Sluice water flow field prediction method and device based on brain-like inspiration and server

Abstract

The invention provides a sluice water flow field prediction method and device based on brain-like inspiration and a server, and relates to the technical field of flow field prediction.The sluice water flow field prediction method comprises the steps that a calculation area of a sluice and boundary conditions, initial conditions and a control equation of the calculation area are obtained, and training data are collected; respectively processing each dimension in the coordinate value of the training data through mutually independent modular sub-network sets to obtain a feature vector set, and carrying out tensor decomposition type feature fusion processing on the feature vector set to obtain a predicted value of the flow field variable; and constructing a total loss function by using the predicted value of the flow field variable, the boundary condition, the initial condition and the control equation, and carrying out brain-like heuristic training processing on the modular sub-network set based on the total loss function to obtain a brain-like heuristic separated physical information neural network so as to carry out prediction processing on the flow field of the sluice under different working conditions. And obtaining a target prediction result. According to the invention, prediction efficiency and prediction accuracy can be significantly improved.

Description

Technical Field

[0001] This invention relates to the technical field of flow field prediction, and in particular to a brain-inspired method, apparatus and server for predicting the flow field of sluice gate water flow. Background Technology

[0002] Currently, traditional grid-based fluid dynamics computational methods and meshless particle methods often face challenges of excessively high computational costs or insufficient accuracy when solving complex frontier problems such as multi-scale coupling, parameter identification, inverse problem solving, and flow field reconstruction. Related technologies propose using physical information neural networks to fuse known physical prior knowledge with available flow field data through machine learning methods to solve complex fluid problems. However, this approach still suffers from high memory consumption, low computational efficiency, and low computational accuracy due to spectral bias. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a brain-inspired method, device and server for predicting the flow field of a sluice gate, which can significantly improve prediction efficiency and prediction accuracy.

[0004] In a first aspect, embodiments of the present invention provide a brain-inspired method for predicting the flow field of a sluice gate. The method includes: acquiring the computational domain of the sluice gate, as well as the boundary conditions, initial conditions, and governing equations of the computational domain, and collecting training data, wherein the training data includes: configuration points within the computational domain, boundary constraint points, and initial condition constraint points; processing each dimension of the coordinate values ​​of the training data through a set of mutually independent modular sub-networks to obtain a set of feature vectors, and performing tensor decomposition-based feature fusion processing on the set of feature vectors to obtain predicted values ​​of the flow field variables; constructing a total loss function using the predicted values ​​of the flow field variables, boundary conditions, initial conditions, and governing equations, and performing brain-inspired training processing on the set of modular sub-networks based on the total loss function to obtain a brain-inspired separable physical information neural network, and using the brain-inspired separable physical information neural network to predict the flow field of the sluice gate under different operating conditions to obtain the target prediction result.

[0005] In one implementation, the step of collecting training data includes: obtaining the sampling range of the longitudinal dimension, lateral dimension, water depth dimension, and time dimension of the river channel; and performing Latin hypercube sampling in each dimension based on the sampling range to obtain the corresponding sampling coordinate values ​​for each dimension; combining the sampling coordinate values ​​through Cartesian product to obtain a four-dimensional structured configuration point set, and determining the four-dimensional structured configuration point set as the configuration points inside the computational domain; performing sampling processing on the boundary surface of the computational region to generate boundary constraint points, and performing sampling processing at the initial time of the computational region to generate initial condition constraint points, so as to determine the training data based on the configuration points inside the computational domain, the boundary constraint points, and the initial condition constraint points.

[0006] In one implementation, the step of processing each dimension of the coordinate values ​​of the training data to obtain a set of feature vectors through a set of independent modular sub-networks includes: sending the longitudinal coordinates of the river channel, the lateral coordinates of the river channel, the water depth coordinates, and the time coordinates of the coordinate values ​​of the training data to the corresponding modular sub-networks in the set of modular sub-networks, so as to process the longitudinal dimension information of the river channel, the lateral dimension information of the river channel, the water depth dimension information, and the time dimension information to obtain a set of feature vectors.

[0007] In one implementation, the step of performing tensor decomposition-based feature fusion processing on the feature vector set to obtain the predicted values ​​of the flow field variables includes: multiplying the values ​​at the same rank position in the feature vector set corresponding to each flow field variable element by element, and summing the product along the rank dimension to obtain the predicted values ​​of the corresponding flow field variables, wherein the flow field variables include: longitudinal flow velocity, transverse flow velocity, depth-direction flow velocity, and pressure field.

[0008] In one implementation, the step of constructing a total loss function using the predicted values ​​of flow field variables, boundary conditions, initial conditions, and governing equations includes: determining the mean square value of the residuals of the points where the governing equations are configured within the computational domain as the partial differential equation residual loss; comparing the predicted values ​​of the flow field variables with the boundary conditions and initial conditions respectively, and calculating the boundary condition loss and initial condition loss; applying regularization constraints to the connection weights in the modular subnetwork set to generate a regularization loss, and determining the brain-like optimization loss based on the regularization loss; and performing a weighted summation of the partial differential equation residual loss, boundary condition loss, initial condition loss, and brain-like optimization loss to obtain the total loss function.

[0009] In one implementation, the step of determining the brain-like optimization loss based on regularization loss includes: assigning two-dimensional geometric coordinates to neurons in each modular sub-network, and performing loss value calculation based on the absolute values ​​of the distance between neurons and the connection weights to obtain a locality penalty loss; and determining the sum of the locality penalty loss and the regularization loss as the brain-like optimization loss.

[0010] In one implementation, the step of performing brain-inspired training on a set of modular subnetworks based on the total loss function to obtain a brain-inspired separable physical information neural network includes: adopting a phased training strategy, performing brain-inspired training on the set of modular subnetworks based on the total loss function in the preliminary fitting stage, the sparse evolution stage, and the fine-tuning stage, respectively, so that the set of modular subnetworks fits the characteristics of the flow field to obtain a brain-inspired separable physical information neural network, wherein the preliminary fitting stage, the sparse evolution stage, and the fine-tuning stage are divided by a preset iteration number threshold.

[0011] Secondly, embodiments of the present invention also provide a brain-inspired sluice gate flow field prediction device. The device includes: a data acquisition module, which acquires the computational domain of the sluice gate, as well as the boundary conditions, initial conditions, and control equations of the computational domain, and collects training data, wherein the training data includes: configuration points within the computational domain, boundary constraint points, and initial condition constraint points; a mesh construction module, which processes each dimension of the coordinate values ​​of the training data through a set of mutually independent modular sub-networks to obtain a set of feature vectors, and performs tensor decomposition-based feature fusion processing on the set of feature vectors to obtain predicted values ​​of flow field variables; and a model training module, which constructs a total loss function using the predicted values ​​of flow field variables, boundary conditions, initial conditions, and control equations, and performs brain-inspired training processing on the set of modular sub-networks based on the total loss function to obtain a brain-inspired separable physical information neural network, so as to use the brain-inspired separable physical information neural network to predict the flow field of the sluice gate under different operating conditions and obtain the target prediction result.

[0012] Thirdly, embodiments of the present invention also provide a server, including a processor and a memory, the memory storing computer-executable instructions executable by the processor, the processor executing the computer-executable instructions to implement any of the methods provided in the first aspect.

[0013] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing computer-executable instructions, which, when invoked and executed by a processor, cause the processor to implement any of the methods provided in the first aspect.

[0014] The embodiments of the present invention bring the following beneficial effects: This invention provides a brain-inspired method, apparatus, and server for predicting the flow field of a sluice gate. The method acquires the computational domain of the sluice gate, along with its boundary conditions, initial conditions, and governing equations. Training data is then collected. Next, through a set of independent modular sub-networks, each dimension of the coordinate values ​​in the training data is processed to obtain a set of feature vectors. Tensor decomposition and feature fusion processing are then performed on the feature vector set to obtain predicted values ​​of the flow field variables. Finally, a total loss function is constructed using the predicted values ​​of the flow field variables, boundary conditions, initial conditions, and governing equations. The modular subnetwork set is trained using a brain-inspired method to obtain a brain-inspired separable physical information neural network. This neural network is then used to predict the flow field of a spillway gate under different operating conditions, yielding the target prediction result. This invention can be used for rapid prediction and analysis of the flow field of a spillway gate under different operating conditions in water conservancy projects. While significantly reducing the computational cost and memory usage of the neural network, it effectively captures the complex structure and multi-scale physical features in the flow field, achieving rapid and high-fidelity prediction of the flow field of the spillway gate under different operating conditions, and significantly improving prediction efficiency and accuracy.

[0015] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a brain-inspired method for predicting the flow field of a sluice gate, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of a brain-inspired, discrete physical information neural network provided in an embodiment of the present invention; Figure 3 A schematic diagram of a network backbone provided in an embodiment of the present invention; Figure 4A schematic diagram illustrating the changes in network topology results provided in an embodiment of the present invention, based on a brain-like optimization method. Figure 5 A schematic diagram of a brain-inspired sluice gate flow field prediction device provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of a server provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0020] As a fundamental discipline that studies the laws of fluid motion and its mechanical behavior, fluid mechanics has played a crucial role in aerospace, marine engineering, energy engineering, and biomedicine over the past few decades. With the continuous growth of computing resources and the significant improvement of computing power, computational fluid dynamics (CFD) has made great strides. Today, CFD has become a core numerical tool for understanding and predicting complex flow phenomena, and its influence extends to all aspects of scientific research and engineering applications.

