framework for subsequent data feature extraction and adaptive algorithm execution but also ensures the boundary continuity and global conservation of physical quantities in each subdomain during the domain decomposition solution process through a collaborative mechanism between the domain and the subdomain, thus avoiding physical inconsistencies caused by interdomain fragmentation. In this way, the divide-and-conquer approach to the solution domain is achieved while maintaining the consistency of the physical structure, reducing overall computational complexity while improving solution stability and physical reliability.

[0058] As mentioned above, the purpose of this step is to divide the global solution domain into multiple computationally parallelizable units (i.e., subdomains) and establish the infrastructure for subsequent collaborative computation. Specifically, based on the geometric characteristics of the physical problem to be solved, the expected distribution of the physical field (such as a known boundary layer or shock wave location), or simple spatial partitioning rules, the entire solution domain is divided into multiple interconnected and partially overlapping subdomains. For example, the one-dimensional Burgers equation is more likely to form a shock wave or become a crest or trough at x=0. This region can be divided into different subdomains, called inter-subdomain overlapping regions, for collaborative solution. Figure 5 As shown, the blue area represents the overall solution domain. After partitioning, x=0 lies in the common area of ​​adjacent subdomains. Different partitioning methods can be selected based on different physical domains, including but not limited to rectangular partitioning, triangular partitioning, and partitioning with arbitrary continuous geometric shapes. Each subdomain is equipped with an independent physical information neural network (PINN) model. During partitioning, it is necessary to ensure that there is a certain coverage area between adjacent subdomains. This area is used to exchange boundary information during training, ensuring the continuity of the final solution at the subdomain boundaries (such as the continuity of velocity and pressure fields) and the global conservation of physical quantities (such as mass and energy). The output of this step is the defined geometric extent, initial network parameters, and relationship definitions between adjacent subdomains for each subdomain.

[0059] This section serves as the foundational structure of the entire system of this invention. Addressing the shortcomings of existing technologies that employ single-subdomain global networks to solve the physical domain, such as high computational complexity, low efficiency, and significant local correction costs, a multi-subdomain-covering architecture is designed. By dividing the overall solution domain into multiple relatively simple subdomains and establishing coverage regions between adjacent subdomains, the continuity and conservation of physical quantities at the boundaries are achieved, thus maintaining global physical structure consistency while solving in partitions. Each subdomain is equipped with an independent Physical Information Neural Network (PINN) model for local data training, utilizing a "divide and conquer" strategy to reduce the fitting scale and complexity of a single network iteration. Simultaneously, the coverage regions ensure smooth data information transfer and structural coupling between subdomains, providing a scalable, locally correctable, and physically consistent computational framework for subsequent feature extraction, adaptive sampling, and network training.

[0060] S2, Subdomain Feature Extraction: This step quantifies the local complexity of the data within the subdomain, providing a computable metric for subsequent adaptive sampling and structural consistency analysis. Based on the subdomains defined in S1, within each subdomain, a feature extraction algorithm based on composite feature metrics performs multi-dimensional feature extraction on the data after one round of computation by the neural network.

[0061] Composite feature index

[0062] Where α, β, and γ represent hyperparameters (all default to 1, determined according to the equation expression. For example, if the 1D thermal equation only contains the second derivative of u, α=1, β=0, and γ=1 can be set). Represents the gradient operator. Represents the Laplace operator, This represents the prediction result of the neural network.

[0063] The extracted features include, but are not limited to, residual distribution characteristics and gradient change rate, which can comprehensively reflect the physical complexity and structural change trends within the subdomain. This provides a basis for subsequent adaptive sampling and structure-preserving optimization. This process enables the model to maintain sensitivity and responsiveness to the system's inherent physical structure during learning, improving the targeting and physical consistency of feature extraction.

[0064] As described above, the purpose of this step is to quantify the local complexity and physical properties of the current solution (or initial guess) within each subdomain, providing a basis for adaptive sampling. Within each subdomain, feature extraction is performed in parallel. The extracted features are composite metrics, including but not limited to:

[0065] Residual distribution characteristics: Calculate the degree to which the predicted solution of the current physical information neural network PINN model satisfies the control partial differential equation at the sampling points in the subdomain, that is, the magnitude distribution of the equation residuals;

[0066] Gradient change rate: Calculates the magnitude of the gradient or the rate of change of a physical field variable (such as velocity or temperature) under the current solution to identify high gradient regions.

[0067] The input to this step is the current network parameters and sampling points of the subdomain, and the output is a feature distribution map or set of eigenvalues ​​that characterizes the "solution difficulty" or "feature strength" of each subdomain.

