Shock wave front capturing method and system based on physical information neural network

Abstract

The application provides a shock wave front capturing method and system based on a physical information neural network, and relates to the technical field of computational fluid dynamics. The method comprises the following steps: obtaining target space-time coordinate data corresponding to a target explosion wave in a propagation process; inputting the target space-time coordinate data into an explosion shock wave front prediction model to obtain shock wave front information corresponding to the target explosion wave in the propagation process, which is output by the explosion shock wave front prediction model, wherein the explosion shock wave front prediction model is constructed based on an improved physical information neural network; and a physical loss function of the improved physical information neural network is constructed according to the Rayleigh-Hugoniot relation and compressible Euler equations with an artificial viscosity term. The application reduces the calculation complexity of the shock wave front while ensuring the prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of computational fluid dynamics, and in particular to a shock wave front capture method and system based on a physical information neural network. Background Technology

[0002] Shock wave front capture is of great significance in modern computational fluid dynamics (CFD). Its importance stems from the physical nature of shock waves as strong discontinuities. Accurate capture of shock waves has a decisive impact on numerical simulations in many fields such as aerospace and astrophysics.

[0003] Shock wave capture methods are the mainstream approach for capturing shock wave fronts. These methods treat the shock wave as part of an intrinsic solution, using the inherent dissipation of the numerical scheme itself to "smooth" and stably capture discontinuities. Among these, the artificial viscosity method requires manual parameter adjustment; the upwind scheme is based on characteristic theory and has a clear physical meaning; while high-resolution schemes such as Total Variation Diminishing (TVD), Essentially Non-Oscillatory (ENO), and especially Weighted Essentially Non-Oscillatory (WENO), attempt to maintain high-order accuracy in smooth regions while adaptively enhancing dissipation near the shock wave to ensure stability through complex nonlinear weighting mechanisms. Another path for capturing shock wave fronts is the shock wave assembly method, which treats the shock wave as a moving boundary and precisely connects the flow fields before and after the wave by solving the Riemann problem. Theoretically, this can yield perfectly sharp shock waves, but it is difficult to use in practical engineering calculations. These methods often require specialized knowledge of fluid dynamics and computational simulation skills, making them relatively difficult to use.

[0004] Therefore, there is an urgent need for a shock wave front capture method and system based on physical information neural networks to solve the above problems. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a shock wave frontal capture method and system based on a physical information neural network.

[0006] This invention provides a shock wave front detection method based on a physical information neural network, comprising:

[0007] Obtain the target's spatiotemporal coordinate data during the propagation of the target's explosion wave;

[0008] The target spatiotemporal coordinate data is input into the explosion shock wave front prediction model to obtain the shock wave front information corresponding to the target explosion wave during the propagation process, output by the explosion shock wave front prediction model. The explosion shock wave front prediction model is constructed based on an improved physical information neural network. The physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and the compressible Euler equation with an artificial viscosity term.

[0009] According to the present invention, a shock wave front capture method based on a physical information neural network is provided, wherein the explosion shock wave front prediction model is trained through the following steps:

[0010] Obtain the spatiotemporal coordinate data of the sample;

[0011] Based on the density field, velocity field, and pressure field corresponding to the spatiotemporal coordinate data of the samples, model label data is constructed.

[0012] Training data is constructed based on the sample spatiotemporal coordinate data and the model label data;

[0013] The improved physical information neural network is trained based on the training data and the physical loss function to obtain the explosion shock wave front prediction model.

[0014] According to the present invention, a shock wave front capture method based on a physical information neural network is provided, wherein the improved forward propagation formula of the physical information neural network is specifically as follows:

[0015] ;

[0016] in, This represents the input data of the first layer of the feedforward structure of the improved physical information neural network. The first part represents the feedforward structure of the improved physical information neural network. The input data of the layer, Indicates the weights of the hidden layer. Indicates the hidden layer bias. This represents the tan activation function.

[0017] According to the present invention, a shock wave front capture method based on a physical information neural network is provided, wherein the physical loss function includes a first loss function, a second loss function, a third loss function, and a fourth loss function, wherein:

[0018] The first loss function is constructed based on the compressible Euler equation with an artificial viscosity term;

[0019] The second loss function is constructed based on the Rayleigh-Hugo Newton relation;

[0020] The third loss function is constructed based on the boundary conditions of the explosion wave propagation process;

[0021] The fourth loss function is constructed based on the initial conditions corresponding to the explosion wave at the initial moment.

