A Method and System for Underwater Target Acoustic Scattering Modeling Based on Physical Information Neural Networks

Abstract

This invention belongs to the field of underwater acoustics technology and discloses a method and system for underwater target acoustic scattering modeling based on a physical information neural network. By establishing a mathematical model of underwater target acoustic-structure interaction, a loss function for the physical information neural network is constructed. A decoupled and parallel dual-network architecture is built: a fluid domain neural network is used to learn and output the scattered sound pressure field of the fluid domain, and an elastic body domain neural network is used to learn and output the displacement field of the elastic body domain. The two networks achieve physical coupling by sharing sampling points and their corresponding boundary condition loss functions at the acoustic-structure interaction boundary. Training data is generated, and the decoupled and parallel physical information neural network is iteratively trained. The trained model is then used to calculate the scattered sound pressure field outside the target and the displacement field inside the elastic body. This invention innovatively applies a physical information neural network to the field of underwater target acoustic scattering, providing a new idea and approach for accurately predicting the acoustic scattering field of underwater targets.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustics technology, and particularly relates to a method and system for underwater target acoustic scattering modeling based on physical information neural networks, used to predict the acoustic scattering field of underwater targets. Background Technology

[0002] Acoustic scattering of underwater targets is a core fundamental problem in fields such as underwater acoustic detection, underwater target identification, and acoustic stealth structure optimization. Research on underwater target acoustic scattering models and their solution methods is of great significance. Currently, the mainstream methods are traditional numerical methods based on mesh discretization (such as the finite element method and the boundary element method) and purely data-driven deep learning methods.

[0003] Traditional numerical methods exhibit a high computational accuracy directly correlated with grid density, leading to exorbitant computation time and power requirements. Particularly when solving inverse problems (such as parameter estimation) or optimization designs, the gradient information of output variables relative to design variables is difficult to obtain directly, necessitating the use of gradient-free optimization methods (such as genetic algorithms). For problems with multiple design variables, this significantly increases computational costs. Furthermore, the difficulty in generating grids for complex geometric problems further limits their applicability. Purely data-driven deep learning methods rely on large amounts of high-quality labeled data. However, underwater environments suffer from significant noise interference, data scarcity, and high acquisition costs, making it difficult to guarantee the quality of labeled data and resulting in insufficient model generalization ability.

[0004] In recent years, Physical Information Neural Networks (PINNs) have transformed numerical solutions into unsupervised optimization problems by embedding governing equations, boundary conditions, and observation data into loss functions, thus avoiding the need for grid discretization and large amounts of labeled data. However, existing PINN-based acoustic scattering research is still limited to rigid targets in the air. Rigid target scattering only involves sound wave reflection, while acoustic scattering of underwater elastic targets needs to consider acoustic-structure interaction (i.e., the interaction between sound waves and the vibration of the elastic body). Its mathematical model consists of the Helmholtz equations in the fluid domain, the Navier-Cauchy equations in the elastic body domain, and coupled boundary conditions. Existing PINN methods lack effective handling of acoustic-structure interaction boundary conditions and cannot accurately describe the physical mechanism of underwater elastic targets, resulting in a research gap in this field. Therefore, there is an urgent need to design a PINN-based method and system for underwater target acoustic scattering modeling.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] (1) Traditional numerical methods rely on discrete grid partitioning, which requires high computation time and computing power.

[0007] (2) Pure data-driven methods rely on a large amount of labeled data and have poor generalization ability in practical applications.

[0008] (3) The existing PINN method is only applicable to rigid targets in the air, and no relevant research has been carried out on acoustic-structure coupling problems for underwater elastic targets.

[0009] To address the aforementioned shortcomings, this invention proposes a PINN-based method for modeling acoustic scattering of underwater elastic targets. Through innovations in decoupling parallel network structures, gain adjustment, Snake activation functions, and adaptive weights, it enables the solution of acoustic-structure coupling mathematical models without the need for discrete mesh generation and labeled data. Summary of the Invention

[0010] To overcome the limitations of traditional numerical methods that rely on discrete grid partitioning, and pure data-driven deep learning methods that depend on large amounts of high-quality labeled data, as well as the technological gap in the field of underwater elastic target acoustic scattering using PINN, this invention discloses a method and system for underwater target acoustic scattering modeling based on PINN. The technical solution is as follows:

[0011] This invention is implemented as follows: a method for modeling underwater target acoustic scattering based on a physical information neural network. This method constructs a physical information neural network model suitable for solving underwater target acoustic scattering problems, employing a decoupled and parallel dual-network architecture, including a fluid domain neural network and an elastic body domain neural network. Specifically, it includes the following steps:

[0012] S1. Establish an acoustic-structure coupling mathematical model to characterize the physical process of acoustic scattering of underwater elastic targets. This model includes the Helmholtz equation in the fluid domain, the Navier-Cauchy equation in the elastic domain, the far-field radiation condition, and the normal displacement and stress continuity condition on the acoustic-structure coupling boundary.

