A lightning-caused forest fire numerical simulation method, system, device and medium based on a neural network

Abstract

The application belongs to the technical field of numerical simulation, and discloses a lightning-caused forest fire numerical simulation method, system, device and medium based on a neural network, which comprises the following steps: constructing a lightning-caused forest fire numerical simulation model based on observed physical quantities, constructing a fully connected neural network, wherein the input of the fully connected neural network is a coordinate point, and the output is a vector representation of an electric field and a magnetic field corresponding to the coordinate point; the coordinate point is a spatial coordinate and a time coordinate; a group of training coordinate point data is sampled in a definition domain; the sampled coordinate data is input into the fully connected neural network for classification prediction, and the fully connected neural network is trained according to a target loss function to obtain a trained fully connected neural network; and the distribution of the electric field and the magnetic field at any coordinate point in the definition domain is predicted based on the trained fully connected neural network. The technical scheme disclosed by the application can efficiently and accurately realize numerical simulation.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology, and in particular relates to a method, system, device and medium for numerical simulation of lightning-induced forest fires based on neural networks. Background Technology

[0002] Lightning strikes are one of the major causes of forest fires. Accurate simulation and prediction of the occurrence and development of lightning-induced forest fires are of great significance for forest resource protection and fire prevention.

[0003] Traditional numerical simulation methods based on physical equations (such as the finite difference method and the finite element method) face challenges in handling complex problems like lightning strikes and forest fires. They suffer from high computational complexity and low efficiency when dealing with complex boundary conditions and high-dimensional problems, and struggle to accurately satisfy physical constraints. Advances in deep learning technology have provided a new perspective for solving partial differential equations. Neural network-based solutions, by embedding the physical equations into a loss function and utilizing automatic differentiation to calculate derivatives, can directly approximate the solutions under meshless conditions. This approach not only overcomes the dependence on mesh generation in traditional methods but also demonstrates significant advantages in high-dimensional problems, complex boundary handling, and multiphysics coupling. Industry has begun exploring its application potential. For example, in the aerospace field, neural networks can be used to solve complex fluid dynamics equations to simulate airflow around an aircraft, enabling rapid and accurate prediction of aerodynamic characteristics. This helps optimize aircraft design, improve flight performance, and increase fuel efficiency. In the mechanical energy field, neural networks can be used to solve combustion and fluid dynamics equations to optimize engine combustion processes and intake / exhaust systems, enabling rapid prediction of engine performance parameters such as power and fuel consumption rate. This helps optimize engine design and improve engine efficiency and reliability. In electronic engineering, neural networks can be used to solve semiconductor physics equations to simulate the electrical characteristics and performance of devices, rapidly predicting current-voltage characteristics, and helping optimize device structural design and process parameters, thereby improving device performance and reliability. Against this backdrop, this invention applies neural networks to solve Maxwell's equations to efficiently and accurately simulate lightning-induced forest fires. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, device, and medium for numerical simulation of lightning-induced forest fires based on neural networks, in order to solve the problems existing in the prior art.

[0005] To achieve the above objectives, this invention provides a method for numerical simulation of lightning-induced forest fires based on neural networks, comprising:

[0006] A numerical simulation model of lightning-induced forest fires based on observed physical quantities is constructed. The numerical simulation model is Maxwell's equations in the form of first-order partial differential equations constructed within the domain based on periodic boundary conditions, initial conditions, and physical quantities.

[0007] A fully connected neural network is constructed, wherein the input of the fully connected neural network is a coordinate point, and the output is a vector representation of the electric field and magnetic field of the corresponding coordinate point; the coordinate point has spatial coordinates and time coordinates;

[0008] Sample a set of training coordinate point data within the defined domain;

[0009] The sampled coordinate data is input into the fully connected neural network for classification and prediction, and trained according to the target loss function to obtain a trained fully connected neural network.

[0010] The distribution of electric and magnetic fields at any coordinate point within the domain is predicted based on a trained fully connected neural network.

[0011] Optionally, the physical quantities include electric field and magnetic field.

[0012] Optionally, the numerical simulation model is specifically:

[0013]

[0014] In the formula, E is the electric field, B is the magnetic field, ρ is the charge density, ε0 ​​is the vacuum permittivity, J is the current density, and μ0 is the permeability. For divergence, t represents curl, and t represents the time coordinate.

[0015] Optionally, the training process of the fully connected neural network specifically includes:

[0016] Based on the quasi-random sampling method, a set of training coordinate point data is sampled within the domain. The training coordinate point data is input into a fully connected neural network, and the spatial and temporal partial derivatives corresponding to the output of the fully connected neural network are calculated. The spatial and temporal partial derivatives are then substituted into Maxwell's equations to calculate the residuals of each component.