[0022] According to the shock wave front capture method based on a physical information neural network provided by the present invention, the formula of the physical loss function is as follows:

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[0036] in, Represents the physical loss function; This represents the first loss function. This represents the weight value corresponding to the first loss function; This represents the second loss function. This represents the weight value corresponding to the second loss function; This represents the third loss function. This represents the weight value corresponding to the third loss function; This represents the fourth loss function. This represents the weight value corresponding to the fourth loss function; This represents the total number of spatiotemporal coordinates in the first loss function. This represents the supercoefficient corresponding to the first loss function. Represents the fluid velocity gradient; In the first loss function, the first... Space variables and the Time variables The corresponding mass conservation equation, In the first loss function, the first... Space variables and the Time variables The corresponding momentum conservation equation, In the first loss function, the first... Space variables and the Time variables The corresponding energy conservation equation, Indicates fluid density, Indicates fluid velocity. Indicates the explosion wave type coefficient. Indicates pressure, Represents total energy. Indicates the adiabatic index. Indicates artificial adhesiveness. Indicates the speed difference; and Indicates the viscosity coefficient of artificial materials. Indicates the reference speed of sound; This represents the total number of spatiotemporal coordinates in the second loss function. This represents the supercoefficient corresponding to the second loss function; and In the second loss function, the first... Space variables and the Time variables The corresponding Rayleigh-Hugo Newton relation; This represents the flow variables in the region behind the shock wave. Represents the flow variables in the region ahead of the shock wave; This represents the total number of spatiotemporal coordinates in the third loss function. This represents the residual between the predicted value and the true value in the third loss function. This represents the total number of spatiotemporal coordinates in the fourth loss function. This represents the residual between the predicted value and the true value in the fourth loss function.

[0037] According to the present invention, a shock wave front capture method based on a physical information neural network is provided, wherein training the improved physical information neural network based on the training data and the physical loss function to obtain the explosion shock wave front prediction model includes:

[0038] Based on the training data, the improved physical information neural network is iteratively trained. When the total loss value corresponding to the physical loss function of the current round is less than the preset total loss threshold, the explosion shock wave front prediction model is obtained.

[0039] The present invention also provides a shock wave front capture system based on a physical information neural network, comprising:

[0040] The data acquisition module is used to acquire the spatiotemporal coordinate data of the target during the propagation of the target explosion wave;

[0041] The shock wave front capture module is used to input the target spatiotemporal coordinate data into the explosion shock wave front prediction model to obtain the shock wave front information corresponding to the target explosion wave during the propagation process, output by the explosion shock wave front prediction model. The explosion shock wave front prediction model is constructed based on an improved physical information neural network. The physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and a compressible Euler equation with an artificial viscosity term.

[0042] The shock wave front capture method and system based on physical information neural network provided by this invention obtains the spatiotemporal coordinate data of the target during the propagation of the target explosion wave, and inputs it into a prediction model constructed based on the improved physical information neural network to directly obtain the shock wave front information, thereby reducing the computational complexity of the shock wave front while ensuring prediction accuracy. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0044] Figure 1 A flowchart illustrating the shock wave front capture method based on a physical information neural network provided by this invention;

[0045] Figure 2 A schematic diagram of the improved physical information neural network architecture provided by the present invention;

[0046] Figure 3This is a comparative schematic diagram of the shock tube problem results provided by the present invention, wherein, Figure 3 (a) in the figure is a comparison diagram of the loss values ​​under different number of iterations; Figure 3 (b) in the figure is a comparative diagram of prediction results under different prediction methods;

[0047] Figure 4 A comparative schematic diagram of the one-dimensional planar results provided by the present invention, wherein, Figure 4 (a) in the diagram is one of the comparison diagrams between the predicted value and the reference value under the spatial distribution; Figure 4 (b) in the diagram is the second illustration comparing the predicted value and the reference value under the spatial distribution. Figure 4 (c) in the diagram is the third illustration comparing the predicted value and the reference value under the spatial distribution. Figure 4 (d) in the figure is one of the schematic diagrams comparing the predicted value and the reference value under the time distribution; Figure 4 (e) in the diagram is the second illustration comparing the predicted value and the reference value under the time distribution; Figure 4 (f) in the diagram is the third illustration comparing the predicted value and the reference value under the time distribution;

[0048] Figure 5 This is a schematic diagram illustrating the verification results of the spherical explosion wave propagation provided by the present invention, wherein... Figure 5 (a) in the figure is a schematic diagram of the verification results of pressure changing over time; Figure 5 (b) in the figure is a schematic diagram of the verification results of density changing over time; Figure 5 (c) in the figure is a schematic diagram of the verification results of velocity changing over time;

[0049] Figure 6 A schematic diagram of the shock wave front capture system based on physical information neural network provided by the present invention;

[0050] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0052] Figure 1 This is a flowchart illustrating the shock wave front capture method based on a physical information neural network provided by the present invention, as shown below. Figure 1As shown, this invention provides a shock wave front detection method based on a physical information neural network, comprising:

[0053] Step 101: Obtain the target spatiotemporal coordinate data corresponding to the target explosion wave during its propagation.

[0054] In this invention, the explosion wave in a real-world scenario propagates within a specific time and space range. To study the propagation characteristics of the explosion wave and predict its shock wave front, it is necessary to collect relevant data on the target explosion wave at different times and locations during its propagation, i.e., target spatiotemporal coordinate data.

[0055] Spatiotemporal coordinate data clearly defines the temporal and spatial locations of key points during the propagation of the blast wave. For example, it specifies the exact coordinates of the blast wave at a particular moment. This data forms the basis for subsequent predictions of the blast shock wave front. This invention accurately acquires this target spatiotemporal coordinate data, providing effective information for subsequent model input, thereby enabling the model to perform accurate predictive analysis based on this actual data.