[0021] Currently, traditional CFD methods can be mainly divided into two categories: mesh-based methods and meshless particle methods. The former is represented by the finite volume method, finite difference method, finite element method, and spectral element method, while the latter includes mainstream techniques such as smoothed particle hydrodynamics, uniform particle method, and dissipative particle dynamics. Although these traditional methods are technically mature and versatile, they often face challenges such as excessively high computational costs or insufficient accuracy when dealing with complex frontier problems such as multi-scale coupling, parameterized identification, inverse problem solving, and flow field reconstruction.

[0022] Considering the limitations of traditional CFD methods in data utilization and the lack of physical interpretability in purely data-driven methods, fusing known physical prior knowledge with available flow field data through machine learning has become a hot research direction in fluid mechanics. In recent years, Physical Information Neural Networks (PINNs) have demonstrated significant application value in the engineering solution of partial differential equations in fluid mechanics. Their core lies in the organic integration of prior constraints of physical laws with empirical observation data. When the system has complete physical background and boundary conditions, PINNs can replace traditional numerical simulation to achieve efficient positive prediction. Conversely, if prior information is limited, they can simultaneously complete parameter identification tasks through labeled data. The core advantages of PINNs are their flexible data requirements, adaptive structural optimization capabilities, and robustness to sparse data and noisy scenarios, effectively addressing nonlinear and time-varying flow scenarios, providing new ideas for solving complex fluid problems.

[0023] However, despite the significant potential shown by PINNs in engineering, they still face several key challenges in CFD problems: (1) Curse of Dimensions and Computational Bottleneck: Real-world three-dimensional unsteady flow is a (3+1)-dimensional problem for traditional PINNs. High-density sampling is required in the time and space domains to ensure accuracy. The number of configuration points increases exponentially with the dimension, and each point needs to repeatedly perform forward and backward propagation and use automatic differentiation to calculate higher-order derivatives, resulting in huge computational and memory overhead.

[0024] (2) The contradiction between model expressive power and efficiency: Capturing complex structures such as turbulence requires a network architecture with strong expressive power, but the traditional PINNs structure based on multilayer perceptrons has problems such as parameter redundancy, optimization difficulty and low efficiency.

[0025] (3) Spectral bias problem: PINNs inherit the structure of traditional neural networks and have spectral bias. That is, the neural network tends to learn smooth low-frequency features first, while the convergence speed of high-frequency and multi-scale flow features such as vortices and shear layers in the flow field is slow and the accuracy is insufficient.

[0026] Although numerous improvements to PINNs have emerged in recent years, such as the Physical Information Fourier Neural Operator (PINO), the Physical Information Deep Learning Operator (PI-DeepOnet), and the Separable Physical Information Neural Network (SPINN), the former two essentially add physical constraints to the operator learning framework, thus still inheriting the inherent shortcomings of PINNs. While works like Separable PINN alleviate computational pressure to some extent by decomposing dimensions, their sub-network structures are still traditional multilayer perceptrons and are not optimized for flow field characteristics, making it difficult to fully utilize the multi-scale feature representation capabilities of the physical field. Therefore, there is an urgent need to design novel PINN architectures for CFD tasks: capable of efficiently handling high-dimensional physical fields, possessing a simplified network structure without sacrificing flow field feature extraction capabilities, exhibiting strong multi-scale feature representation capabilities, and balancing computational efficiency and numerical accuracy, thereby breaking through the performance bottlenecks of existing PINNs in practical fluid applications.

[0027] Based on this, the brain-inspired sluice gate flow field prediction method, device and server provided by the present invention can be used for rapid prediction and analysis of the flow field of the sluice gate under different working conditions of the water conservancy hub. While significantly reducing the computational cost and memory occupation of the neural network to solve the high-dimensional Navier-Stokes equation, it effectively captures the complex structure and multi-scale physical features in the flow field, realizes rapid and high-fidelity prediction of the flow field of the sluice gate under different working conditions, and significantly improves the prediction efficiency and prediction accuracy.

[0028] See Figure 1 The diagram shows a flowchart of a brain-inspired sluice gate flow field prediction method, which mainly includes the following steps S102 to S106: Step S102: Obtain the computational domain of the spillway, as well as the boundary conditions, initial conditions, and governing equations of the computational domain, and collect training data, which includes: configuration points within the computational domain, boundary constraint points, and initial condition constraint points.

[0029] In one implementation, firstly, the computational domain of the physical problem to be solved is determined. The computational domain refers to the spatial extent and time span occupied by fluid motion, and is the solution domain of the numerical simulation. After determining the computational domain, the Navier-Stokes equations are used as the governing equations describing the fluid motion. The Navier-Stokes equations are the fundamental governing equations of fluid mechanics, consisting of the momentum equation and the continuity equation. The momentum equation describes the relationship between the rate of change of fluid velocity over time and the pressure gradient, viscous diffusion, and volume forces. The continuity equation describes the mass conservation constraint, that is, the difference in mass of fluid flowing into and out of a certain infinitesimal element is equal to the rate of change of mass within that infinitesimal element. The governing equations include physical quantities such as the fluid's velocity field, pressure field, density, viscosity, and volume forces.

[0030] Secondly, the boundary conditions and initial conditions of the computational domain are set. Initial conditions refer to the distribution of physical quantities at each spatial point within the computational domain at the initial moment, typically including the initial velocity field and initial pressure field, used to describe the fluid's motion state at the initial moment. Boundary conditions and initial conditions are necessary components for solving partial differential equations, together with the governing equations, constituting a complete and solvable physical problem.

[0031] Finally, training data is collected. The training data includes placement points within the computational domain, boundary constraint points, and initial condition constraint points. Placement points within the computational domain are discrete points selected within the computational region to constrain the network's predicted values ​​to satisfy the governing equations. Boundary constraint points are discrete points selected on the boundaries of the computational region to constrain the network's predicted values ​​to satisfy boundary conditions. Initial condition constraint points are discrete points selected within the spatial computational domain at the initial time step to constrain the network's predicted values ​​to satisfy initial conditions. These three types of placement points together constitute the training data of the neural network, providing supervision signals for subsequent network training.

[0032] Step S104: Through a set of independent modular sub-networks, each dimension of the coordinate values ​​in the training data is processed to obtain a set of feature vectors. Then, tensor decomposition and feature fusion processing is performed on the set of feature vectors to obtain the predicted values ​​of the flow field variables.

[0033] In one implementation, a set of independent modular subnetworks is constructed to process the coordinate values ​​in the training data. Each sample in the training data contains a four-dimensional coordinate, corresponding to the longitudinal dimension of the river channel, the transverse dimension of the river channel, the depth dimension, and the time dimension, respectively. The modular subnetwork set consists of four independent subnetworks, each responsible for processing the coordinate values ​​of one of the dimensions. See [link to relevant documentation]. Figure 2 The diagram shown illustrates the structure of a brain-inspired, separable physical information neural network. It displays the network backbone (four independent subnetworks), the automatic differentiation module, the loss function construction, and the parameter update process. For details of the network backbone, please refer to [link to relevant documentation]. Figure 3 As shown, the network backbone is a schematic diagram of independent input and multi-channel output. The four inputs are independent and separable, and the four output variables correspond to four channels. Each channel is responsible for one output. The output is obtained by summing the outer products of each subnetwork.

[0034] Specifically, the first subnetwork receives the longitudinal coordinates of the river channel as input, the second subnetwork receives the transverse coordinates of the river channel as input, the third subnetwork receives the water depth coordinates as input, and the fourth subnetwork receives the time coordinates as input. Each subnetwork independently performs forward propagation, mapping the scalar coordinate values ​​it receives into a high-dimensional feature vector. A feature vector is a vector composed of multiple values, used to characterize the flow field features in that dimension. Each of the four subnetworks outputs a feature vector, and these feature vectors together constitute a feature vector set.

[0035] Furthermore, tensor decomposition-based feature fusion is performed on the feature vector set to obtain the predicted values ​​of the flow field variables. Tensor decomposition-based feature fusion is a computational method that combines multiple low-dimensional feature vectors into a high-dimensional output. Specifically, for each flow field variable, the values ​​at the corresponding rank positions are extracted from the feature vectors output by the four sub-networks. These values ​​are then multiplied element-wise to obtain a product value. Element-wise multiplication means multiplying the values ​​at the same position in each of the four feature vectors. Then, the products at all rank positions are summed along the rank dimension to obtain the predicted value of the flow field variable. The rank dimension refers to the length direction of the feature vector, and the rank parameter determines the size of the feature vector dimension. Through the above fusion operation, the predicted values ​​of the longitudinal flow velocity, transverse flow velocity, depth velocity, and pressure field of the river can be calculated separately. Since the four sub-networks are independent and each only processes one-dimensional input, the computational complexity of the entire network is linearly related to the number of sampling points in each dimension, rather than exponentially, thus significantly reducing the computational cost.