[0068] This section follows the results of domain decomposition and subdomain construction, calculating residuals, gradients, and frequency information in parallel within each subdomain to comprehensively reflect the degree of local complexity and physical structure changes. The composite feature vector formed by fusing these three factors can be used to quantitatively describe high-gradient regions, nonlinear regions, and sensitive regions that may lead to structural damage within a subdomain. This feature vector, as the sole intermediate result, is directly fed into the adaptive sampling and training set update section, providing a quantitative basis for subsequent sampling probability allocation and structural constraint strengthening. This stage represents the initial data processing phase. Through independent data mining and structural bias assessment within subdomains, it completes the transition and coupling at the physical structure level from basic domain construction to adaptive sampling, providing physical consistency assurance for subsequent adaptive training.

[0069] S3. Adaptive Sampling and Training Set Update: This step uses the feature indicators obtained in S2 to construct a probability function to dynamically supplement high information entropy samples, breaking the limitations of traditional fixed sampling.

[0070]

[0071] in, Physical field coordinates , is a composite feature index, k is the structure preservation weight coefficient (default is 1), and P(x) is a probability function.

[0072] Based on the feature extraction results, an adaptive sampling strategy is implemented according to the probability function. Samples are selectively chosen and the training set is updated based on the importance and structural bias of data in different regions. This strategy focuses on supplementing samples from regions with high gradients, nonlinearity, or inconsistent structures, making the training data more representative in terms of coverage. In this way, the training set can more accurately reflect the distribution characteristics of the data, improving the quality and effectiveness of the training data, thereby enhancing the performance of subsequent model training. This part is one of the core improvements of this invention; adaptive sampling breaks the limitations of traditional fixed sampling methods, dynamically adjusting the training data to make the model training more closely match the actual data situation.

[0073] As described above, the purpose of this step is to dynamically optimize the training set based on the features extracted by S2, allocating more computational resources to solving difficult or critical regions. For each subdomain, the density of sampling points is dynamically adjusted according to its internal feature distribution (e.g., high residual, high gradient regions). Specifically, the strategy is to add new sampling points with a higher probability in regions with high eigenvalues ​​(regions where the physical field changes drastically or the current solution error is large), while maintaining or reducing sampling points in regions with low eigenvalues. The updated training set will contain newly added samples that better represent local physical features. This strategy breaks the limitation of uniform sampling across the entire domain in traditional PINNs, allowing the training process to actively focus on critical regions. The output of this step is the updated, non-uniformly distributed training set for each subdomain.

[0074] This section utilizes composite features extracted from subdomains, performs real-time resampling based on probability density, and dynamically replays the new samples back into the training set. A structure-preserving weight coefficient is introduced during this process, balancing local information entropy and structural bias in the sampling probability calculation. This allows for higher sampling density in high-entropy and structurally unstable regions, thereby improving the representativeness of the training data in terms of structure preservation. The updated training set is then fed as the sole data stream into the adaptive weight adjustment and model convergence section, structurally forming a "feature-sampling-training" closed loop. This dynamically overcomes the distribution shift and structural imbalance problems caused by traditional fixed sampling, achieving a seamless transition from local feature mining to global structure-preserving optimization.

[0075] S4. Adaptive Weight Adjustment and Model Convergence: This step dynamically adjusts the multi-task loss weights at the end of the first training round, ensuring that the neural network optimization process focuses on the physical quantity whose fitting error decreases the slowest. At the end of a model training round, due to the different loss magnitudes between different training tasks, directly using a fixed weighting method can easily lead to training bias towards a single task, thereby disrupting the overall balance of the system structure. This invention employs an adaptive weighting method, dynamically optimizing the loss function weights based on the changing trends of different loss terms, and considering structural consistency constraints during the adjustment process. This addresses the inherent conservation laws or dissipation laws (such as energy equations) of the physical system to be solved (e.g., Burgers equations). ), by explicitly constructing its mathematical form as a physical constraint loss term Together with the physical residual loss function, they constitute the residual loss. .in, This represents the loss of the governing equations. By monitoring the loss magnitude for different tasks during training, and dynamically adjusting the loss function weights based on the model's training loss and the loss calculation function and PyTorch's built-in update function, the model's generalization ability and training efficiency are improved. Compared to the traditional fixed-weight approach, it is more adaptable to complex and changing data and model training needs. The loss weight parameter s is updated based on the total loss function. :

[0076]

[0077] in, The number of representative neural networks, Loss Representative model calculation process loss in different parts ( res Residual loss bc Boundary loss, ic (Initial value loss) Represents the internal parameters of the neural network. L This represents the loss of physical field coordinates in the neural network prediction results. i Represents the neural network number. s This represents a hyperparameter (default is 0, updated during training; for terms with larger losses, a larger s value indicates a higher loss). The smaller the value, the better to balance out excessive losses, and vice versa.