[0056] Step 102: Input the target spatiotemporal coordinate data into the explosion shock wave front prediction model to obtain the shock wave front information corresponding to the target explosion wave during the propagation process, output by the explosion shock wave front prediction model. The explosion shock wave front prediction model is constructed based on an improved physical information neural network. The physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and the compressible Euler equation with an artificial viscosity term.

[0057] In this invention, the blast shock wave front prediction model (BLAST-PINN) is constructed based on an improved Physics-Informed Neural Network (PINN). Unlike ordinary neural networks, the improved PINN is specifically optimized for the physical problem of blast shock wave front prediction. It can handle complex physical information related to blast wave propagation and achieves shock wave front prediction through a specific network architecture and algorithm.

[0058] Figure 2 A schematic diagram of the improved physical information neural network architecture provided by this invention can be referred to. Figure 2As shown, the physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation (i.e., the Rankine–Hugoniot relation) and a compressible Euler equation with an artificial viscosity term. In blast wave propagation studies, the Rayleigh-Hugo Newton relation ensures the physical consistency of the shock wave front, guaranteeing that the predicted shock wave front conforms to actual physical laws. For example, during blast wave propagation, physical quantities such as pressure, density, and velocity on both sides of the shock wave front change. The Rayleigh-Hugo Newton relation describes the changes in these physical quantities at the shock wave front. By incorporating it into the loss function, the model can adhere to these physical constraints during prediction.

[0059] A compressible Euler equation with an artificial viscosity term is used to accurately capture the shock wave front during blast wave propagation. During blast wave propagation, pressure, density, and velocity at the shock wave front undergo drastic changes. This discontinuity leads to discontinuous solutions in the compressible Euler equation, affecting prediction accuracy. This invention introduces an artificial viscosity term to smooth these drastic changes in physical quantities at the shock wave front, making the equation solutions more continuous and stable, thereby improving the model's accuracy in predicting the shock wave front.

[0060] In this invention, the target spatiotemporal coordinate data obtained in step 101 is input into an explosion shock wave front prediction model constructed based on an improved physical information neural network. The explosion shock wave front prediction model takes the spatiotemporal coordinates as input and performs calculations and processing through its internal network architecture to obtain the shock wave front information corresponding to the target explosion wave during its propagation process.

[0061] During training, the blast shock wave front prediction model uses embedded Euler equations, artificial viscosity, Rankine–Hugoniot relations, and physical loss functions for initial and boundary conditions to constrain the network output. The physical loss function measures the deviation between the model output and the actual physical situation, continuously optimizing the network parameters through a backpropagation mechanism of the loss. After multiple iterations and optimizations, the model finally outputs information about the shock wave front corresponding to the propagation of the target blast wave. This information includes relevant physical quantities such as the density field, velocity field, and pressure field at the shock wave front, thereby achieving accurate prediction of the blast shock wave front.

[0062] The shock wave front capture method based on physical information neural network provided by this invention obtains the spatiotemporal coordinate data of the target during the propagation of the target explosion wave, and inputs it into a prediction model built based on the improved physical information neural network to directly obtain the shock wave front information, thereby reducing the computational complexity of the shock wave front while ensuring prediction accuracy.

[0063] Based on the above embodiments, the explosion shock wave front prediction model is trained through the following steps:

[0064] Obtain the spatiotemporal coordinate data of the sample;

[0065] Based on the density field, velocity field, and pressure field corresponding to the spatiotemporal coordinate data of the samples, model label data is constructed.

[0066] Training data is constructed based on the sample spatiotemporal coordinate data and the model label data;

[0067] The improved physical information neural network is trained based on the training data and the physical loss function to obtain the explosion shock wave front prediction model.

[0068] In this invention, during the study of blast wave propagation and the construction of a blast shock wave front prediction model, the sample spatiotemporal coordinate data encompasses both time and space dimensions. It records the spatial location of each sample point at a specific moment during blast wave propagation. For example, in a defined blast experiment scenario, high-precision sensors or measuring devices record information from multiple locations along the blast wave propagation path at different time points. This location information and corresponding time information constitute the sample spatiotemporal coordinate data. This data reflects the dynamic changes of the blast wave in time and space, providing necessary input information for subsequent model construction and helping the model learn the spatiotemporal patterns of blast wave propagation.

[0069] Model label data is the target data used to guide model training, representing the correct output corresponding to the sample spatiotemporal coordinates under actual physical conditions. For the problem of explosion wave propagation, density field, velocity field, and pressure field are important physical quantities describing the state of the explosion wave.

[0070] Specifically, the density field reflects the degree of density of matter at various points in space during the propagation of the explosion wave. The density changes at different locations can reflect the compression or rarefaction effect of the explosion wave on the surrounding medium.

[0071] The velocity field describes the velocity of particles in the medium during the propagation of the explosion wave. The changes in the magnitude and direction of the velocity are crucial for understanding the propagation direction and energy transfer of the explosion wave.