[0036] Step S106: Construct a total loss function using the predicted values ​​of flow field variables, boundary conditions, initial conditions, and governing equations. Based on the total loss function, perform brain-inspired training on the modular sub-network set to obtain a brain-inspired separable physical information neural network. Use this brain-inspired separable physical information neural network to predict the flow field of the spillway gate under different operating conditions and obtain the target prediction result.

[0037] In one implementation, a total loss function is constructed using the predicted values ​​of the flow field variables, as well as pre-set boundary conditions, initial conditions, and governing equations. The loss function is a quantitative metric used to measure the difference between the neural network's predicted values ​​and the target values; the total loss function is composed of a weighted sum of multiple sub-loss terms. Specifically, the total loss function comprises four parts: partial differential equation residual loss, boundary condition loss, initial condition loss, and brain-like optimization loss. The partial differential equation residual loss is the mean square value of the residuals calculated by substituting the predicted values ​​of the flow field variables into the governing equations, used to constrain the predicted values ​​to meet the physical laws of fluid motion. The boundary condition loss is the mean square error obtained by comparing the predicted values ​​of the flow field variables with the boundary conditions, used to constrain the predicted values ​​to meet the physical constraints on the boundary of the computational domain. The initial condition loss is the mean square error obtained by comparing the predicted values ​​of the flow field variables with the initial conditions, used to constrain the predicted values ​​to meet the physical state at the initial moment. The brain-like optimization loss includes regularization loss and locality penalty loss. Regularization loss simplifies the network structure by imposing sparsity constraints on the connection weights, while locality penalty loss encourages functionally related neurons to cluster in space by assigning geometric coordinates to neurons and penalizing long-distance connections.

[0038] Furthermore, based on the total loss function, the modular subnetwork set is subjected to brain-inspired training to obtain a trained brain-inspired separable physical information neural network. Brain-inspired training refers to a training method that simulates the sparse connection characteristics of biological neural networks. It adopts a phased training strategy, successively going through an initial fitting stage, a sparse evolution stage, and a fine-tuning stage. In the initial fitting stage, low-intensity regularization constraints and locality penalty constraints are used to enable the subnetwork to initially learn the main structural features of the flow field. In the sparse evolution stage, the strength of regularization constraints and locality penalty constraints is increased, and a weight pruning mechanism is activated to set connections with absolute weight values ​​below a preset threshold to zero, causing the subnetwork to evolve from a fully connected structure to a sparse minimal structure. In the fine-tuning stage, the strength of regularization constraints is reduced, and the weights and biases retained in the sparse structure are fine-tuned to further improve prediction accuracy. After training, this type of brain-inspired separable physical information neural network is used to predict the flow field under different working conditions. The coordinate values ​​to be predicted are input into the network, and after forward propagation and tensor decomposition fusion, the predicted values ​​of the flow field variables at the corresponding locations can be output, thus obtaining the target prediction result.

[0039] The brain-inspired sluice gate flow field prediction method provided in this invention can significantly improve prediction efficiency and accuracy.

[0040] This invention also provides an implementation method for predicting the flow field of a water spillway gate in a hydraulic engineering project, as detailed in (1) to (5) below: (1) Determine the computational domain, adopt the Navier-Stokes equations as the governing equations, and set boundary conditions and initial conditions, as detailed in (1-1) to (1-5) below: (1-1) Determination of the Calculation Domain. Taking the spillway gate of the water conservancy project as the engineering object, a typical working section of the spillway gate is selected as the calculation domain, including the water area in front of the gate, the interior of the gate opening, and the downstream energy dissipation zone. The calculation domain is described by three-dimensional spatial coordinates (x, y, z), where x is the longitudinal direction of the river channel (downstream direction), y is the transverse direction of the river channel, and z is the water depth direction. A time dimension t is also introduced to describe the unsteady flow process. The spatial extent of the calculation domain is determined according to the actual engineering situation, for example, from upstream to the flow measurement section and downstream to the end of the energy dissipation section. The inputs for this step are the engineering geometric parameters of the spillway gate (gate chamber dimensions, bottom elevation, upstream and downstream river channel cross-sections, etc.) and operating parameters (upstream water level range, downstream water level range, gate opening range). The output is the defined three-dimensional calculation domain. and its boundaries .

[0041] (1-2) Governing Equations. The three-dimensional incompressible Navier-Stokes (NS) equations are adopted as the governing equations, including the momentum equation and the continuity equation: Momentum equation:

[0042] Continuity equation:

[0043] in, The velocity field of a fluid is a function of spatial coordinates and time. The longitudinal flow velocity of the river channel. For lateral flow velocity, The velocity is the velocity in the direction of water depth. Pressure field; Fluid density (for incompressible fluids, (for constants) Kinematic viscosity ( (dynamic viscosity); Volume force per unit mass (e.g., gravitational acceleration g). The physical meaning of each term in the momentum equation is: This is a non-steady term (local acceleration). This is the convection term (inertia term, and also the only nonlinear term in the Navier-Stokes equations). For the pressure gradient term, This is the viscous diffusion term.

[0044] After making the momentum equation dimensionless, the Reynolds number is introduced. ,in Characteristic velocity (e.g., average inlet velocity). Let the characteristic length be (e.g., the gate height). The dimensionless momentum equation is:

[0045] (1-3) Setting Boundary Conditions. Based on the actual physical characteristics of the spillway, the following four types of boundary conditions are set: (a) Inlet Boundary Conditions (Dirichlet Boundary Conditions): At the upstream inlet of the computational domain, a given inlet velocity distribution is established. The inlet velocity is related to the upstream water level and can be determined based on the water level-discharge relationship. That is, at the inlet boundary... superior:

[0046] in, This is a given inlet velocity calculated based on the upstream water level. The input for this condition is the upstream water level value, and the output is the velocity vector at each point at the inlet.

[0047] (b) Export boundary conditions (Newman boundary conditions): At the downstream outlet of the computational domain, pressure Newman boundary conditions are used, i.e., the pressure gradient at the outlet is specified or the outlet pressure value is given: or

[0048] in, The direction of the outer normal to the boundary. Determined based on downstream water level. The input to this condition is the downstream water level value, and the output is the pressure constraint at the outlet.

[0049] (c) Solid wall boundary conditions (no-slip condition): Apply no-slip boundary conditions to the solid walls such as the gate surface, the bottom plate of the gate chamber, and the side walls:

[0050] That is, the fluid velocity at the wall is zero. The input to this condition is the geometric position information of the solid wall boundary, and the output is the constraint that the velocity at the wall is zero.

[0051] (1-4) Setting initial conditions. Setting the initial time. The velocity and pressure distribution of the flow field at that time. For the sluice gate problem, the initial flow field can be assumed to be in a static state:

[0052] in, This step represents the hydrostatic pressure distribution. Initial conditions can also be provided based on existing measured data or numerical simulation results. The input to this step is a description of the physical state at the initial moment, and the output is the initial velocity and pressure field distributions across the entire computational domain.

[0053] The mechanism by which boundary and initial conditions affect network optimization: Boundary and initial conditions exert constraints on the optimization of network parameters through the loss function. Specifically, during training, the network calculates predicted values ​​at boundary points and initial time points. For boundary conditions, based on the coordinates of the boundary points, the network outputs the predicted velocity and pressure values ​​at those boundary points after forward propagation and tensor decomposition fusion through four sub-networks. Then compare the predicted value with the true value of the given boundary conditions. By comparison, the mean squared error is calculated as the boundary condition loss. Similarly, given the initial conditions, the network outputs predicted values ​​at the initial time-determined configuration point. , with the given initial value By comparison, the initial conditional loss is obtained. These losses drive the optimizer to update network parameters through backpropagation, gradually ensuring that the network's predictions meet the physical boundaries and initial constraints. It's important to note that the sub-networks themselves do not predict boundary or initial conditions independently. Instead, they construct the loss by performing a complete forward propagation process at the boundary / initial time points (each of the four sub-networks processes its corresponding dimensional coordinates, which are then fused through tensor decomposition to output flow field variables). This results in flow field predictions at these specific locations, which are then compared with the known boundary / initial conditions.

[0054] (2) Collect training data. In one implementation, the sampling ranges of the longitudinal dimension, transverse dimension, water depth dimension, and time dimension of the river channel are first obtained. Based on the sampling ranges, Latin hypercube sampling is performed in each dimension to obtain the corresponding sampling coordinate values. Then, the sampling coordinate values ​​are combined by Cartesian product to obtain a four-dimensional structured configuration point set. The four-dimensional structured configuration point set is determined as the configuration points inside the computational domain. Finally, sampling is performed on the boundary surface of the computational domain to generate boundary constraint points. Sampling is also performed at the initial time of the computational domain to generate initial condition constraint points. The training data is determined based on the configuration points inside the computational domain, the boundary constraint points, and the initial condition constraint points. See (2-1) to (2-3) below for details: (2-1) Sampling of configuration points within the computational domain. To fully utilize the computational advantages of the split sub-network structure, this invention adopts a structured sampling strategy of independent sampling and recombination across dimensions. The specific process is as follows: Step 1: Determine the sampling dimensions and range. Treat the four dimensions—three-dimensional spatial coordinates (x, y, z) and time t—as independent sampling objects. Determine the sampling range for each dimension based on the computational domain: , , , .in , These are the upstream and downstream boundary coordinates of the computational domain, respectively. , The coordinates of the horizontal boundary. , The elevation of the bottom plate and the water surface. , The start and end times are for calculation.