[0013] S2, Construct the loss function of the physical information neural network. The loss function is composed of the weighted sum of the fluid domain partial differential equation residuals, the elastic body domain partial differential equation residuals, the far-field radiation condition loss, and the acoustic-structure coupling boundary condition loss.

[0014] S3. Construct a decoupled and parallel physical information neural network architecture. The fluid domain neural network is used to learn and output the scattered sound pressure field of the fluid domain, and the elastic body domain neural network is used to learn and output the displacement field of the elastic body domain. The two networks achieve physical coupling by sharing sampling points and their corresponding boundary condition loss functions at the acoustic-structure coupling boundary.

[0015] S4, Generate training data, which includes a set of configuration points collected in the fluid domain, the elastic body domain, the artificially truncated boundary, and the acoustic-structure coupling boundary;

[0016] S5. Using the set of configuration points and environmental parameters, the decoupled parallel physical information neural network is iteratively trained to minimize the loss function, thereby obtaining a trained model for calculating the scattered sound pressure field outside the target and the displacement field inside the elastic body.

[0017] In step S1, the model includes the Helmholz equation for the fluid domain, the Navier-Cauchy equation for the elastic domain, the far-field radiation condition, and the continuity condition of normal displacement and stress on the acoustic-structure interaction boundary, including:

[0018] In the fluid domain In the middle, the scattered sound pressure field satisfies the Helmholz equation as follows:

[0019] ;

[0020] In the formula, For the Laplace operator, This refers to the scattered sound pressure in the fluid domain. For the fluid domain, For wave number, , The speed at which sound waves propagate in a fluid. Let be the unit normal vector of the incident sound wave, and represent the direction of the incident sound wave. The frequency of the incident sound wave;

[0021] Displacement field within an elastic body Satisfies the Navier-Cauchy equations of elastic dynamics:

[0022] ;

[0023] In the formula, For Cauchy stress tensor, For the stress tensor with respect to coordinates The sum of the partial derivatives, For the displacement field of the elastic body Directional components, Indicates the region of elasticity; subscript Repeated indices use the Einstein summation convention; symbols This represents the operation of differentiation with respect to coordinates, i.e. ; For solid density, Angular frequency;

[0024] At the acoustic-structure interaction boundary, the total sound pressure field and displacement field should satisfy the transmission conditions:

[0025] ;

[0026] ;

[0027] In the formula, For the density of the fluid, Let be the component of the elastic body displacement along the boundary normal. This represents the total sound pressure in the fluid domain. Let be the unit normal vector of the acoustic-structure coupling boundary. They are the unit normal vectors of Directional components, This is indicated at the acoustic-structure coupling boundary.

[0028] In step S2, when constructing the loss function of physical constraints, the real and imaginary parts of the scattered sound pressure field in the fluid domain and the displacement field in the elastic body domain are evaluated independently and the residuals are calculated.

[0029] The real and imaginary parts of the displacement field of the elastic body domain are evaluated and the residuals are calculated independently.

[0030] Considering the sound pressure field and displacement field Due to the complex-valued nature of the loss function, each loss function needs to independently evaluate the real and imaginary parts of the predicted value. Let be the real part of the predicted scattered sound pressure value. This represents the imaginary part of the predicted scattered sound pressure value. This represents the real part of the predicted displacement value of the elastic body. This represents the imaginary part of the predicted displacement of the elastic body.