[0072] The pressure field reflects the pressure exerted on the surrounding medium by the propagating explosion wave. Changes in pressure are closely related to the intensity and propagation characteristics of the explosion wave.

[0073] Furthermore, through experimental measurements, numerical simulations, or other methods, specific values ​​of the density, velocity, and pressure fields corresponding to the sample's spatiotemporal coordinate data are obtained. These values ​​are then combined to form the model label data. For example, at a specific spatiotemporal coordinate point, the measured fluid density at that point is... ρ The fluid velocity is u Pressure is p ,So( ρ , u , p ) represents the model label data corresponding to the sample spatiotemporal coordinate data.

[0074] In this invention, the training data consists of input data and corresponding output data (i.e., label data). Sample spatiotemporal coordinate data serves as input data, providing spatiotemporal information about the propagation of the explosion wave; while model label data (density field, velocity field, and pressure field) serves as output data, representing the correct state of the explosion wave under those spatiotemporal coordinates. Furthermore, the sample spatiotemporal coordinate data and the corresponding model label data are paired and combined to form a training dataset. This training dataset will be used to guide the improved physical information neural network in learning the mapping relationship from spatiotemporal coordinates to the density field, velocity field, and pressure field.

[0075] In this invention, to solve the problem of predicting the shock wave front of an explosion wave, improvements were made to the existing physical information neural network. Physical knowledge and constraints related to the propagation of explosion waves were incorporated, such as the compressible Euler equation, artificial viscosity, and the Rankine–Hugoniot relationship, so that the model can better understand and handle the physical process of explosion wave propagation.

[0076] The physical loss function is an indicator that measures the difference between the model's predictions and the actual physical conditions. This invention not only considers the error between the model output and the model's labeled data but also incorporates the physical constraints of the explosion wave propagation. For example, by introducing the physical constraints of the compressible Euler equations, it ensures that the density, velocity, and pressure fields predicted by the model satisfy the basic laws of fluid dynamics; artificial viscosity is used to smooth the drastic changes in physical quantities at the shock wave front, avoiding discontinuous solutions; and the Rankine–Hugoniot relation is combined to ensure the physical consistency of the shock wave front. The physical loss function in this invention transforms these physical constraints into mathematical forms to guide the model training process.

[0077] Furthermore, the constructed training data is input into the improved physical information neural network (PEN). The PSN calculates and predicts based on the input spatiotemporal coordinate data of the samples, outputting corresponding predicted values ​​for the density, velocity, and pressure fields. Then, the predicted values ​​are compared with the model label data, and the difference (i.e., the loss value) is calculated using a physical loss function. Based on the loss value, the parameters in the neural network (such as weights and biases) are adjusted using the backpropagation algorithm, so that the model's prediction results gradually approach the actual model label data. After multiple iterations of training, the training process ends when the model's loss value reaches a small threshold or a preset training stopping condition is met. The resulting improved PSN is the blast shock wave front prediction model. The blast shock wave front prediction model can accurately predict the shock wave front information (including density, velocity, and pressure fields) during the propagation of the blast wave based on the input spatiotemporal coordinate data.

[0078] Based on the above embodiments, the improved forward propagation formula of the physical information neural network is specifically as follows:

[0079] ;

[0080] in, This represents the input data of the first layer of the feedforward structure of the improved physical information neural network. The first part represents the feedforward structure of the improved physical information neural network. The input data of the layer, Indicates the weights of the hidden layer. Indicates the hidden layer bias. This represents the tan activation function.

[0081] In this invention, the improved forward propagation formula of the physical information neural network describes the forward propagation from the first layer to the second layer in the improved feedforward structure of the physical information neural network. L The process of input data transmission and transformation in each layer reflects the unidirectional information propagation characteristic of feedforward neural networks. Data starts at the input layer, passes through each hidden layer sequentially, and finally reaches the output layer, with the output of each layer serving as the input for the next. Within each layer, the data, after linear transformation by weights and biases, is input to the activation function. The activation function performs a non-linear transformation on the data and then passes the transformed result to the next layer.

[0082] The forward propagation formula in this invention starts with the input spatiotemporal coordinate data, and through multiple layers of transformation with weights, biases and activation functions, gradually generates the input data for each layer, ultimately providing a computational basis for predicting the velocity, density and pressure field in the propagation of the explosion wave.

[0083] Based on the above embodiments, the physical loss function includes a first loss function, a second loss function, a third loss function, and a fourth loss function, wherein:

[0084] The first loss function is constructed based on the compressible Euler equation with an artificial viscosity term;

[0085] The second loss function is constructed based on the Rayleigh-Hugo Newton relation;

[0086] The third loss function is constructed based on the boundary conditions of the explosion wave propagation process;

[0087] The fourth loss function is constructed based on the initial conditions corresponding to the explosion wave at the initial moment.

[0088] In this invention, a physical loss function is used to measure the difference between the network output and the physical reality. This physical loss function consists of four different loss functions, each constructed based on specific physical principles or conditions, constraining the network's prediction results from different aspects to ensure that the predicted propagation results of the explosion wave conform to physical laws.