[0055] Step 2: Perform Latin hypercube sampling independently in each dimension. Specifically, for a given dimension (using...),... (taking dimensions as an example) the range of this dimension. Evenly divided into Divide the data into three equally spaced subintervals; within each subinterval, randomly select a point to obtain the data along that dimension. Each sampled coordinate value Latin hypercube sampling ensures uniform coverage of sampling points along that dimension, avoiding clustering or gaps that may occur with purely random sampling. Similarly, performing Latin hypercube sampling along the y, z, and t dimensions yields... Each y-coordinate value The z-coordinate values ​​and Each t-coordinate value. The typical number of sampling points per spatial location dimension is... =50-200 can be adjusted according to the complexity of the flow field and computational resources.

[0056] Step 3: Generate a structured configuration point set using Cartesian product. Combine the sampled coordinates in the four dimensions using Cartesian product to generate a four-dimensional structured mesh point set:

[0057] The total number of configuration points generated is For example, each spatial dimension takes One point, Therefore, the total number of configuration points is 3,750,000. Each configuration point represents a specific spatiotemporal location within the computation domain. At this location, the flow field needs to satisfy the Navier-Stokes equations (i.e., the PDE residual is zero). The denser the placement of points, the more fully the constraints of the Navier-Stokes equations are covered, and the more accurate the flow field solution learned by the network. Latin hypercube sampling ensures the uniform distribution of sampling points in each dimension, while introducing randomness to avoid systematic biases that may be introduced by regular grids.

[0058] Because Brain-Inspired Separable PINNs (BIS-PINNs) employ a separate sub-network structure, with each of the four sub-networks independently processing inputs in one dimension (x, y, z, t), only the four sub-networks need to be processed separately. , , , Second forward propagation (total) (once), all can be calculated through tensor decomposition and fusion. Flow field predictions at each configuration point. This reduces the computational complexity of forward propagation from that of traditional PINNs. (Exponential) decrease to (Linear level) This achieves an exponential reduction in computational load.

[0059] The inputs for this step are the spatial and temporal extent of the computational domain and the number of sampling points for each dimension. The output is a structured set of points S, containing 3,750,000 four-dimensional spatiotemporal coordinates.

[0060] (2-2) Sampling of Boundary and Initial Condition Constraint Points. Boundary constraint points: Sampling is performed on various boundary surfaces (inlet, outlet, solid wall) of the computational domain. For regular boundaries, structured sampling can also be used. For complex geometric boundaries (such as gate surfaces, irregular river walls), traditional random sampling is used to randomly generate sampling points on the boundary surface. Approximately 1,000-2,000 constraint points are set on each type of boundary, and the total number of boundary constraint points is approximately... Each boundary constraint point carries its coordinate information. And the boundary condition values ​​at that point (such as inlet velocity, wall zero velocity, outlet pressure, etc.).

[0061] Initial constraint point: at the initial time. The entire spatial computational domain is sampled to generate a set of spatial coordinate points, each carrying the initial velocity and pressure values ​​(e.g., zero velocity and static pressure distribution in still water).

[0062] (2-3) Hybrid sampling strategy for complex boundary regions. For regions near complex geometric boundaries such as gates, guide walls, and fishway walls, a hybrid strategy combining structured sampling and random sampling is adopted: in regular regions far from complex boundaries, the above-mentioned structured sampling is used and BIS-PINNs are used for training; in local regions near complex boundaries, traditional random sampling is used and traditional PINNs are combined with the brain-like optimization training method of this invention. The two regions are connected at the boundary by freezing the BIS-PINNs structured sampling points to ensure the continuity of the overall flow field solution.

[0063] (3) Construct four independent sub-networks, and merge the outputs of the sub-networks to generate the velocity field and pressure field through tensor decomposition feature fusion. In one implementation, the longitudinal coordinates of the river channel, the transverse coordinates of the river channel, the water depth coordinates, and the time coordinates in the coordinate values ​​of the training data are sent to the corresponding modular sub-networks in the modular sub-network set to process the longitudinal dimension information, the transverse dimension information, the water depth dimension information, and the time dimension information of the river channel to obtain a set of feature vectors. Then, the values ​​of the same rank position in the feature vector set corresponding to each flow field variable are multiplied element by element, and the product is summed along the rank dimension to obtain the predicted value of the corresponding flow field variable. The flow field variables include: longitudinal velocity of the river channel, transverse velocity of the river channel, water depth velocity, and pressure field, as detailed in (3-1) to (3-2) below: (3-1) Construction of Four Independent Sub-networks. Instead of using a single multilayer perceptron (MLP) to process the entire four-dimensional coordinate vector (x,y,z,t), this invention constructs four independent modular sub-networks, each responsible for processing only one dimension of the scalar input. The four sub-networks are as follows: Subnetwork The input is spatial coordinate x (scalar), and the longitudinal dimension information of the river channel is processed.

[0064] Subnetwork The input is spatial coordinate y (scalar), and the lateral dimension information of the river channel is processed.

[0065] Subnetwork The input is the spatial coordinate z (scalar), and the dimension information in the water depth direction is processed.

[0066] Subnetwork The input is a time coordinate t (scalar), and the time dimension information is processed.

[0067] The initial structure (fully connected state) of the subnetwork is as follows: Each subnetwork is a standard fully connected multilayer perceptron (MLP), and its initial structure is determined by the following parameters: Input layer: 1 neuron, receiving a scalar input (one of x, y, z or t).

[0068] Hidden layers: 4-6 fully connected hidden layers, each containing 32-128 neurons (each sub-network can be set independently according to the complexity of the flow field in its corresponding dimension); each layer uses the Tanh activation function (the Tanh function has the characteristics of smoothness and central symmetry, which is suitable for fitting the continuous change characteristics of flow field variables); the layers are fully connected, that is, each neuron in the previous layer has a connection weight with each neuron in the next layer.

[0069] Output layer: k×r neurons, where k=4 corresponds to 4 flow field output variables ( ), where r is the rank parameter (the rank in tensor decomposition, usually taken as 32-128), therefore the output layer dimension is 4r (for example, when r=32, the output dimension is 128). No activation function is used in the output layer.

[0070] The above describes the fully connected structure of the subnetwork in the initial training stage. During subsequent brain-inspired training, the subnetwork will gradually evolve from a fully connected structure to a sparse, minimally oriented network structure (the final structure) through L1 regularization, locality penalty, and weight pruning. Redundant connections are removed, retaining only neurons and connections crucial for flow field feature extraction. The final sparse structure is adaptively determined during training, and the number of parameters can be reduced by more than 90% compared to the initial fully connected structure.

[0071] Since the output dimension is k×r (multidimensional), multiple output channels need to be constructed in the sub-network. Specifically, the k×r neurons of the output layer are grouped according to the flow field variables to form k=4 channels: the first channel (the first to the rth output neurons) corresponds to the velocity component. The velocity component corresponds to the second channel (from the (r+1)th to the 2rth output neuron). The third channel corresponds to The pressure corresponding to the fourth channel Each channel outputs an r-dimensional feature vector. The input to this step is the network structure hyperparameters (number of hidden layers, number of neurons per layer, rank parameter r, activation function type). The output is four initialized independent subnetworks.

[0072] (3-2) Tensor decomposition-based feature fusion. After each of the four sub-networks performs forward propagation on its scalar input, it outputs a k×r dimensional feature vector. In order to merge the outputs of the four sub-networks to generate the final flow field variables (velocity field and pressure field), a tensor decomposition-based feature fusion method is adopted.

[0073] The specific fusion method is as follows: For the k-th flow field output variable (k=1,2,3,4 respectively correspond to...) , , , Its value is calculated using the following formula:

[0074] in, For sub-networks The output value of the i-th neuron in the output layer in response to input x; For sub-networks The output value of the i-th neuron in the output layer in response to input y; For sub-networks The output value of the i-th neuron in the output layer for input z; For sub-networks The output value of the i-th neuron in the output layer for input t; sum from arrive That is, take the r feature values ​​corresponding to the k-th channel in the output of each sub-network.

[0075] The essence of this operation is to perform element-wise multiplication of the r-dimensional output vectors of the four sub-networks on the k-th channel, and then sum them along the rank dimension. This is equivalent to performing a tensor outer product on the sub-network outputs and then shrinking them along the rank dimension, achieving efficient fusion of features from various dimensions.