[0017] Calculate the mean square error between the sampling points of the initial conditions and periodic boundary conditions and the output of the fully connected neural network, and construct the target loss function based on the calculated residuals and mean square errors;

[0018] The target loss function is minimized using the gradient descent optimization algorithm. The optimization process iteratively adjusts the network parameters until the residual approaches zero, thus completing the training of the fully connected neural network.

[0019] Optionally, the fully connected neural network is validated after training, specifically including:

[0020] After training is complete, select test coordinate points within the domain;

[0021] Input the test points into the trained fully connected neural network to obtain the predicted values;

[0022] By visualizing the spatiotemporal distribution of predicted values, the predicted values ​​are compared with analytical or numerical solutions to evaluate accuracy and physical precision.

[0023] A neural network-based numerical simulation system for lightning-induced fires includes:

[0024] The numerical model construction module is used to construct a numerical simulation model of lightning-induced forest fires based on observed physical quantities. The numerical simulation model is Maxwell's equations in the form of first-order partial differential equations constructed based on periodic boundary conditions, initial conditions, and physical quantities within the domain.

[0025] The prediction model training module is used to construct a fully connected neural network. The input of the fully connected neural network is a coordinate point, and the output is a vector representation of the electric field and magnetic field of the corresponding coordinate point. The coordinate point has spatial coordinates and time coordinates. A set of training coordinate point data is sampled within the domain. The sampled coordinate data is input into the fully connected neural network for classification and prediction, and trained according to the target loss function to obtain a trained fully connected neural network.

[0026] The numerical simulation module for lightning-induced forest fires is used to predict the distribution of electric and magnetic fields at any coordinate point within the defined domain based on a trained fully connected neural network.

[0027] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor running the computer program to enable the electronic device to perform the aforementioned neural network-based numerical simulation method for lightning-induced forest fires.

[0028] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned neural network-based numerical simulation method for lightning-induced forest fires.

[0029] The technical effects of this invention are as follows:

[0030] This invention constructs a numerical simulation model of lightning-induced forest fires based on observed physical quantities. The mathematical model is Maxwell's equations constructed on the domain of periodic boundary conditions. A physical information neural network is used to solve the partial differential equations, and the mean square error function is used to calculate the residual loss. Automatic differentiation is used to replace the traditional numerical method of constructing differences. The simulation results characterize the convergence trend of the numerical solution of the mathematical model. This embodiment can achieve numerical simulation efficiently and accurately. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0033] Figure 1 This is a flowchart illustrating the implementation of this invention.

[0034] Figure 2 This is a structural diagram of the neural network in an embodiment of the present invention;

[0035] Figure 3 This is a graph showing the change of the loss function during the training of the neural network in an embodiment of the present invention;

[0036] Figure 4 This is a comparison diagram between the solution obtained by using a neural network to solve the equation in an embodiment of the present invention and the standard solution;

[0037] Figure 5 This is a schematic diagram illustrating the mean square error between the predicted solution and the standard solution in an embodiment of the present invention. Detailed Implementation

[0038] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0039] It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the invention. Furthermore, with respect to numerical ranges in this invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Every smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included in this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0040] Various modifications and variations can be made to the specific embodiments described in this specification without departing from the scope or spirit of the invention, as will be apparent to those skilled in the art. Other embodiments derived from this specification will also be obvious to those skilled in the art. This application specification and embodiments are merely exemplary.

[0041] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0042] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] like Figure 1 As shown in the figure, this embodiment provides a method for numerical simulation of lightning-induced forest fires based on neural networks, including: constructing a numerical simulation model of lightning-induced forest fires based on observed physical quantities, wherein the numerical simulation model is a Maxwell equation in the form of a first-order partial differential equation constructed within a domain based on periodic boundary conditions, initial conditions, and physical quantities; constructing a fully connected neural network, wherein the input of the fully connected neural network is a coordinate point, and the output is a vector representation of the electric field and magnetic field of the corresponding coordinate point; the spatial coordinates and time coordinates of the coordinate point; sampling a set of training coordinate point data within the domain; inputting the sampled coordinate data into the fully connected neural network for classification and prediction, and training it according to a target loss function to obtain a trained fully connected neural network; and predicting the distribution of the electric field and magnetic field at any coordinate point within the domain based on the trained fully connected neural network.