[0078] As mentioned above, the purpose of this step is to coordinate the balance of various loss objectives (such as equation residuals, boundary conditions, initial conditions, and continuity constraints between subdomains) during the optimization process, ensuring stable convergence of training and maintaining the physical structure. At the end of each (or several) round of global training iteration, the system monitors the changing trends of various loss terms (such as PDE loss, boundary loss, and interface continuity loss) in each subdomain. Then, according to the adjustment strategy preset in the above formula (e.g., increasing the weight of terms with slow loss decreases and decreasing the weight of terms with very small loss), the weight coefficients of each term in the total loss function are dynamically updated.

[0079] Simultaneously, physical structure preservation constraints (such as weak forms of global mass and momentum conservation constraints) are explicitly added to the total loss function. This combination of dynamic weight adjustment and structural constraints guides the optimization process towards both reducing error and preserving physical laws. Training iterations continue until the validation error and structural constraint residuals in all subdomains are below a preset threshold (this threshold is a hyperparameter, typically set for internal automatic convergence, and has no definite value). At this point, the model is considered converged, and the final physics prediction result is output.

[0080] This part receives the updated training set and dynamically adjusts the weights of the loss function at the end of each training round based on the error change rate of each task and the structural consistency constraint index. Traditional fixed weighting methods can easily cause the model to ignore some physical structural constraints during training, leading to the destruction of energy conservation or boundary continuity. To solve this problem, this invention introduces an adaptive dynamic weight adjustment mechanism: by monitoring the changing trend of multi-task loss and structural constraint residuals in real time, the weight ratio is automatically redistributed, so that the model maintains structural consistency and physical conservation characteristics while maintaining the error reduction rate. When the validation error and structural constraint loss of all subdomains simultaneously meet the preset threshold, the training process converges, thereby closing the full-link optimization loop of "domain decomposition - feature extraction - adaptive sampling - weight self-adjustment - structural consistency" at the system level, realizing end-to-end adaptive structure-preserving solution from data distribution to physical structure, and from local training to global coordination.

[0081] The steps S1 to S4 described above constitute a complete iterative optimization loop. In implementation, S1 is first executed to partition and initialize the solution domain. Then, steps S2, S3, and S4 are executed iteratively: within each training cycle, features of the current solution in each subdomain are extracted (S2), and the sampling points are adaptively updated based on these features (S3). Next, the updated training set is used for training, and the loss weights are dynamically adjusted at the end of training (S4). After each round of S4, the loss for each subdomain is calculated, and the overall subdomain error is calculated and judged. If the error does not meet the convergence condition, the process returns to S2; if the error meets the convergence condition, training ends, and physics prediction is performed. This process is repeated until the overall model error and structural constraint loss meet the preset convergence threshold (since the structural constraint loss is included in the loss function, it is considered to meet the structural constraint condition when the model converges), ultimately outputting a high-precision numerical solution for the physics field.

[0082] The proposed adaptive structure-preserving multi-region collaborative computation method for physical scenarios is primarily applied in the field of physical information neural network technology. It is suitable for numerical computation of physical problems in various engineering scenarios, including water flow analysis in hydraulic engineering, heat-fluid coupling calculation in energy engineering, flow field characteristic simulation in aerospace, and vibration control design in mechanical engineering, as well as model training scenarios corresponding to these engineering scenarios. Through innovative structural design and functional implementation, this method possesses significant technical advantages in both structural rationality and functional effectiveness, and can achieve significant and verifiable technical results for the numerical computation and model training needs of physical problems in the aforementioned engineering scenarios. Compared with existing technologies, the technical advantages of this invention are reflected in the following points:

[0083] 1. Modular decomposition and collaborative interaction structure

[0084] To address the high computational complexity and low processing efficiency of traditional global solution methods, this invention employs a modular decomposition strategy, such as... Figure 2 As shown, the solution domain of a complex physical problem is divided into multiple independent subdomains, and information exchange channels are built between these subdomains. This modular decomposition and collaborative interaction structure reduces the computational load of a single subdomain by breaking down tasks, while relying on the collaborative linkage between subdomains to ensure the consistency and integrity of the solution results within the overall domain. This achieves the technical goals of "efficient computation" and "accurate results," effectively improving the applicability of solving complex physical problems.