[0031] The specific mathematical expressions for each loss function are defined as follows:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, For the first Coordinates of each sampling point The square of the absolute value. The sampling point number, For direction components, for The real part of the derivative of directional stress. For solid density, for The real part of the directional displacement. for The imaginary part of the derivative of directional stress. for Imaginary part of directional displacement for The real part of the derivative of directional stress. for The real part of the directional displacement. for The imaginary part of the derivative of directional stress. for Imaginary part of directional displacement Let be the real part of the displacement vector. This represents the real part of the predicted total sound pressure level. Let be the vector of the real part of the Cauchy stress tensor. Let be the vector of the imaginary part of the displacement. This represents the imaginary part of the total sound pressure prediction value. Let the vector be the imaginary part of the Cauchy stress tensor; and They represent the real part and the imaginary part, respectively. These represent the total number of sampling points for fluid domain placement points, elastic body domain placement points, far-field absorption radiation boundary conditions, and acoustic-structure interaction boundary conditions, respectively.

[0037] In step S3, in the decoupled parallel physical information neural network architecture, a gain adjustment based on prior knowledge is applied to the network output; specifically, the amplitude of the incident sound pressure is used to adjust the scattered sound pressure output of the fluid domain neural network, and the reciprocal of the target Young's modulus is used to adjust the displacement output of the elastic body domain neural network.

[0038] In step S3, the two networks achieve physical coupling by sharing sampling points and their corresponding boundary condition loss functions at the acoustic-structure coupling boundary. This includes: the total loss function is defined as the weighted sum of the loss functions of each sub-network, expressed as:

[0039] ;

[0040] In the formula, For the total loss function, For the residual loss of partial differential equations in the fluid domain, For the boundary condition loss of far-field absorbed radiation, For the residual loss of the partial differential equation in the elastic body domain, For acoustic-structure interaction boundary condition loss, Representing the sound pressure field in the fluid domain and the displacement field of the elastic body domain Network parameters;

[0041] An adaptive weighting method based on a soft attention mechanism is introduced. By designing a trainable weight function for the configuration points, the soft multiplication mask attention mechanism is incorporated into the loss function of PINN. The loss function of adaptive PINN can be expressed as:

[0042] ;

[0043] In the formula, The total loss function for adaptive weights, For the residual loss of fluid domain partial differential equations with adaptive weights, For adaptive weighted far-field absorbed radiation boundary condition loss, For the residual loss of the partial differential equation in the elastic body domain with adaptive weights, For adaptive weighted acoustic-structure coupling boundary condition loss;

[0044] Adaptive weight vector It consists of four components, fluid domain weights Manually truncated boundary weights Elastic domain weights and coupling boundary weights ;

[0045] Each sub-loss term corresponds to the residual mean square error of different physical regions:

[0046] ;

[0047] ;

[0048] ;

[0049] ;

[0050] In the formula, Let be the excitation function. , For the region Adaptive weights, Defined over the field of nonnegative real numbers, This indicates that the function is in Differentiable and strictly increasing within the interval, at points with large residuals. Increasing the corresponding weight coefficients guides the model to automatically focus on high-gradient regions during training; the adaptive loss function training strategy adjusts the network weights. Execution loss function Minimize, while adjusting the adaptive weights Maximize execution, that is The corresponding parameter updates employ an alternating gradient descent / ascent strategy:

[0051] ;

[0052] In the formula, For the first Neural network parameters for the next iteration. For the first Neural network parameters for the next iteration. For loss function For network parameters gradient, For the first Adaptive weights for the fluid domain in the next iteration. For the first Adaptive weights for the fluid domain in the next iteration. The learning rate for the fluid domain adaptive weights. For loss function For adaptive weights gradient, For the first Adaptive weights for the far-field absorbing radiation boundary in the next iteration. For the first Adaptive weights for the far-field absorbing radiation boundary in the next iteration. The learning rate is the adaptive weight for the far-field absorbing radiation boundary. For loss function For adaptive weights gradient, For the first Adaptive weights for the elastic body domain in the next iteration. For the first Adaptive weights for the elastic body domain in the next iteration. The learning rate is the adaptive weight for the elastic body domain. For loss function For adaptive weights gradient, For the first Adaptive weights for acoustic-structure coupling boundary in the next iteration For the first Adaptive weights for acoustic-structure coupling boundary in the next iteration The learning rate is the adaptive weight of the acoustic-structure coupling boundary. For loss function For adaptive weights gradient, The learning rate is the weight of the neural network.

[0053] The update step size is represented as follows:

[0054] ;

[0055] In the formula, For the first In this iteration, the loss function is used to calculate the gradient of the stream neural network parameters. For the k-th iteration, the fluid domain is... Gradient scaling factor for adaptive weights at each sampling point;

[0056] The network architecture of the decoupled parallel model allows for independent optimization of the network structure and hyperparameters of the fluid domain and the elastic domain.