[0089] Specifically, the first loss function is constructed based on a compressible Euler equation with an artificial viscosity term.

[0090] The compressible Euler equations, as the fundamental equations describing the motion of fluids (which can be considered compressible fluids in the context of blast wave propagation), contain important physical laws such as the conservation of mass, momentum, and energy. However, during the propagation of blast waves, the pressure, density, and velocity at the shock wave front undergo drastic changes, leading to discontinuous solutions in the equations, which poses difficulties for numerical calculations and network predictions.

[0091] To address the aforementioned issues, this invention introduces an artificial viscosity term, which can smooth out drastic changes in physical quantities at the shock wave front, making the equation solutions more continuous and stable. A first loss function is constructed based on the compressible Euler equation with the artificial viscosity term. The predicted velocity, density, and pressure fields from the network are substituted into this equation to calculate the deviation between the predicted values ​​and the physical laws represented by the equation. For example, by calculating whether the predicted momentum change satisfies the momentum conservation equation after adding the artificial viscosity term, the deviation is quantified as the value of the first loss function. If the network prediction conforms to the equation, the value of the first loss function will be smaller; conversely, the value will be larger, thus guiding the network to adjust its parameters to better conform to the physical laws.

[0092] The second loss function is constructed based on the Rayleigh-Hugoniot relation. In the propagation of an explosion wave, the physical quantities (such as pressure, density, velocity, etc.) on both sides of the shock wave front have specific changing relationships. The Rankine-Hugoniot relation is used to describe the physical laws of these relationships, ensuring the physical consistency of the shock wave front and serving as an important constraint in the study of explosion wave propagation.

[0093] In this invention, the physical quantities on both sides of the shock wave front predicted by the network are substituted into the Rankine-Hugoniot relation to calculate the difference between the predicted values ​​and the physical changes specified by the relation. For example, according to the Rankine-Hugoniot relation, the pressure and density changes in front of and behind the shock wave front should satisfy a certain proportional relationship. If the pressure and density changes predicted by the network do not conform to this proportion, a large second loss function value will be generated. By minimizing the second loss function, the network can better predict the changes in physical quantities of the shock wave front that conform to the physical reality.

[0094] The third loss function is constructed based on the boundary conditions of the explosion wave propagation process. In the physical scenario of explosion wave propagation, the boundary conditions define the behavior of the explosion wave at the boundary. For example, on a closed boundary, the normal velocity of the explosion wave may be zero; on an open boundary, it may need to satisfy certain radiation conditions, etc. Boundary conditions are important constraints for determining the solution to the explosion wave propagation problem.

[0095] In this invention, the physical quantities such as velocity and pressure of the explosion wave at the boundary predicted by the network need to satisfy given boundary conditions. The boundary physical quantities predicted by the network are compared with the actual boundary conditions, and the deviation between the two is calculated. This deviation is the value of the third loss function. For example, if the boundary conditions require the normal velocity at a certain boundary to be zero, but the normal velocity predicted by the network is not zero, a positive loss value will be generated, prompting the network to adjust its parameters to make the prediction result more consistent with the boundary conditions.

[0096] The fourth loss function is constructed based on the initial conditions of the explosion wave at the initial moment. The initial conditions describe the state of the explosion wave at the initial moment (t=0), including the distribution of physical quantities such as pressure, density, and velocity at various locations at the initial moment. The initial conditions are the starting point of the explosion wave propagation problem and have a significant impact on the subsequent propagation process.

[0097] In this invention, the distribution of physical quantities of the explosion wave predicted by the network at the initial moment should be consistent with the given initial conditions. The physical quantities predicted by the network at the initial moment are compared with the actual initial conditions, and the difference between the two is calculated; this difference is the value of the fourth loss function. For example, if the initial conditions specify a certain pressure value for a certain region at the initial moment, but the pressure predicted by the network does not match this, a corresponding loss will occur, guiding the network to optimize its parameters so that the predicted initial state is closer to the actual situation.

[0098] The four loss functions constructed in this invention constrain the prediction results of the improved physical information neural network from different perspectives. By comprehensively minimizing these loss functions, the network can better learn the physical laws of explosion wave propagation and improve the accuracy of predicting the explosion wave shock wave front and related physical quantities.