[0085] 2. Feature-driven dynamic data optimization structure

[0086] To address the shortcomings of traditional fixed sampling methods, such as low matching degree between training data and actual physical features and redundant data interfering with model training, this invention designs a feature-driven dynamic sampling mechanism: such as... Figure 3As shown, the key features of the training data are first identified through a feature extraction module, and then the sampling strategy is adaptively adjusted based on the identification results, synchronously updating the model training dataset. This feature-driven dynamic data optimization structure enables the training data to accurately map the core features of the physical problem, eliminates invalid and redundant data, provides a high-quality data foundation for model training, and significantly improves the model's fitting accuracy to physical laws.

[0087] 3. Weight adjustment structure that adapts to training state

[0088] To avoid local optima caused by fixed weights during model training and to ensure the stability of the training process, this invention constructs a training state feedback-based weight adjustment structure: (e.g.) Figure 4 As shown, during the model training phase, the training status (such as error distribution and convergence trend) is monitored in real time, and the weight allocation of the loss function is dynamically optimized based on the monitoring results, adjusting the model's priority for different data samples and errors. This adaptive weight adjustment structure effectively avoids training bias, ensures stable model convergence, and thus improves the model's generalization ability and reliability in practical applications.

[0089] The core steps involved in the improvements are based on the following principle: The adaptive sampling strategy of this invention is based on a fusion mechanism of "physical feature information extraction - sampling density proportionality principle" and "structural consistency constraint driving principle". Specifically, local physical feature information is quantified through a composite feature index of residual-gradient-frequency within a subdomain, and combined with a structural deviation metric to jointly evaluate regional complexity and physical structural stability. In high-entropy regions (such as large gradient, high curvature, or high-frequency oscillation regions), if structural deviation is significant, more sampling points are allocated proportionally to the feature information and deviation; in regions with low error and stable structure, redundant samples are automatically reduced. This principle overcomes the structural defect of traditional fixed sampling's "average effort," transforming the sampling point distribution from a priori uniform distribution to a posterior feature-structure collaboratively driven distribution. While maintaining the integrity and energy conservation characteristics of low-frequency signals, the sampling density in high-frequency regions is significantly improved. Thus, through the combined effect of adaptive reconfiguration of data distribution and structural consistency constraints, the model accuracy, generalization ability, and physical structure preservation characteristics are simultaneously enhanced, thereby ensuring the stability and reliability of the intelligent solution model in long-term evolution and multi-physics coupling scenarios.

[0090] Applicable Scenario Example: To more clearly demonstrate the specific implementation process and beneficial effects of this invention, the following explanation uses "viscous fluid flow analysis in oil transportation pipelines" as an example. It is necessary to solve for the fluid velocity distribution, pressure gradient changes, and turbulent boundary layer thickness within the pipeline (oil transportation pipeline, chemical raw material transmission pipeline), requiring high solution efficiency and high accuracy in the turbulent region.

[0091] Scenario Requirements: High solution efficiency is required, outputting flow analysis results for the entire pipeline section within 1 hour to support pipeline transport parameter optimization; high accuracy in the turbulent region is required, with a turbulent boundary layer velocity calculation error ≤3.5%, and it must adapt to changes in fluid viscosity within the pipeline. Experimental parameters and descriptions are shown in Table 2.

[0092] 1. Adopting a "modular decomposition and collaborative interaction structure", based on the characteristics of the scene spatial domain, the solution domain is divided into 4 solution subdomains, and the turbulent boundary layer region is further subdivided into smaller modules. Each subdomain is solved in parallel, and the fluid velocity and pressure boundary conditions of adjacent modules are transmitted in real time through the information interaction channel (coverage area) (such as the feedback of turbulent data of straight pipe section to flow calculation of curved pipe section), so as to avoid mutual interference between the calculation of turbulent region and laminar region when solving the overall domain.

[0093] 2. Activate the "Feature-Driven Dynamic Data Optimization Function". Combining the characteristics of nonlinear convection terms, for the turbulent boundary layer (the region with the largest fluid velocity gradient and the most complex flow state), the sampling point density is redistributed according to physical characteristics. The sampling density is appropriately reduced in the central region of the laminar and stable pipe to ensure that the training data accurately covers the key flow characteristics and reduce redundant calculations.