[0057] Furthermore, the fluid domain neural network and the elastic body domain neural network adopt a fully connected structure, and the hidden layer adopts the Snake activation function; an adaptive weight based on the soft attention mechanism is introduced into the loss function to assign trainable weight coefficients to the loss terms of different physical region configuration points, and the network parameters and the weight coefficients are jointly optimized during the training process;

[0058] The training process of the adaptive weights based on the soft attention mechanism includes: minimizing the loss function of the network weights, maximizing the adaptive weights, and updating the parameters using an alternating gradient descent and gradient ascent strategy.

[0059] Furthermore, the input configuration points of the physical information neural network include the inputs of the fluid domain neural network and the elastic body domain neural network. The input of the fluid domain neural network is a set of fluid domain configuration points, artificially truncated boundary sampling points, and acoustic-structure coupling boundary sampling points. The input of the elastic body domain neural network is a set of elastic body domain configuration points and acoustic-structure coupling boundary sampling points. The environmental parameters for calculating the problem include the incident sound wave frequency, the sound velocity and density of the seawater medium, and the target radius, density, Young's modulus, and Poisson's ratio.

[0060] The number of fluid domain placement points, elastic body domain placement points, artificially truncated boundary sampling points, and acoustic-structure coupling boundary sampling points should be at least per wavelength. The principle of point determination;

[0061] For a two-dimensional solution domain, the total number of sampling points in the geometric domain The expression is:

[0062] ;

[0063] Let the perimeter of the boundary be... Each wavelength requires at least Number of sampling points, total number of sampling points on the boundary Represented as:

[0064] ;

[0065] In the formula, For wavelength, The maximum feature length of the domain. This indicates rounding up to the nearest integer.

[0066] Furthermore, the iterative training of the decoupled parallel fully connected physical information neural network employs a hybrid optimizer of Adam and LBFGS to train the model.

[0067] Furthermore, the scattered sound pressure field outside the target and the displacement field inside the elastic body respectively represent the real and imaginary parts of the scattered sound pressure field output by the fluid domain neural network and the real and imaginary parts of each displacement field component output by the elastic body domain neural network.

[0068] Another objective of this invention is to provide an underwater target acoustic scattering modeling system based on a physical information neural network, for implementing the underwater target acoustic scattering modeling method based on a physical information neural network. The system includes:

[0069] A network architecture building module is used to construct the decoupled and parallel physical information neural network architecture;

[0070] The loss function construction module is used to construct and embed the loss function of the physical constraints in the physical information neural network based on the acoustic-structure coupling mathematical model.

[0071] The training data generation module is used to generate the set of configuration points for the fluid domain, elastic body domain, artificially truncated boundary, and acoustic-structure coupling boundary;

[0072] The network prediction module is used to load the trained model and calculate the sound pressure value at any coordinate point in the fluid domain and / or the displacement value at any coordinate point in the elastic body.

[0073] The network architecture building module, loss function construction module, training data generation module, and network prediction module are implemented by the processor executing computer program instructions stored in the memory.

[0074] Combining all the above technical solutions, the beneficial effects of this invention are as follows:

[0075] First, this invention innovatively applies physical information neural networks to the field of underwater target acoustic scattering, providing a new approach and method for accurately predicting underwater target acoustic scattering fields. The underwater target acoustic scattering modeling method of this invention can accurately solve for the underwater target acoustic scattering field without the need for grid discretization and supervised datasets. Furthermore, the trained model can quickly predict the scattered sound pressure at any point within the computational domain. In addition, this invention designs an initial configuration point calculation scheme and significantly improves model performance through network structure, activation function, and adaptive weights.

[0076] Decoupled parallel network architecture: By separating the networks of the fluid domain and the elastic body domain, gradient conflicts when a single network learns different physical laws are avoided, and independent optimization improves convergence speed and accuracy.

[0077] Output gain adjustment: Based on the prior information of incident sound pressure amplitude and Young's modulus, the sound pressure and displacement outputs are normalized, which balances the gradient magnitude of the loss function, solves the training instability problem caused by differences in numerical range, and speeds up the convergence.

[0078] Snake activation function: Utilizing its periodicity, it better matches the oscillating solution of the acoustic wave equation, and significantly accelerates convergence compared to traditional activation functions (such as tanh).