[0099] Based on the above embodiments, the formula for the physical loss function is as follows:

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[0113] in, Represents the physical loss function; This represents the first loss function. This represents the weight value corresponding to the first loss function; This represents the second loss function. This represents the weight value corresponding to the second loss function; This represents the third loss function. This represents the weight value corresponding to the third loss function; This represents the fourth loss function. This represents the weight value corresponding to the fourth loss function; This represents the total number of spatiotemporal coordinates in the first loss function. This represents the supercoefficient corresponding to the first loss function. Represents the fluid velocity gradient; In the first loss function, the first... Space variables and the Time variables The corresponding mass conservation equation, In the first loss function, the first... Space variables and the Time variables The corresponding momentum conservation equation, In the first loss function, the first... Space variables and the Time variables The corresponding energy conservation equation, Indicates fluid density, Indicates fluid velocity; Represents the explosion wave type coefficient, where, At that time, it corresponds to a one-dimensional spherically symmetric wave; At that time, it corresponds to a one-dimensional plane wave; Indicates pressure, Represents total energy. Indicates the adiabatic index. Indicates artificial adhesiveness. Indicates the speed difference; and Indicates the viscosity coefficient of artificial materials. Indicates the reference speed of sound; This represents the total number of spatiotemporal coordinates in the second loss function. This represents the supercoefficient corresponding to the second loss function; and In the second loss function, the first... Space variables and the Time variables The corresponding Rayleigh-Hugo Newton relation; This represents the flow variables in the region behind the shock wave. Represents the flow variables in the region ahead of the shock wave; This represents the total number of spatiotemporal coordinates in the third loss function; This represents the residual between the predicted value and the true value in the third loss function, where, This refers to the network output in Predicted velocity, density, and pressure at the location. This refers to the actual velocity, density, and pressure at the same location; the difference between the two values ​​represents the residual between the predicted and actual values. This represents the total number of spatiotemporal coordinates in the fourth loss function; This represents the residual between the predicted value and the true value in the fourth loss function, where, This refers to the network output in Predicted velocity, density, and pressure at the location. This refers to the actual velocity, density, and pressure at the same location; the difference between the two values ​​represents the residual between the predicted and actual values.

[0114] Based on the above embodiments, the step of training the improved physical information neural network according to the training data and the physical loss function to obtain the explosion shock wave front prediction model includes:

[0115] Based on the training data, the improved physical information neural network is iteratively trained. When the total loss value corresponding to the physical loss function of the current round is less than the preset total loss threshold, the explosion shock wave front prediction model is obtained.

[0116] In this invention, the training data includes sample spatiotemporal coordinate data and corresponding model label data (i.e., density field, velocity field, and pressure field information). This training data provides the learning and fitting objects for the improved physical information neural network. The improved physical information neural network establishes an accurate mapping relationship from the input spatiotemporal coordinates to the output density field, velocity field, and pressure field by continuously adjusting its own parameters (weights and biases).

[0117] In each training round, the spatiotemporal coordinate data of the samples in the training data are input into the improved physical information neural network. After forward propagation calculation, the network outputs the corresponding predicted values ​​of density field, velocity field and pressure field.

[0118] In this invention, the physical loss function consists of a first loss function, a second loss function, a third loss function, and a fourth loss function, which are respectively constructed based on the compressible Euler equation with an artificial viscosity term, the Rankine-Hugoniot relation, the boundary conditions of the explosion wave propagation process, and the initial conditions corresponding to the explosion wave at the initial moment. The predicted value output by the network is substituted into these four loss functions to calculate the corresponding loss value. Then, these four loss values ​​are combined according to a certain rule (such as weighted summation) to obtain the total loss value corresponding to the physical loss function of the current round. This total loss value reflects the overall deviation between the network's current prediction result and the physical reality and given conditions.

[0119] Furthermore, using the backpropagation algorithm, starting from the output layer, the gradient of the total loss with respect to each weight and bias in the network is calculated progressively in reverse. The gradient represents the rate of change of the total loss function at the current parameter values; that is, the magnitude and direction of the change in the total loss value caused by a small change in the parameters. Then, the calculated gradients are used to update the network's weights and biases. By adjusting the parameters, the total loss value is continuously reduced, and the network gradually adjusts its calculation method to make the prediction results closer to reality.

[0120] After each training iteration, the total loss value corresponding to the physical loss function of the current round is obtained. This total loss value is compared with a preset total loss threshold. The preset total loss threshold is a standard set based on actual needs and experience. When the total loss value is less than this threshold, it means that the network's prediction result is close enough to the physical reality and meets the given conditions, that is, the network has achieved a good fit on the training data.

[0121] When the total loss value of the current round is determined to be less than the preset total loss threshold, iterative training stops. At this point, the improved physical information neural network, after multiple parameter updates and optimizations, serves as the explosion shock wave front prediction model. The explosion shock wave front prediction model can accurately predict the shock wave front information (including density field, velocity field, and pressure field, etc.) during the propagation of the explosion wave based on the input spatiotemporal coordinate data, and is used for practical explosion wave propagation analysis and prediction tasks.

[0122] In one embodiment, Figure 3 The diagram showing the comparison of the shock tube problem results provided by this invention can be referred to. Figure 3As shown, at different times (1ms, 3ms, 5ms), the BLAST-PINN and Finite Difference Method (FDM) provided by this invention exhibit good consistency in predicting the spatial distribution of pressure, velocity, and density. For example, during the shock wave propagation process in a shock tube, the changes in pressure, velocity, and density before and after the shock wave front show similar trends in the predictions of the two methods. BLAST-PINN can better simulate the changes of physical quantities over time, and its results are in high agreement with those of FDM. This demonstrates that this invention can accurately capture the shock wave propagation characteristics in shock tube problems, verifying the effectiveness of the algorithm.