[0094] 3. Through the "adaptive weight adjustment function", the solution error of each subdomain is monitored in real time (such as when the velocity calculation error increases due to fluid deflection in the bend section, the weight of the loss function of that module is automatically increased), and the fluid viscosity is adapted to ensure the solution accuracy under different working conditions.

[0095] Optimal application results: On an RTX 4090 24G computing device, the solution for this scenario was completed in 1 hour (model parameter settings in Table 2). The model prediction results greatly reproduced the real-world scene. Figure 6 (The exact solution is compared with the model's predicted solution). Meanwhile, the sampling points are dynamically distributed within the gradient change region. Figure 7 The probability density resampling effect diagram of this invention (compared with other sampling methods) enhances the accuracy of scene solution and the mining of complex scene features, with the maximum model error controlled within 0.1%.

[0096] Table 2 Model Parameter Settings

[0097]

[0098] The maximum number of iterations of the L-BFGS optimizer mentioned in Table 2, which is 50,000, is only an experimental parameter setting and does not represent the actual number of iterations.

[0099] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for multi-region collaborative computing of a physical scene based on adaptive protection structure, characterized in that, Includes the following steps: S1. Domain Decomposition and Subdomain Construction: The global solution domain is divided into multiple interconnected and partially overlapping subdomains through the domain decomposition method. Coverage regions are set between adjacent subdomains, and each subdomain is equipped with an independent physical information neural network PINN model. S2. Subdomain Feature Extraction: Within each subdomain, a feature extraction algorithm based on composite feature indices is used to extract multi-dimensional features from the data after one round of computation by the neural network; the calculation formula for the composite feature indices is as follows: ； Where α, β, and γ represent hyperparameters, all with a default value of 1. Represents the gradient operator. Represents the Laplace operator, The multi-dimensional features represent the neural network prediction results; these features include residual distribution features and gradient rate of change, whereby the residual distribution features are the predicted solutions of the current physical information neural network PINN model. The degree to which the control partial differential equation is satisfied at sampling points within the subdomain, wherein the gradient change rate is the gradient magnitude or the rate of change of the physical field variable under the current solution; S3. Adaptive Sampling and Training Set Update: Based on the feature indicators extracted in S2, a probability function is constructed. Samples are selected and the training set is updated selectively according to the importance and structural bias of data in different regions. The formula for calculating the probability function is: ； Where x is the physical field coordinate. , For spatial coordinates, ω is the time coordinate, k is the composite feature index described in S2, and k is the structure preservation weight coefficient, with a default value of 1. S4. Adaptive Weight Adjustment and Model Convergence: At the end of each round of model training, the weights of the loss function are dynamically optimized based on the changing trends of different loss terms. Simultaneously, a physical structure preservation constraint term is explicitly added to the total loss function. Steps S2-S4 are executed iteratively until the convergence condition is met, and the numerical solution of the physics field is output. The formula for calculating the total loss function is: ； in, Represents the number of neural networks. For residual loss, For boundary loss, For initial value loss, θ Represents the internal parameters of the neural network. , , This is a hyperparameter with a default value of 0, which is updated during training.

2. The method for multi-region collaborative computation of physical scenes based on adaptive structure preservation according to claim 1, characterized in that, The domain decomposition described in S1 is based on the geometric characteristics of the physical problem to be solved, the expected distribution of physical fields, or simple spatial partitioning rules; the covered area is used to exchange boundary information during training to ensure the continuity of the final solution at the boundary of the subdomain and the global conservation of physical quantities.

3. The adaptive security based physical scene multi-region cooperative computing method according to claim 1, wherein, The independent physical information neural network PINN model for each subdomain in S1 is used to train the local data training set of the subdomain, realize personalized learning for the features inside the subdomain, and transmit the training results to the adjacent subdomains to realize dynamic coordination of information between regions.

4. The adaptive security based physical scene multi-region cooperative computing method according to claim 1, wherein, The adaptive sampling strategy in S3 is as follows: add new sampling points with a higher probability in regions with high eigenvalues, and maintain or reduce sampling points in regions with low eigenvalues. The regions with high eigenvalues ​​are regions where the physical field changes drastically or where the current solution error is large.

5. The adaptive security based physical scene multi-region cooperative computing method according to claim 1, wherein, The physical structure preservation constraints described in S4 include weak-form constraints on global mass conservation and momentum conservation.

6. The adaptive security based physical scene multi-region cooperative computing method according to claim 1, wherein, The convergence condition described in S4 is that the verification error and structural constraint residual of all subdomains are lower than a preset threshold.

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