[0079] Adaptive weighting mechanism: By dynamically adjusting the weights of each loss term through soft attention, it automatically focuses on high gradient regions, avoiding the difficulty of manual parameter tuning, enhancing training robustness, and accelerating convergence.

[0080] Secondly, this invention combines acoustic-structure interaction theory with the unsupervised optimization characteristics of PINN, enabling the direct solution of underwater target acoustic scattering fields without discrete mesh generation and data labeling. The trained model can quickly predict sound pressure and displacement at any point, supporting inverse problem solving and optimization design. This provides a new and practical tool for underwater acoustic detection, target recognition, and stealth design, contributing to the intelligent development of underwater acoustic technology.

[0081] Third, underwater target acoustic scattering modeling is a fundamental technology. Its value lies not only in directly saving costs and shortening time, but also in providing a repeatable, controllable, and deeply insightful digital capability. After the technical solution of this invention is transformed, it will greatly reduce R&D and testing costs: Traditional acoustic characteristic research relies on marine field tests, requiring ships, expensive acoustic equipment, and is greatly affected by weather and sea conditions; a single marine test can cost millions or even hundreds of millions of yuan. Modeling and simulation can replace most of the preliminary tests, using the field tests for final verification. It significantly shortens the R&D cycle: Modeling and simulation can complete a full acoustic scenario simulation within hours or days, while organizing a marine test may require a preparation period of months or even years, which increases the speed of product development and scientific research by orders of magnitude. It enhances cognitive and decision-making capabilities: Numerical models can reveal details that are difficult to observe in physical experiments, such as the transient process of sound wave-target interaction and the contribution of specific parts, deepening the understanding of the physical mechanism of acoustic scattering.

[0082] Fourth, after the technical solution of this invention is transformed, it can generate and optimize a series of products and services, mainly including: (1) Sonar system development: optimize the detection efficiency of active sonar and simulate the detection, identification and tracking capabilities of various targets under different environments. (2) Underwater facility monitoring: perform acoustic modeling of facilities such as submarine pipelines, cables, and drilling platforms for structural health monitoring and foreign object detection. (3) Fish resource assessment: establish acoustic scattering models of fish schools and single fish for accurate interpretation of fish finder data, estimate biomass and achieve sustainable fishing. (4) Professional simulation software: develop and sell dedicated underwater target acoustic scattering modeling software, such as modules or independent software integrated with COMSOL, ACTRA and others. This invention innovatively applies PINN to underwater target acoustic scattering modeling, providing a feasible solution for predicting the acoustic scattering field of underwater elastic targets represented by an acoustic-structure coupling mathematical model, providing new ideas and approaches for accurately predicting the acoustic scattering field of underwater targets, and filling the technical gap of PINN in the field of underwater elastic target acoustic scattering. Attached Figure Description

[0083] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure;

[0084] Figure 1 This is a flowchart of the underwater target acoustic scattering modeling method based on physical information neural network provided in this embodiment of the invention;

[0085] Figure 2 Here are schematic diagrams of the underwater target acoustic-structure coupling model provided in the embodiments of the present invention; (a) is a schematic diagram of the elastic body structure in an infinite fluid, (b) is a schematic diagram of the artificially truncated acoustic field, and (c) is a schematic diagram of the acoustic scattering of the elastic target.

[0086] Figure 3 This is a diagram of the decoupled parallel model provided in the embodiments of the present invention;

[0087] Figure 4 This is a schematic diagram of the relative error between the predicted solution and the analytical solution under the number of wavelength configuration points in different regions provided by the embodiments of the present invention; wherein, (a) is a fluid domain diagram, (b) is an elastic body domain diagram, (c) is an absorption radiation boundary diagram, and (d) is a coupling boundary diagram;

[0088] Figure 5 This is a schematic diagram of the real part of the predicted scattered sound using a decoupled parallel model provided in an embodiment of the present invention; wherein, (a) is the predicted solution diagram, (b) is the reference solution diagram, and (c) is the absolute error diagram;

[0089] Figure 6This is a schematic diagram of the imaginary part of the predicted scattered sound pressure using a decoupled parallel model provided in an embodiment of the present invention; wherein, (a) is the predicted solution diagram, (b) is the reference solution diagram, and (c) is the absolute error diagram;