[0076] Through this fusion operation, the predicted values ​​of the four flow field variables are finally obtained: (Predicted longitudinal flow velocity in the river channel); (Predicted cross-flow velocity in the river channel); (Predicted velocity in the direction of water depth); (Predicted value of pressure field).

[0077] The physical meaning of the rank parameter r: r is the rank in tensor decomposition, which can be understood as the number of separable basis functions the network uses to approximate the solution of the PDE. The larger r is, the more complex the function that the model can express and the higher the accuracy, but the computational cost also increases accordingly. The value of r needs to be balanced between accuracy and efficiency, and is usually taken as 32-128.

[0078] Computational complexity analysis: Traditional PINNs use a single MLP to process the four-dimensional input, and its computational complexity is O(n log n). Where N is the number of sampling points per dimension. This invention reduces the computational complexity to [value missing] by combining dimensionality separation and tensor decomposition. This resulted in an exponential reduction in computational load.

[0079] The input to this step is the scalar input (sampled values ​​of x, y, z, and t) of each of the four sub-networks. The output is the predicted values ​​of the four flow field variables. ).

[0080] (4) Train the subnetwork using training data to obtain the trained BIS-PINNs network. In one implementation, the total loss function needs to be calculated first: the mean square value of the residuals of the control equations at the points configured within the computational domain is determined as the partial differential equation residual loss, and the predicted values ​​of the flow field variables are compared with the boundary conditions and initial conditions respectively to calculate the boundary condition loss and the initial condition loss. Then, regularization constraints are applied to the connection weights in the modular subnetwork set to generate regularization loss, and the brain-like optimization loss is determined based on the regularization loss. That is, two-dimensional geometric coordinates are assigned to the neurons in each modular subnetwork, and the loss value is calculated based on the distance between neurons and the absolute value of the connection weights to obtain the local penalty loss. The sum of the local penalty loss and the regularization loss is determined as the brain-like optimization loss. Finally, the partial differential equation residual loss, boundary condition loss, initial condition loss and brain-like optimization loss are weighted and summed to obtain the total loss function, as detailed in (4-1) to (4-4) below: (4-1) Basic training method of traditional PINNs. Before introducing the improved training method of the present invention, the basic training process of existing PINNs will be explained in order to clarify in which aspects the present invention has made improvements.

[0081] The basic training method for existing PINNs is as follows: input the coordinates of the training configuration points into the network, perform forward propagation to obtain the flow field prediction values; use automatic differentiation (usually reverse mode automatic differentiation, ReverseModeAD) to calculate the partial derivatives of the flow field prediction values ​​with respect to the coordinates; substitute the partial derivatives into the governing equations (such as the Navier-Stokes equations) to calculate the PDE residuals; construct a total loss function that includes PDE residual loss, boundary condition loss, and initial condition loss; use an optimizer (usually the Adam optimizer) to update the network parameters using gradient descent to minimize the total loss function; repeat the above steps until the loss converges.

[0082] The main problems with existing PINN training methods include: the network is a single fully connected MLP with serious parameter redundancy; the use of inverse mode automatic differentiation is not computationally efficient when the input dimension is low and the output dimension is high; there is a lack of mechanisms for optimizing the network structure, and the network always maintains a fully connected structure during training; and the training strategy is simplistic and does not distinguish between training stages.

[0083] (4-2) The brain-inspired training mechanism of this invention. This invention independently applies brain-inspired modular training to each sub-network, driving each sub-network to gradually evolve from an initial fully connected structure into a minimally sparse network containing only a few key neurons and connections by introducing the following three mechanisms: (4-2-1) L1 sparsification regularization: An L1 penalty term (Lasso regularization) is introduced during subnetwork training. Its mathematical expression is:

[0084] in, The weights of all connections in the subnetwork. Represents the absolute value of the weight. for Regularization strength hyperparameter. L1 regularization promotes sparsity in the network weight matrix, with some weights approaching zero or even becoming completely zero during training, thereby eliminating redundant connections and enhancing the sparsity and modularity of the network.

[0085] The input to this regularization term is the total connection weights of the subnetwork. The output is a scalar loss value, which is added to the total loss function for optimization.

[0086] (4-2-2) Locality penalty based on neuron geometric coordinates: This invention innovatively assigns two-dimensional geometric coordinates to each neuron in the sub-network, integrating spatial location and distance information into the network architecture. The specific construction process is as follows: Coordinate system definition: Define a two-dimensional Euclidean space. ,in Dimension describes the horizontal distribution of neurons in the same layer. Dimensions distinguish different layers (the direction from the input layer to the hidden layer and then to the output layer), and the vertical distance between layers is fixed. .

[0087] Coordinate assignment: Assign coordinates to the j-th neuron in the i-th layer. Neurons within the same layer are evenly distributed in the interval [0,1], i.e. / (Total number of neurons in this layer); each layer in Arranged in tiers along the axis, .

[0088] Distance metric: The distance connecting the j-th neuron in layer i-1 to the k-th neuron in layer i is defined as:

[0089] Locality penalty function: Construct a locality penalty loss based on distance metric:

[0090] in, This is a hyperparameter for the intensity of locality regularization, which controls the degree of locality penalty. Cost of weighted connections: That is, for each connection, its distance d is multiplied by the absolute value of its weight. Multiply and then sum. The greater the distance and the larger the absolute value of the weight, the higher the cost. For the first Layer The weights from the i-th neuron to the k-th neuron in the i-th layer. This is the core regularization term for the locality penalty; L_b is the bias connection cost. The offset is only related to the fixed distance between layers. This is a simplification. Experiments have shown that this item is not decisive for the outcome and can be considered an option.

[0091] The effect of the locality penalty function is reflected in two aspects: first, sparsity, in the weights and biases. and The term is equivalent to Regularization suppresses small weights; secondly, locality is addressed by a distance metric, d, which penalizes long-distance connections, forcing functionally related neurons to cluster spatially, forming a biologically plausible brain-like structure. The input to this penalty term is the geometric coordinates and connection weights of all neurons in the subnetwork. The output is a scalar locality penalty loss value.

[0092] (4-2-3) Weighted pruning mechanism: To further simulate the sparse connectivity characteristics of biological neural networks, weight pruning is performed on subnetworks during training: when the absolute value of the weight of a connection falls below a preset threshold... (For example When a connection is not explicitly defined, its weight is forcibly set to zero, and gradient calculation for that connection is disabled, preventing it from being updated in subsequent training. Weight pruning eliminates redundant small weight connections, reducing the number of model parameters and computational cost.

[0093] The input to this operation is the current weight matrix of the subnetwork and the pruning threshold ε. The output is the pruned sparse weight matrix.

[0094] By combining the three mechanisms of L1 regularization, locality penalty, and weight pruning, the subnetwork will gradually evolve from a fully connected network to a sparse minimal network during training, reducing the number of parameters by more than 90%.

[0095] (4-3) Construction of the physical information loss function. The total loss function L constructed in this invention is defined as:

[0096] The detailed definitions of each loss term are as follows: PDE residual loss : This represents the mean square value of the residuals of the Navier-Stokes equations at the placement points within the computational domain. Specifically, the flow field predictions and their partial derivatives at each placement point are substituted into the dimensionless Navier-Stokes equations to calculate the residuals: Momentum equation residual =

[0097] Continuity equation residual =

[0098] Let be the mean square value of the residuals over all internal configuration points. When this loss approaches zero, it indicates that the flow field predicted by the network satisfies the Navier-Stokes equations.

[0099] The input to this loss term is the network's flow field predictions at the internal configuration points. It also includes the partial derivatives of each order with respect to x, y, z, and t. The output is a scalar PDE residual loss value.

[0100] Initial condition loss : Initial time The mean square error between the network prediction and the given initial conditions:

[0101] in Configure the network with predicted values ​​(velocity and stress) at the points at the initial time. Given initial values. The network uses the coordinates of the initial time point. The forward propagation is performed to obtain the predicted value. Then, the error is calculated by comparing it with the known initial value.

[0102] The input to this loss term is the network prediction at the initial conditional configuration point and the given initial conditional true values. The output is a scalar initial conditional loss value.

[0103] Boundary condition loss : The mean square error between the network predictions at the boundary and the given boundary conditions comprises two parts: the Dirichlet boundary and the Newman boundary.

[0104] The first term is the normal derivative error of the Newman boundary condition (such as the outlet pressure gradient), and the second term is the value error of the Dirichlet boundary condition (such as the inlet velocity and the zero velocity at the wall). This represents the derivative along the direction of the boundary normal. The network obtains the predicted values ​​at the boundary by performing forward propagation along the coordinates of the boundary points. Then, compared with the given boundary condition values Compare them.

[0105] The input to this loss term is the network prediction (and its normal derivative) at the boundary placement points and the given boundary condition values. The output is a scalar boundary condition loss value.

[0106] Data loss (Optional): In solving forward problems, if some experimental measurement data or high-fidelity numerical simulation data are available, a data-driven loss term can be added:

[0107] in and For network prediction speed and stress, and The data is the known observation data. The data loss term is necessary in solving inverse problems (such as parameter identification).