[0044] This embodiment provides a numerical simulation method for lightning-induced forest fires based on the ARC-PINN physical information neural network, belonging to the field of numerical simulation. The method includes: constructing a numerical simulation model of lightning-induced forest fires based on observed physical quantities; the mathematical model is Maxwell's equations constructed on the domain of periodic boundary conditions; using a physical information neural network to solve the partial differential equations, and using a mean square error function to calculate the residual loss; using automatic differentiation to replace the traditional numerical method of constructing differences; the simulation results characterize the convergence trend of the numerical solution of the mathematical model; this embodiment can achieve numerical simulation efficiently and accurately.

[0045] The purpose of this embodiment is to provide a numerical simulation method for lightning-induced forest fires based on the ARC-PINN physical information neural network, which can efficiently achieve numerical simulation.

[0046] To achieve the above objectives, this embodiment provides the following solution:

[0047] Problem definition and physical model: The model is Maxwell's equations with periodic boundary conditions, constructed based on observed physical quantities related to lightning strikes and forest fires.

[0048] Maxwell's equations, specifically including:

[0049]

[0050] Where E is the electric field, B is the magnetic field, ρ is the charge density, J is the current density, ε0 ​​is the vacuum permittivity, and μ0 is the permeability. Maxwell's equations involve vector fields (E, B), and vector operations (divergence) are used. curl This makes them more complex than scalar partial differential equations. The electric field E is the function to be solved in the equation.

[0051] The initial condition is E x (x,y,0)=sin(πx),E y (x,y,0)=0,B z (x,y,0),

[0052] The periodic boundary condition is u(0,y,t)=u(1,y,t).

[0053] Sampling point allocation: The sampling point allocation method generates random points within the defined domain, specifically implemented using PyTorch's `torch.rand` function. This method belongs to uniform random sampling.

[0054] The number of PDE residuals (xyt_pde) is N. p =10000, with a domain of (Ω = [0,1]×[0,1]×[0,0.5]) (corresponding to x, y, t). The specific process involves using the `torch.rand` function to generate a 10000×3 tensor, with each element uniformly and randomly distributed in the interval [0,1). The tensor is then multiplied by `torch.tensor([1.0,1.0,0.5])` to scale the time dimension to [0,0.5], while keeping x and y within [0,1]. This results in sampling points uniformly distributed throughout the entire three-dimensional spacetime.

[0055] Building neural networks: such as Figure 2 As shown, the ARC_PINN neural network is a multilayer perceptron (MLP) consisting of one input layer, three hidden layers, and one output layer.

[0056] The input layer is a linear layer with an input dimension of 3, corresponding to spatial coordinates x, y and time coordinate t, representing the spatial and temporal dimensions in a two-dimensional problem. The output dimension is 50, mapping the 3-dimensional features of the input to a 50-dimensional feature space, providing greater expressive power for subsequent nonlinear transformations.

[0057] The hidden layer has three layers, each consisting of a fully connected layer and a Tanh activation function layer. Each hidden layer has 50 neurons, and each fully connected layer recombines the 50-dimensional features from the previous layer to form a new feature representation. This linear mapping allows the network to explore different linear combinations of the input space. The nonlinear activation function layer introduces the Tanh activation function, enabling the network to capture nonlinear patterns (such as the sinusoidal shape of fluctuations) in the solutions to Maxwell's equations. The three hidden layers increase the depth of the network; deep networks have stronger expressive power than single-layer networks and can better fit the higher-order features of partial differential equations. Here, the deep neural network progressively constructs complex E values ​​from spatiotemporal coordinates (x, y, t). x E y B z distributed.

[0058] The output layer has 3 neurons that map the high-dimensional features (50-dimensional) extracted from the hidden layer back to the electromagnetic field components (3-dimensional) in physical space, representing E. x E y B z These directly correspond to the variables in Maxwell's equations and are used to calculate physical residuals and satisfy initial and boundary conditions.

[0059] Constructing the Loss Function: When using the ARC-PINN deep neural network to solve Maxwell's equations, constructing the loss function is a core part, incorporating physical constraints, initial conditions, and boundary conditions into the neural network's training process. The training objective of the neural network is to minimize the loss function. This loss function comprises several parts:

[0060] Construct the total loss function, in the form L = L PDE +λ1L IC +λ2L BC L PDE L is the mean square sum of the residuals of the equation. IC and L BC λ1 and λ2 are the mean square errors of the initial and boundary conditions, and λ1 and λ2 are weighting factors.