[0090] Figure 7 This is a schematic diagram of the real part of the x-component displacement predicted by the decoupled parallel model provided in the embodiment of the present invention; wherein, (a) is the prediction solution diagram, (b) is the reference solution diagram, and (c) is the absolute error diagram;

[0091] Figure 8 This is a schematic diagram of the prediction of the imaginary part of the x-component displacement using a decoupled parallel model provided in an embodiment of the present invention; wherein, (a) is the predicted solution, (b) is the reference solution, and (c) is the absolute error diagram;

[0092] Figure 9 This is a schematic diagram of the real part of the displacement of the y component predicted by the decoupled parallel model provided in the embodiment of the present invention; wherein, (a) is the prediction solution diagram, (b) is the reference solution diagram, and (c) is the absolute error diagram;

[0093] Figure 10 This is a schematic diagram of the prediction of the imaginary part of the y-component displacement using a decoupled parallel model provided in an embodiment of the present invention; wherein, (a) is the prediction solution diagram, (b) is the reference solution diagram, and (c) is the absolute error diagram;

[0094] Figure 11 These are loss function curves at different frequencies provided in the embodiments of the present invention; wherein, (a) is the training loss graph and (b) is the test loss graph;

[0095] Figure 12 These are echo intensity comparison diagrams at the unit circle provided in the embodiments of the present invention; wherein, (a) is... (b) Figure is (c) Figure is (100), (d) Figure is (100), the figure title corresponds to Figure 11 In the figure caption, (100) indicates that there are 100 neurons in each layer;

[0096] Figure 13 These are comparison graphs of loss function curves for different network structure models provided in the embodiments of the present invention; where (a) is the training loss graph and (b) is the test loss graph.

[0097] Figure 14 These are comparison graphs of loss function curves for different activation functions provided in this embodiment of the invention; where (a) is the training loss graph and (b) is the test loss graph.

[0098] Figure 15This is a comparison chart of the loss curves of the masking function and the adaptive weighting method provided in the embodiments of the present invention; wherein, (a) is the masking function chart, (b) is the training loss chart, and (c) is the test loss chart. Detailed Implementation

[0099] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0100] The innovation of this invention lies in the fact that it is the first to apply the PINN framework to acoustic scattering modeling of underwater elastic targets, breaking through the limitation of existing PINN acoustic scattering research being confined to rigid targets in the air. By introducing an acoustic-structure interaction mathematical model, it achieves an accurate description of the physical mechanism of fluid-elastic body interaction. Furthermore, a method for calculating the number of input configuration points is designed, and the model performance is significantly improved by combining network structure, activation function, and adaptive weights.

[0101] In Example 1, this invention derives a mathematical model of acoustic-structure coupling, defines various loss functions, builds a decoupled parallel neural network architecture, and randomly selects several configuration points in each training region as network inputs based on the configuration point quantity criterion to construct a complete decoupled parallel physical information neural network; the trained network is used to approximate the solution of the underwater target acoustic scattering field.

[0102] like Figure 1 As shown, the underwater target acoustic scattering modeling method based on physical information neural networks provided in this embodiment of the invention specifically includes the following steps:

[0103] S1. Establish an acoustic-structure coupling mathematical model to characterize the physical process of acoustic scattering of underwater elastic targets. This model includes the Helmholz equation in the fluid domain, the Navier-Cauchy equation in the elastic body domain, the far-field radiation condition, and the normal displacement and stress continuity condition on the acoustic-structure coupling boundary.

[0104] like Figure 2 As shown in Figure (a), consider a linear isotropic elastic solid domain. Its outer region is a compressible inviscid fluid domain. The two domains are coupled through the interface. interaction. for Vioclimatic space The spatial dimension; under frequency domain harmonic excitation (time factor) , The base of the natural logarithm, The imaginary unit, (Time), displacement field within the elastic body Satisfies the Navier-Cauchy equations of elastic dynamics:

[0105] ;

[0106] In the formula, For Cauchy stress tensor, For the stress tensor with respect to coordinates The sum of the partial derivatives, For the displacement field of the elastic body Directional components, Indicates the region within the elastic body (spatial region); subscript Repeated indices use the Einstein summation convention; symbols This represents the operation of differentiation with respect to coordinates, i.e. ; For solid density, ω is the angular frequency.