[0108] The input to this loss term is the network prediction value and the known observation data at the data points. The output is a scalar data loss value.

[0109] Brain-like optimization loss :

[0110] That is, the above The sum of regularization loss and locality penalty loss. This loss term drives the network structure to evolve towards sparsity and brain-like characteristics.

[0111] The input to this loss term is all the weights, biases, and neuron coordinates of the subnetwork. The output is a scalar brain-like optimization loss value.

[0112] Weighting coefficient : Weighting coefficients before each loss item , , , , This is used to balance the convergence contributions of different physical constraints and brain-like constraints. The values ​​of the weighting coefficients need to be determined through empirical optimization and dynamically adjusted during the phased training process.

[0113] The input to the total loss function consists of the five loss values ​​mentioned above and their weight coefficients. The output is a scalar total loss value L, which drives the optimizer to update the network parameters.

[0114] (4-4) Efficient differentiation based on forward mode automatic differentiation. Constructing the PDE residual loss requires calculating the partial derivatives of the flow field variables with respect to spatial and temporal coordinates (e.g., , , Traditional PINNs typically use Reverse Mode Automatic Differentiation (Reverse Mode AD) to calculate partial derivatives. The computational complexity of Reverse Mode AD is proportional to the output dimension, which is inefficient when the output dimension is much larger than the input dimension.

[0115] Given that the input to each subnetwork in BIS-PINNs is a one-dimensional scalar (x, y, z, or t), while the output is a high-dimensional feature vector (with dimensions of k×r, up to 128 dimensions or higher), this invention employs ForwardModeAD instead of BackwardModeAD to calculate partial derivatives. The computational complexity of ForwardModeAD is proportional to the input dimension. For subnetwork structures with an input dimension of 1 and an output dimension much greater than 1, only one forward propagation is needed to simultaneously obtain all partial derivatives of the output with respect to that dimension of the input, resulting in significantly higher computational efficiency than BackwardMode.

[0116] Specifically, performing forward-mode AD on each subnetwork allows for the efficient calculation of the first and second partial derivatives of all k×r output components of that subnetwork with respect to its scalar input in a single operation. These partial derivatives are then combined through tensor decomposition and fusion to obtain the flow field variables. The required partial derivatives with respect to x, y, z, t are used to construct the residual terms of the Navier-Stokes equations (including convection terms, viscous diffusion terms, pressure gradient terms, and continuity equation residuals).

[0117] The input to this step is the forward propagation results of each sub-network, and the output is the first and second partial derivatives of the flow field variables with respect to each coordinate dimension, which are used to construct the PDE residuals.

[0118] In another implementation, a phased training strategy is adopted, in which the modular sub-network set is subjected to brain-inspired training based on the total loss function in the initial fitting stage, the sparse evolution stage, and the fine-tuning stage, respectively. This enables the modular sub-network set to fit the characteristics of the flow field, resulting in a brain-inspired separable physical information neural network. The initial fitting stage, the sparse evolution stage, and the fine-tuning stage are divided by a preset iteration number threshold, as detailed in (4-5) to (4-7) below: (4-5) Phased training strategy.

[0119] This invention employs a three-stage training process: initial fitting, sparse evolution, and fine-tuning. At different training stages, the weights of each regularization term and the pruning strategy are dynamically adjusted to achieve adaptive evolution of the subnetwork from fully connected to sparse and minimalist.

[0120] Phase 1: Initial fitting (approximately 50,000-100,000 iterations).

[0121] Training objective: To enable the network to initially learn the main structural features and low-frequency features of the flow field.

[0122] Training strategy: Use low-intensity L1 penalty ( Set to a smaller value, such as 1e-4) and low-intensity locality penalty ( (Set to a smaller value) to allow the network to initially fit the flow field while maintaining sufficient expressive power. No weight pruning is performed at this stage. PDE residual loss, boundary condition loss, and initial condition loss are the main driving forces.

[0123] Key note: The local penalty at this stage should not be too large, to avoid suppressing the network's ability to capture high-frequency features due to excessively strong penalties in the early stages of training, which would lead to a decrease in training accuracy.

[0124] Phase switching condition: When the network has completed the initial fitting of the main structure of the flow field (which can be judged by observing the downward trend of the total loss), it enters the second phase.

[0125] The input for this stage is the configuration point data and the initial network parameters. The output is the network parameters after preliminary training (still a fully connected or near-fully connected structure).

[0126] Second stage: Sparse evolution (approximately 100,000-200,000 iterations).

[0127] Training objective: To drive the subnetwork to evolve from a fully connected structure to a sparse and minimalist structure, which is the core stage of brain-like optimization.

[0128] Training strategy: Increase the intensity of L1 penalty (increase) ) and local penalty intensity (increase) At the same time, a weight pruning mechanism is activated (weights with absolute values ​​below a threshold are pruned). (The connections are set to zero). In the previous stage, the network has captured the main characteristics of the flow field. In this stage, the network is forced to remove redundant connections, so that the network topology evolves into a sparser form that is adapted to the physics of the flow (such as boundary layer structure, vortex structure).

[0129] Phase switching conditions: When the PDE residual decrease rate is less than 1e-3 or the verification error tends to stabilize, the third phase is entered.

[0130] The input to this stage is the network parameters output from the first stage and the enhanced regularization hyperparameters. The output is the sub-network parameters after sparse evolution (a large number of connections have been pruned).

[0131] Phase 3: Fine-tuning (approximately 50,000 iterations or until loss convergence).

[0132] Training objective: To fine-tune the evolved minimalist sparse structure to precisely satisfy physical conservation laws and boundary conditions.

[0133] Training strategy: Reduce the intensity of L1 penalty (reduce) ), you can choose to enable bias penalty ( This stage involves fine-tuning the weights and biases retained in the solidified sparse structure. The primary focus of this stage is improving the accuracy of the PDE residuals and the degree to which boundary / initial conditions are met.

[0134] Stage switching condition: Total loss converges or the preset iteration limit is reached.

[0135] The input to this stage is the sparse network parameters output from the second stage and the reduced regularization hyperparameters. The output is the final trained BIS-PINNs network parameters. In one implementation, see [link to implementation details]. Figure 4 The diagram shows the changes in network topology resulting from a neuromorphic optimization, where the subnetwork gradually transforms from a fully connected network into a sparse minimal network, further reducing the number of network parameters.

[0136] (4-6) Optimizer selection and configuration. Existing PINNs typically use the Adam optimizer (adaptive learning rate optimizer), with a learning rate usually set to 1e-3, combined with a learning rate decay strategy. Some PINN schemes switch to the L-BFGS optimizer (quasi-Newton method) for fine-tuning during the later stages of Adam training.

[0137] The optimizer configuration of this invention: This invention also uses the Adam optimizer as the main optimizer, but employs different learning rate configurations at different training stages: The first stage (preliminary fitting) uses a large initial learning rate (e.g., 1e-3) and employs a cosine annealing or exponential decay learning rate scheduling strategy to help the network quickly converge to the basic structure of the flow field.

[0138] The second stage (sparse evolution): appropriately reduce the learning rate (e.g., from 5e-4 to 1e-4) to perform structural evolution with a finer step size, avoiding excessive gradient updates that could destroy the already formed sparse structure.

[0139] The third stage (fine-tuning): Further reduce the learning rate (e.g., from 1e-4 to 1e-5), and you can choose to switch to the L-BFGS optimizer for fine-tuning to obtain more accurate convergence results.

[0140] The optimizer configuration at each stage can be adjusted according to the specific problem and convergence status. The selection of the optimizer and the learning rate scheduling strategy play an important role in the phased training of this invention, coordinating with the changes in regularization intensity and promoting the evolution of the network structure.

[0141] The inputs for this step are the total loss function value and the current network parameters. The output is the updated network parameters.

[0142] (4-7) Training Process Summary. Combining the above parts, the complete training process of this invention is as follows: (4-7-1) Initialize the four sub-networks into a fully connected MLP structure, and initialize all connection weights and biases.

[0143] (4-7-2) Load the collected configuration point data, boundary condition constraint point data and initial condition constraint point data.

[0144] (4-7-3) Enter the first stage of training (preliminary fitting), and execute the following loop: Input the coordinates of the configuration points into the four sub-networks respectively, perform forward propagation, and obtain the output feature vectors of each sub-network.

[0145] The flow field prediction values ​​at each configuration point are calculated by tensor decomposition-based feature fusion. .

[0146] Automatic differentiation is employed in forward mode to calculate the partial derivatives of the flow field predictions with respect to x, y, z, and t.

[0147] Calculate the PDE residual loss, initial condition loss, boundary condition loss, data loss (if any), and neuromorphic optimization loss.

[0148] The total loss L is obtained by weighting and summing the values ​​according to the weighting coefficients.

[0149] Backpropagation is performed using the Adam optimizer to update all parameters of the four sub-networks.

[0150] Repeat the above process until the conditions for the first phase of switching are met.

[0151] (4-7-4) Enter the second stage of training (sparse evolution), increase the intensity of L1 and locality penalty, start weight pruning, and continue training until the conditions for switching to the second stage are met.