[0123] Verification of planar explosion wave propagation, Figure 4 A comparative schematic diagram of the one-dimensional planar results provided by the present invention can be referred to. Figure 4 The figure shows the changes in pressure, density, and velocity over time at different locations for BLAST-PINN and FDM. Planar blast wave propagation exhibits specific physical laws; as time progresses, the physical quantities change accordingly as the blast wave propagates to different locations. From... Figure 4 As can be seen, the pressure, density, and velocity curves predicted by BLAST-PINN over time are quite close to the results of FDM. For example, in the pressure change curve, the sudden pressure changes at each location when the explosion wave arrives and the subsequent trends are well-predicted by both methods, indicating that the present invention can accurately simulate the changes of physical quantities with time and space during the propagation of a plane explosion wave, verifying its applicability to the problem of plane explosion wave propagation.

[0124] Figure 5 The schematic diagram illustrating the verification results of the spherical explosion wave propagation provided by this invention can be referred to. Figure 5 As shown, the changes in pressure, density, and velocity over time for BLAST-PINN and FDM at different distances (2.0m, 2.5m, 3.0m) are compared. The propagation of spherical explosion waves differs from that of plane explosion waves; its propagation exhibits characteristics such as spherical symmetry. Figure 5 In the prediction of spherical explosion wave propagation, BLAST-PINN can provide relatively accurate results for the changes in pressure, density and velocity over time. The prediction results are in good agreement with FDM in terms of both trend and numerical values, indicating that the present invention can handle more complex physical scenarios such as spherical explosion wave propagation, and further verifying the reliability and accuracy of the algorithm.

[0125] The shock wave front capture method based on physical information neural network provided by this invention can capture the shock wave front with high precision. By forcibly implementing the Rayleigh-Hugo Newton relation as a physical constraint at the shock wave front and introducing an artificial viscosity term into the compressible Euler equation, non-physical oscillations are effectively suppressed, avoiding the need for complex numerical formats or strict stability conditions, highlighting its simplicity and efficiency.

[0126] Furthermore, the BLAST-PINN constructed in this invention exhibits robust and accurate performance in various explosion wave problems, reliably predicting core physical fields (pressure, density, velocity) and accurately capturing the shock front. In the shock tube problem, compared to finite difference decomposition (t=0.2), R... 2 The value exceeds 0.97; it reaches 0.98 in the case of a planar explosion wave (t=5ms). This invention is also effective for spherical explosion waves, with the pressure versus density R... 2 The value reaches 0.94, and the velocity field reaches 0.87 (at x=2.5m), demonstrating high accuracy and generalization ability.

[0127] The shock wave front capture system based on physical information neural network provided by the present invention will be described below. The shock wave front capture system based on physical information neural network described below can be referred to in correspondence with the shock wave front capture method based on physical information neural network described above.

[0128] Figure 6 This is a schematic diagram of the shock wave front capture system based on a physical information neural network provided by the present invention, as shown below. Figure 6 As shown, this invention provides a shock wave front capture system based on a physical information neural network, including a data acquisition module 601 and a shock wave front capture module 602. The data acquisition module 601 is used to acquire the target spatiotemporal coordinate data corresponding to the target explosion wave during propagation. The shock wave front capture module 602 is used to input the target spatiotemporal coordinate data into an explosion shock wave front prediction model to obtain the shock wave front information corresponding to the target explosion wave during propagation, output by the explosion shock wave front prediction model. The explosion shock wave front prediction model is constructed based on an improved physical information neural network. The physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and a compressible Euler equation with an artificial viscosity term.

[0129] The shock wave front capture system based on physical information neural network provided by this invention obtains the spatiotemporal coordinate data of the target during the propagation of the target explosion wave, and inputs it into a prediction model built based on the improved physical information neural network to directly obtain the shock wave front information, thereby reducing the computational complexity of the shock wave front while ensuring prediction accuracy.

[0130] The system provided in this embodiment of the invention is used to execute the above-described method embodiments. For specific processes and details, please refer to the above embodiments, which will not be repeated here.

[0131] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 7 As shown, the electronic device may include: a processor 701, a communication interface 702, a memory 703, and a communication bus 704. The processor 701, communication interface 702, and memory 703 communicate with each other via the communication bus 704. The processor 701 can call logical instructions in the memory 703 to execute a shock wave front capture method based on a physical information neural network. This method includes: acquiring target spatiotemporal coordinate data corresponding to the target explosion wave during propagation; inputting the target spatiotemporal coordinate data into an explosion shock wave front prediction model to obtain shock wave front information corresponding to the target explosion wave during propagation, output by the explosion shock wave front prediction model. The explosion shock wave front prediction model is constructed based on an improved physical information neural network; the physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and a compressible Euler equation with an artificial viscosity term.