[0061] PDE Residual Loss: This part of the loss calculates the difference between the model's predicted solution and the actual physical equations, ensuring that the physical quantities output by the neural network satisfy the dynamic relationships of Maxwell's equations. The specific PDE residual loss is as follows:

[0062]

[0063] in N p =10000 represents the number of sampling points.

[0064] Initial condition residual loss: Ensures the network output conforms to the physical initial state at (t=0). The initial condition is E. x (x,y,0)=sin(πx),E y (x,y,0)=0,B z (x,y,0). The specific initial condition residual loss is as follows.

[0065]

[0066] Where N ic =1000 represents the number of sampling points.

[0067] Boundary condition loss: This part of the loss calculates the error due to the boundary conditions. The network needs to satisfy predefined boundary conditions, meaning that at given boundaries (x=0) and (x=1), the neural network output should be consistent, reflecting periodic physical constraints. The periodic boundary condition is u(0,y,t) = u(1,y,t). The specific boundary condition loss is as follows:

[0068]

[0069] Where N bc =1000 represents the number of sampling points.

[0070] The total loss function is Loss = Loss PDE +Loss ic +Loss bc .

[0071] Automatic differentiation for calculating derivatives: Automatic differentiation is a core technique for calculating residuals in solving Maxwell's equations using ARC-PINN deep neural networks. It is an efficient and accurate differentiation method widely used in deep learning and scientific computing, especially in embedding physical constraints in physical information neural networks.

[0072] This is implemented using PyTorch's `torch.autograd.grad` function, employing a reverse mode to extract E from the neural network output. x E y E y Calculate the partial derivatives with respect to inputs x, y, t. The calculation process is based on the chain rule and computational graphs to ensure accuracy and efficiency, directly supporting the construction and optimization of Maxwell's equation residuals.

[0073] Training the Neural Network: In solving Maxwell's equations using the ARC-PINN neural network, training the network is an iterative process based on gradient optimization. The aim is to adjust the network parameters by minimizing the loss function so that the output satisfies the physical equations, initial conditions, and boundary conditions. The training objective is to adjust the neural network parameters (weights and biases) to achieve a loss function Loss = Loss PDE +Loss ic +Loss bc The loss function should be as close to zero as possible. It consists of three parts: PDE residuals, initial condition residuals, and boundary condition residuals. During training, the Adam optimizer is used to optimize the network parameters. The Adam (Adaptive Moment Estimation) optimizer is a commonly used optimization algorithm that adaptively adjusts the learning rate of each parameter, thereby accelerating convergence. Specific steps include:

[0074] Initialize the network and optimizer, using the Adam optimizer; set the learning rate lr = 0.001 and control the parameter update step size; generate sampling points using random sampling; train for 100,000 iterations; update parameters; save the network.

[0075] like Figure 3 As shown, the loss function value decreases with the increase of training iterations.

[0076] Solving the equation and verifying:

[0077] After the network is trained, it can make predictions on new input data (i.e., predict the corresponding electric field given new spatial and temporal coordinates). The performance of the model can be evaluated by comparing the prediction results of the neural network with the true solution.

[0078] The data is plotted using the Matplotlib library to visualize the distribution of physical fields through numerical simulation. For example... Figure 4 As shown, the solution obtained using the ARC-PINN deep neural network is close to the standard solution with a small error. Figure 5 As shown, by calculating the mean square error between the predicted solution and the standard solution, the accuracy is obtained as 91.49%. Numerical simulation experiments show that the numerical solution of this algorithm has stable convergence and high accuracy.

[0079] This invention provides a high-precision numerical simulation algorithm based on observed physical quantities related to lightning strikes and forest fires. For Maxwell's equations with periodic boundary conditions, automatic differentiation technology is used to replace traditional numerical algorithms, and a physical information neural network is used to numerically solve the equations. The residual loss is calculated through the mean square error function. Numerical simulation experiments show that the numerical solution of this algorithm has stable convergence and high accuracy.

[0080] An ARC-PINN neural network is constructed to analyze the mathematical model. Physical constraints are satisfied through loss function embedding. The partial derivatives are calculated using the automatic differentiation of the neural network to evaluate the residuals of the equations. The gradient descent optimization algorithm is used to make the residuals approach zero to obtain the analysis results. After training, test points are selected in Ω and input into the network to obtain predicted values. The spatiotemporal distribution of the solution is visualized and compared with the analytical solution or numerical solution to evaluate the accuracy and physical accuracy.

[0081] This embodiment also provides a neural network-based numerical simulation system for lightning-induced fires, comprising:

[0082] The numerical model construction module is used to construct a numerical simulation model of lightning-induced forest fires based on observed physical quantities. The numerical simulation model is Maxwell's equations in the form of first-order partial differential equations constructed based on periodic boundary conditions, initial conditions, and physical quantities within the domain.