[0152] (4-7-5) Enter the third stage of training (fine-tuning), reduce the L1 penalty, fine-tune the weights and biases, and train until the loss converges.

[0153] (4-7-6) Training is complete, and the final trained BIS-PINNs network is obtained.

[0154] (5) Predict the flow field using the trained BIS-PINNs network. After training, the trained BIS-PINNs network is used to predict the flow field of the spillway under various operating conditions. The prediction process is as follows: 1. Determine the parameters such as upstream water level, downstream water level and gate opening according to the operating conditions to be predicted, and calculate the boundary condition parameters such as inlet velocity and outlet pressure accordingly; 2. Generate a prediction point grid in the computational domain. The prediction points can be set according to the actual required spatial and temporal resolution, or they can be consistent with the training; 3. Input the coordinates (x, y, z, t) of each prediction point into the four trained sub-networks respectively, and each sub-network performs forward propagation to output feature vectors; 4. Calculate the predicted values ​​of the flow field variables at each prediction point through tensor decomposition feature fusion. 5. Output the prediction results, including the three components of the velocity field. and pressure field The distribution that varies over time throughout the entire computational domain.

[0155] In practical applications, a certain water conservancy project has a controlled drainage area of ​​approximately 62,700 square kilometers. It is a comprehensive water conservancy project with flood control as its main function, while also taking into account power generation and navigation. The project has 18 spillway gates and overflow dam sections.

[0156] Engineering parameters include: model simulation range: river section from 630 meters upstream to 720 meters downstream; upstream water level range: 36-46m; downstream water level range: 32-42m; gate opening range: 0-16m, with a total of 18 gates that can be combined to form different discharge conditions; fluid density. (Water); kinematic viscosity .

[0157] Data sources: General layout engineering documents of the hub (providing geometric information); cross-sectional view of the spillway chamber (providing detailed chamber structural dimensions); measured water level data from hydrological stations (the measuring points are approximately 630 meters upstream and 720 meters downstream of the spillway, used to verify the inlet and outlet boundary conditions).

[0158] Network structure parameters: 4 independent subnetworks, processing x, y, z, and t dimensions respectively; each subnetwork has 5 hidden layers, each with 64 neurons, using the Tanh activation function; rank parameter r = 64; output layer dimension k × r = 4 × 64 = 256; locant points: Number of boundary and initial condition constraint points: Approximately [number] in total; Individual; pruning threshold .

[0159] The training parameters are shown in Table 1 below: Table 1

[0160] Prediction Results: Using the trained BIS-PINNs network, flow field predictions were performed for the following typical operating conditions: Typical operating condition 1: Upstream water level 42m, downstream water level 36m, gate No. 9 fully open (16m opening), all other gates closed. The prediction results include the three-dimensional velocity and pressure field distributions upstream of the gate, inside the gate opening, and in the downstream energy dissipation zone. The predicted maximum longitudinal velocity at the gate opening is approximately 8.5m / s.

[0161] Typical operating condition 2: Upstream water level 46m, downstream water level 38m, all 18 gates are discharging water uniformly at an opening of 8m. The predicted flow velocity distribution in each gate is basically uniform, with an average longitudinal flow velocity of approximately 5.2m / s. The relative error between the predicted total discharge and the measured value at the hydrological station is less than 7%.

[0162] Extreme Condition 3: Upstream water level 46m (design maximum water level), downstream water level 32m (minimum water level), all gates fully open. The predicted maximum flow velocity at the gate openings is approximately 12.3m / s.

[0163] Performance: Computational efficiency: Thanks to the separable modular subnetwork structure, the computational complexity of forward propagation is reduced from that of traditional PINNs. Reduced to After neuromorphic optimization, the number of subnetwork parameters is reduced by more than 90%, and the time taken for a single forward prediction is less than 0.1 seconds on a consumer-grade GPU (such as NVIDIA RTX 4090), which can meet the timeliness requirements of real-time flow scheduling auxiliary decision-making.

[0164] Prediction accuracy: Under the above typical working conditions, the relative error (L2 norm) between the flow field prediction results and the high-fidelity CFD numerical simulation results is within 5%; compared with the measured water level data of the hydrological station, the relative error of the predicted water level is less than 7%.

[0165] Structural compression ratio: After three stages of brain-like optimization training, the effective number of connections in each sub-network is only 5%-10% of that in the initial fully connected state. The network structure is simplified but retains the ability to capture key flow field features.

[0166] Generalization ability: The trained network can perform interpolation prediction within the parameter space of upstream water level 36-46m, downstream water level 32-42m, and gate opening 0-16m, and can quickly obtain the flow field distribution under different working conditions without retraining.

[0167] In summary, the present invention has the following significant advantages: 1. Significantly improved computational efficiency: Combining a brain-inspired separable architecture with forward-mode automatic differentiation reduces the computational complexity and memory footprint of solving high-dimensional transient flow problems by several orders of magnitude. Independent subnetworks reduce complexity from... Down to The sparse subnetwork further reduces the number of parameters, making it possible to perform fast flow field prediction on a single consumer-grade GPU using PINNs, breaking through the bottleneck of low computational efficiency and slow convergence of traditional PINNs.

[0168] 2. Maintaining Accuracy and Physical Consistency: The simplified network structure evolved from the brain-inspired mechanism is not simply a pruning, but retains the ability to capture key physical features. The simplified subnetworks maintain the general approximation ability of neural networks. The sparsity of the network reduces the risk of overfitting, making the solution more closely match physical laws, especially exhibiting better numerical stability when simulating complex flow phenomena. In addition, the evolved subnetwork structure is visualized, which provides a new way to understand the inner working mechanism of neural networks and the physics of flow.

[0169] 3. Strong flexibility and practicality: Although the configuration points need to be structured, the method is essentially meshless. For complex geometries, it can be combined with traditional PINNs and neuromorphic optimization for hybrid computation, which can significantly improve computational efficiency and reduce computational complexity. This invention is suitable for rapid prediction, parameterization study, and inverse problem solving of the flow field of spillway gates in hydraulic engineering projects, and can provide an efficient auxiliary decision-making tool for spillway scheduling and engineering design.

[0170] Regarding the brain-inspired sluice gate flow field prediction method provided in the foregoing embodiments, this invention provides a brain-inspired sluice gate flow field prediction device. (See also...) Figure 5 The diagram shows a structural schematic of a brain-inspired sluice gate flow field prediction device, which includes the following components: The data acquisition module 502 acquires the calculation domain of the spillway gate, as well as the boundary conditions, initial conditions, and control equations of the calculation domain, and collects training data, which includes: configuration points within the calculation domain, boundary constraint points, and initial condition constraint points. The mesh construction module 504 processes each dimension of the coordinate values ​​in the training data through a set of independent modular sub-networks to obtain a set of feature vectors, and performs tensor decomposition-based feature fusion processing on the set of feature vectors to obtain the predicted values ​​of the flow field variables. Model training module 506 constructs a total loss function using the predicted values ​​of flow field variables, boundary conditions, initial conditions, and control equations. Based on the total loss function, it performs brain-inspired training on the modular sub-network set to obtain a brain-inspired separable physical information neural network. This brain-inspired separable physical information neural network is then used to predict the flow field of the spillway gate under different operating conditions to obtain the target prediction result.

[0171] The brain-inspired sluice gate flow field prediction device provided in this application embodiment can significantly improve prediction efficiency and prediction accuracy.

[0172] In one embodiment, during the step of collecting training data, the data acquisition module 502 is further configured to: acquire the sampling range of the longitudinal dimension, transverse dimension, water depth dimension, and time dimension of the river channel; and based on the sampling range, perform Latin hypercube sampling in each dimension to obtain the corresponding sampling coordinate values; combine the sampling coordinate values ​​through Cartesian product to obtain a four-dimensional structured configuration point set, and determine the four-dimensional structured configuration point set as the configuration points within the computational domain; perform sampling processing on the boundary surface of the computational region to generate boundary constraint points, and perform sampling processing at the initial moment of the computational region to generate initial condition constraint points, so as to determine the training data based on the configuration points within the computational domain, the boundary constraint points, and the initial condition constraint points.

[0173] In one embodiment, when performing the step of processing each dimension of the coordinate values ​​of the training data through a set of mutually independent modular sub-networks to obtain a set of feature vectors, the grid construction module 504 is further configured to: send the longitudinal coordinates of the river channel, the transverse coordinates of the river channel, the water depth coordinates, and the time coordinates of the coordinate values ​​of the training data to the corresponding modular sub-networks in the set of modular sub-networks, so as to process the longitudinal dimension information of the river channel, the transverse dimension information of the river channel, the water depth dimension information, and the time dimension information to obtain a set of feature vectors.

[0174] In one embodiment, when performing tensor decomposition-based feature fusion processing on the feature vector set to obtain the predicted values ​​of the flow field variables, the grid construction module 504 is further configured to: perform element-wise multiplication of the values ​​at the same rank position in the feature vector set corresponding to each flow field variable, and sum the products along the rank dimension to obtain the predicted values ​​of the corresponding flow field variables, wherein the flow field variables include: longitudinal flow velocity of the river channel, transverse flow velocity of the river channel, flow velocity in the water depth direction, and pressure field.