[0132] Furthermore, the logical instructions in the aforementioned memory 703 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] On the other hand, the present invention also provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, wherein when the program instructions are executed by a computer, the computer is able to execute the shock wave front capture method based on the physical information neural network provided by the above methods, the method comprising: acquiring target spatiotemporal coordinate data corresponding to the target explosion wave during propagation; inputting the target spatiotemporal coordinate data into an explosion shock wave front prediction model to obtain shock wave front information corresponding to the target explosion wave during propagation output by the explosion shock wave front prediction model, wherein the explosion shock wave front prediction model is constructed based on an improved physical information neural network; the physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and a compressible Euler equation with an artificial viscosity term.

[0134] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the shock wave front capture method based on a physical information neural network provided in the above embodiments. The method includes: acquiring target spatiotemporal coordinate data corresponding to the target explosion wave during propagation; inputting the target spatiotemporal coordinate data into an explosion shock wave front prediction model to obtain shock wave front information corresponding to the target explosion wave during propagation output by the explosion shock wave front prediction model, wherein the explosion shock wave front prediction model is constructed based on an improved physical information neural network; the physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and a compressible Euler equation with an artificial viscosity term.

[0135] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0136] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A shock wave front capture method based on a physical information neural network, characterized in that, include: Obtain the target's spatiotemporal coordinate data during the propagation of the target's explosion wave; The target spatiotemporal coordinate data is input into the explosion shock wave front prediction model to obtain the shock wave front information corresponding to the target explosion wave during the propagation process, output by the explosion shock wave front prediction model. The explosion shock wave front prediction model is constructed based on an improved physical information neural network. The physical loss function of the improved physical information neural network is constructed based on the Rayleigh-Hugo Newton relation and a compressible Euler equation with an artificial viscosity term. The forward propagation formula of the improved physical information neural network is as follows: ； in, This represents the input data of the first layer of the feedforward structure of the improved physical information neural network. The first part represents the feedforward structure of the improved physical information neural network. The input data of the layer, Indicates the weights of the hidden layer. Indicates the hidden layer bias. Represents the tan activation function; The physical loss function includes a first loss function, a second loss function, a third loss function, and a fourth loss function, wherein: The first loss function is constructed based on the compressible Euler equation with an artificial viscosity term; The second loss function is constructed based on the Rayleigh-Hugo Newton relation; The third loss function is constructed based on the boundary conditions of the explosion wave propagation process; The fourth loss function is constructed based on the initial conditions corresponding to the explosion wave at the initial moment; The formula for the physical loss function is as follows: ； ； ； ； ； ； ； ； ； ； ； ； ； in, Represents the physical loss function; This represents the first loss function. This represents the weight value corresponding to the first loss function; This represents the second loss function. This represents the weight value corresponding to the second loss function; This represents the third loss function. This represents the weight value corresponding to the third loss function; This represents the fourth loss function. This represents the weight value corresponding to the fourth loss function; This represents the total number of spatiotemporal coordinates in the first loss function. This represents the supercoefficient corresponding to the first loss function. Represents the fluid velocity gradient; In the first loss function, the first... Space variables and the Time variables The corresponding mass conservation equation, In the first loss function, the first... Space variables and the Time variables The corresponding momentum conservation equation, In the first loss function, the first... Space variables and the Time variables The corresponding energy conservation equation, Indicates fluid density, Indicates fluid velocity. Indicates the explosion wave type coefficient. Indicates pressure, Represents total energy. Indicates the adiabatic index. Indicates artificial adhesiveness. Indicates the speed difference; and Indicates the viscosity coefficient of artificial materials. Indicates the reference speed of sound; This represents the total number of spatiotemporal coordinates in the second loss function. This represents the supercoefficient corresponding to the second loss function; and In the second loss function, the first... Space variables and the Time variables The corresponding Rayleigh-Hugo Newton relation; This represents the flow variables in the region behind the shock wave. Represents the flow variables in the region ahead of the shock wave; This represents the total number of spatiotemporal coordinates in the third loss function. This represents the residual between the predicted value and the true value in the third loss function. This represents the total number of spatiotemporal coordinates in the fourth loss function. This represents the residual between the predicted value and the true value in the fourth loss function.

2. The shock wave front capture method based on a physical information neural network according to claim 1, characterized in that, The explosion shock wave front prediction model is trained through the following steps: Obtain the spatiotemporal coordinate data of the sample; Based on the density field, velocity field, and pressure field corresponding to the spatiotemporal coordinate data of the samples, model label data is constructed. Training data is constructed based on the sample spatiotemporal coordinate data and the model label data; The improved physical information neural network is trained based on the training data and the physical loss function to obtain the explosion shock wave front prediction model.

3. The shock wave front capture method based on a physical information neural network according to claim 2, characterized in that, The step of training the improved physical information neural network based on the training data and the physical loss function to obtain the explosion shock wave front prediction model includes: Based on the training data, the improved physical information neural network is iteratively trained. When the total loss value corresponding to the physical loss function of the current round is less than the preset total loss threshold, the explosion shock wave front prediction model is obtained.

4. A shock wave front capture system based on a physical information neural network, characterized in that, The system is used to implement the shock wave front capture method based on a physical information neural network as described in any one of claims 1 to 3.

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