[0083] The prediction model training module is used to construct a fully connected neural network. The input of the fully connected neural network is a coordinate point, and the output is a vector representation of the electric field and magnetic field of the corresponding coordinate point. The coordinate point has spatial coordinates and time coordinates. A set of training coordinate point data is sampled within the domain. The sampled coordinate data is input into the fully connected neural network for classification and prediction, and trained according to the target loss function to obtain a trained fully connected neural network.

[0084] The numerical simulation module for lightning-induced forest fires is used to predict the distribution of electric and magnetic fields at any coordinate point within the defined domain based on a trained fully connected neural network.

[0085] In practice, this embodiment also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the aforementioned neural network-based numerical simulation method for lightning-induced forest fires.

[0086] In practice, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned neural network-based numerical simulation method for lightning-induced forest fires.

[0087] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A numerical simulation method for lightning-caused forest fires based on neural networks, characterized in that, include: A numerical simulation model of lightning-induced forest fires based on observed physical quantities is constructed. The numerical simulation model is Maxwell's equations in the form of first-order partial differential equations constructed within the domain based on periodic boundary conditions, initial conditions, and physical quantities. A fully connected neural network is constructed, wherein the input of the fully connected neural network is a coordinate point, and the output is a vector representation of the electric field and magnetic field of the corresponding coordinate point; the coordinate point has spatial coordinates and time coordinates; Sample a set of training coordinate point data within the defined domain; The sampled coordinate data is input into the fully connected neural network for classification and prediction, and trained according to the target loss function to obtain a trained fully connected neural network. The distribution of electric and magnetic fields at any coordinate point within the domain is predicted based on a trained fully connected neural network. The numerical simulation model is specifically as follows: ； In the formula, For electric field, It is a magnetic field. For charge density, The vacuum permittivity, For current density, Permeability, For divergence, For curl, Use time coordinates; The training process of the fully connected neural network specifically includes: Based on the quasi-random sampling method, a set of training coordinate point data is sampled within the domain. The training coordinate point data is input into a fully connected neural network, and the spatial and temporal partial derivatives corresponding to the output of the fully connected neural network are calculated. The spatial and temporal partial derivatives are then substituted into Maxwell's equations to calculate the residuals of each component. Calculate the mean square error between the sampling points of the initial conditions and periodic boundary conditions and the output of the fully connected neural network, and construct the target loss function based on the calculated residuals and mean square errors; The target loss function is minimized using the gradient descent optimization algorithm. The optimization process iteratively adjusts the network parameters until the residual approaches zero, thus completing the training of the fully connected neural network.

2. The method for numerical simulation of lightning-caused forest fires based on neural networks according to claim 1, characterized in that, The physical quantities include electric field and magnetic field.

3. The method for numerical simulation of lightning-caused forest fires based on neural networks according to claim 1, characterized in that, After the fully connected neural network is trained, it is validated, specifically including: After training is complete, select test coordinate points within the domain; Input the test points into the trained fully connected neural network to obtain the predicted values; By visualizing the spatiotemporal distribution of predicted values, the predicted values ​​are compared with analytical or numerical solutions to evaluate accuracy and physical precision.

4. A numerical simulation system for lightning-induced fire based on neural networks, using the method described in any one of claims 1-3, characterized in that, include: The numerical model construction module is used to construct a numerical simulation model of lightning-induced forest fires based on observed physical quantities. The numerical simulation model is Maxwell's equations in the form of first-order partial differential equations constructed based on periodic boundary conditions, initial conditions, and physical quantities within the domain. The prediction model training module is used to construct a fully connected neural network. The input of the fully connected neural network is a coordinate point, and the output is a vector representation of the electric field and magnetic field of the corresponding coordinate point. The coordinate point has spatial coordinates and time coordinates. A set of training coordinate point data is sampled within the domain. The sampled coordinate data is input into the fully connected neural network for classification and prediction, and trained according to the target loss function to obtain a trained fully connected neural network. The numerical simulation module for lightning-induced forest fires is used to predict the distribution of electric and magnetic fields at any coordinate point within the defined domain based on a trained fully connected neural network.

5. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores a computer program and the processor runs the computer program to enable the electronic device to perform a neural network-based numerical simulation method for forest fires according to any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, It stores a computer program, which, when executed by a processor, implements a neural network-based numerical simulation method for forest fires as described in any one of claims 1-3.

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