[0175] In one implementation, when constructing the total loss function using the predicted values ​​of flow field variables, boundary conditions, initial conditions, and governing equations, the model training module 506 is further configured to: determine the mean square value of the residuals of the points configured within the computational domain of the governing equations as the partial differential equation residual loss; compare the predicted values ​​of the flow field variables with the boundary conditions and initial conditions respectively, and calculate the boundary condition loss and initial condition loss; apply regularization constraints to the connection weights in the modular sub-network set to generate regularization loss, and determine the brain-like optimization loss based on the regularization loss; and perform weighted summation of the partial differential equation residual loss, boundary condition loss, initial condition loss, and brain-like optimization loss to obtain the total loss function.

[0176] In one implementation, when performing the step of determining the brain-like optimization loss based on regularization loss, the model training module 506 is further configured to: assign two-dimensional geometric coordinates to neurons in each modular sub-network, and perform loss value calculation based on the absolute values ​​of the distance between neurons and the connection weights to obtain the locality penalty loss; and determine the sum of the locality penalty loss and the regularization loss as the brain-like optimization loss.

[0177] In one embodiment, when performing the step of performing brain-inspired training on the modular sub-network set based on the total loss function to obtain a brain-inspired separable physical information neural network, the model training module 506 is further configured to: adopt a phased training strategy, and perform brain-inspired training on the modular sub-network set based on the total loss function in the preliminary fitting stage, the sparse evolution stage, and the fine-tuning stage, respectively, so that the modular sub-network set fits the characteristics of the flow field to obtain a brain-inspired separable physical information neural network, wherein the preliminary fitting stage, the sparse evolution stage, and the fine-tuning stage are divided by a preset iteration number threshold.

[0178] The device provided in this embodiment of the invention has the same implementation principle and technical effect as the aforementioned method embodiment. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0179] This invention provides a server, specifically, the server includes a processor and a storage device; the storage device stores a computer program, which, when run by the processor, executes the method described in any of the above embodiments.

[0180] Figure 6 This is a schematic diagram of the structure of a server provided in an embodiment of the present invention. The server 100 includes: a processor 60, a memory 61, a bus 62, and a communication interface 63. The processor 60, the communication interface 63, and the memory 61 are connected through the bus 62. The processor 60 is used to execute executable modules, such as computer programs, stored in the memory 61.

[0181] The memory 61 may include high-speed random access memory (RAM) or non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 63 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc.

[0182] Bus 62 can be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0183] The memory 61 is used to store programs. After receiving an execution instruction, the processor 60 executes the program. The method executed by the device for defining the flow process disclosed in any of the foregoing embodiments of the present invention can be applied to the processor 60 or implemented by the processor 60.

[0184] Processor 60 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 60 or by instructions in software form. Processor 60 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in memory 61. Processor 60 reads the information in memory 61 and, in conjunction with its hardware, completes the steps of the above method.

[0185] The computer program product of the readable storage medium provided in the embodiments of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the foregoing method embodiments. For specific implementation, please refer to the foregoing method embodiments, which will not be repeated here.

[0186] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0187] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A brain-inspired method for predicting the flow field of a sluice gate, characterized in that, The method includes: Obtain the computational domain of the spillway, as well as the boundary conditions, initial conditions, and governing equations of the computational domain, and collect training data, wherein the training data includes: configuration points within the computational domain, boundary constraint points, and initial condition constraint points; By using a set of independent modular sub-networks, each dimension of the coordinate values ​​in the training data is processed to obtain a set of feature vectors. Then, tensor decomposition feature fusion processing is performed on the set of feature vectors to obtain the predicted values ​​of the flow field variables. A total loss function is constructed using the predicted values ​​of the flow field variables, the boundary conditions, the initial conditions, and the control equations. Based on the total loss function, the modular sub-network set is subjected to brain-inspired training to obtain a brain-inspired separable physical information neural network. This brain-inspired separable physical information neural network is then used to predict the flow field of the spillway gate under different operating conditions to obtain the target prediction result.

2. The method for predicting the flow field of a sluice gate based on brain-inspired design, as described in claim 1, is characterized in that... The steps for collecting training data include: The sampling ranges of the longitudinal dimension, transverse dimension, water depth dimension, and time dimension of the river channel are obtained, and Latin hypercube sampling is performed in each dimension based on the sampling ranges to obtain the corresponding sampling coordinate values ​​of each dimension. The sampled coordinate values ​​are combined using a Cartesian product to obtain a four-dimensional structured configuration point set, and the four-dimensional structured configuration point set is determined as the configuration points within the computational domain; Sampling is performed on the boundary surface of the computational region to generate the boundary constraint points, and sampling is performed at the initial moment of the computational region to generate the initial condition constraint points, so as to determine the training data based on the configuration points inside the computational domain, the boundary constraint points, and the initial condition constraint points.

3. The method for predicting the flow field of a sluice gate based on brain-inspired design, as described in claim 1, is characterized in that... The step of processing each dimension of the coordinate values ​​of the training data through a set of independent modular sub-networks to obtain a set of feature vectors includes: The longitudinal, lateral, water depth, and time coordinates of the training data are sent to the corresponding modular subnetworks in the modular subnetwork set to process the longitudinal, lateral, water depth, and time dimension information of the river channel, thereby obtaining the feature vector set.

4. The method for predicting the flow field of a sluice gate based on brain-inspired design, as described in claim 1, is characterized in that... The step of performing tensor decomposition-based feature fusion processing on the feature vector set to obtain the predicted values ​​of the flow field variables includes: The values ​​at the same rank position in the feature vector set corresponding to each flow field variable are multiplied element by element, and the product is summed along the rank dimension to obtain the predicted value of the corresponding flow field variable. The flow field variables include: longitudinal flow velocity, transverse flow velocity, depth-direction flow velocity, and pressure field.

5. The method for predicting the flow field of a sluice gate based on brain-inspired design, as described in claim 1, is characterized in that... The step of constructing the total loss function using the predicted values ​​of the flow field variables, the boundary conditions, the initial conditions, and the governing equations includes: The mean square value of the residuals of the control equations at the points within the computational domain is determined as the residual loss of the partial differential equations. The predicted values ​​of the flow field variables are compared with the boundary conditions and the initial conditions, respectively, and the boundary condition loss and the initial condition loss are calculated. Regularization constraints are applied to the connection weights in the modular subnetwork set to generate a regularization loss, and a brain-like optimization loss is determined based on the regularization loss. The total loss function is obtained by weighted summation of the partial differential equation residual loss, the boundary condition loss, the initial condition loss, and the brain-like optimization loss.

6. The method for predicting the flow field of a sluice gate based on brain-inspired design, as described in claim 5, is characterized in that... The step of determining the brain-like optimization loss based on the regularization loss includes: Two-dimensional geometric coordinates are assigned to neurons in each modular subnetwork, and the loss value is calculated based on the distance between neurons and the absolute value of the connection weights to obtain the locality penalty loss. The sum of the locality penalty loss and the regularization loss is determined as the brain-like optimization loss.

7. The method for predicting the flow field of a sluice gate based on brain-inspired design, as described in claim 1, is characterized in that... The step of performing neuromorphic heuristic training on the modular subnetwork set based on the total loss function to obtain a neuromorphic heuristic separable physical information neural network includes: A phased training strategy is adopted, in which the modular sub-network set is subjected to brain-inspired training based on the total loss function in the preliminary fitting stage, the sparse evolution stage and the fine-tuning stage, respectively, so that the modular sub-network set fits the characteristics of the flow field and obtains the brain-inspired separable physical information neural network. The preliminary fitting stage, the sparse evolution stage and the fine-tuning stage are divided by a preset iteration number threshold.

8. A brain-inspired sluice gate flow field prediction device, characterized in that, The device includes: The data acquisition module acquires the calculation domain of the spillway gate, as well as the boundary conditions, initial conditions, and control equations of the calculation domain, and collects training data, wherein the training data includes: configuration points within the calculation domain, boundary constraint points, and initial condition constraint points; The grid construction module processes each dimension of the coordinate values ​​in the training data through a set of independent modular sub-networks to obtain a set of feature vectors, and performs tensor decomposition-based feature fusion processing on the set of feature vectors to obtain the predicted values ​​of the flow field variables. The model training module constructs a total loss function using the predicted values ​​of the flow field variables, the boundary conditions, the initial conditions, and the control equations. Based on the total loss function, it performs neuromorphic heuristic training on the modular sub-network set to obtain a neuromorphic heuristic separable physical information neural network. This neuromorphic heuristic separable physical information neural network is then used to predict the flow field of the spillway gate under different operating conditions to obtain the target prediction result.

9. A server, characterized in that, The method includes a processor and a memory, the memory storing computer-executable instructions executable by the processor, the processor executing the computer-executable instructions to implement the method of any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions that, when invoked and executed by a processor, cause the processor to perform the method according to any one of claims 1 to 7.

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