[0107] like Figure 2 As shown in Figure (b), in the fluid domain In the middle, the scattered sound pressure field satisfies the Helmholz equation as follows:

[0108] ;

[0109] In the formula, For the Laplace operator, This refers to the scattered sound pressure in the fluid domain. It is a fluid domain (spatial region). For wave number, , The speed at which sound waves propagate in a fluid. Let be the unit normal vector of the incident sound wave, and represent the direction of the incident sound wave. The frequency of the incident sound wave;

[0110] Displacement field within an elastic body Satisfies the Navier-Cauchy equations of elastic dynamics:

[0111] ;

[0112] In the formula, For Cauchy stress tensor, For the stress tensor with respect to coordinates The sum of partial derivatives, For the displacement field of the elastic body Directional components, Indicates the region of elasticity; subscript Repeated indices use the Einstein summation convention; symbols This represents the operation of differentiation with respect to coordinates, i.e. ; For solid density, Angular frequency;

[0113] like Figure 2 As shown in Figure (c), at the acoustic-structure interaction boundary, the total acoustic pressure field and displacement field should satisfy the transmission conditions:

[0114] ;

[0115] ;

[0116] In the formula, For the density of the fluid, This represents the component of the elastic body displacement along the boundary normal. This represents the total sound pressure in the fluid domain. Let be the unit normal vector of the acoustic-structure coupling boundary. unit normal vector of Directional components, Indicated at the acoustic-structure coupling boundary;

[0117] In summary, the acoustic-structure coupling mathematical model is described by the following four parts:

[0118] (1) Elastic dynamics governing equations;

[0119] (2) Pressure acoustic wave equation;

[0120] (3) Sommerfeld radiation conditions;

[0121] (4) Transmission conditions at the coupling interface.

[0122] The equations are based on the scattered sound pressure. and structural displacement For unknown quantities, the specific form is:

[0123] ;

[0124] In the formula, For the incident background field, The unit normal vector of the boundary;

[0125] S2, Construct the loss function of the physical information neural network. The loss function is composed of the weighted sum of the fluid domain partial differential equation residuals, the elastic body domain partial differential equation residuals, the far-field radiation condition loss, and the acoustic-structure coupling boundary condition loss.

[0126] Based on the equations of the acoustic-structure coupling mathematical model derived above, the PINN loss function for the underwater target acoustic scattering problem is... It can be broken down into four parts:

[0127] (1) Residual loss of partial differential equations in the fluid domain ;

[0128] (2) Loss of far-field absorbed radiation boundary conditions ;

[0129] (3) Residual loss of partial differential equations in the elastic body domain ;

[0130] (4) Loss due to acoustic-structure interaction boundary conditions .

[0131] Considering the sound pressure field and displacement field Due to the complex value characteristics, each loss function needs to independently evaluate the real and imaginary parts of the predicted value. Let be the real part of the predicted scattered sound pressure value. This represents the imaginary part of the predicted scattered sound pressure value. This represents the real part of the predicted displacement value of the elastic body. This represents the imaginary part of the predicted displacement of the elastic body.

[0132] The specific mathematical expressions for each loss function are defined as follows:

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] In the formula, For the first Coordinates of each sampling point The square of the absolute value. The sampling point number, For direction components, for The real part of the derivative of directional stress. For solid density, for The real part of the directional displacement. for The imaginary part of the derivative of directional stress. for Imaginary part of directional displacement for The real part of the derivative of directional stress. for The real part of the directional displacement. for The imaginary part of the derivative of directional stress. for Imaginary part of directional displacement Let be the real part of the displacement vector. This represents the real part of the predicted total sound pressure level. Let be the vector of the real part of the Cauchy stress tensor. Let be the vector of the imaginary part of the displacement. This represents the imaginary part of the total sound pressure prediction value. Let the vector be the imaginary part of the Cauchy stress tensor; and They represent the real part and the imaginary part, respectively. These represent the total number of sampling points for fluid domain placement points, elastic body domain placement points, far-field absorption radiation boundary conditions, and acoustic-structure interaction boundary conditions, respectively.

[0138] S3. Construct a decoupled and parallel physical information neural network architecture. The fluid domain neural network is used to learn and output the scattered sound pressure field of the fluid domain, and the elastic body domain neural network is used to learn and output the displacement field of the elastic body domain. The two networks achieve physical coupling by sharing sampling points and their corresponding boundary condition loss functions at the acoustic-structure coupling boundary.

[0139] For the acoustic scattering problem of two-dimensional underwater elastic targets, spatial coordinates are defined. For network input, output includes scattered sound pressure. , Directional displacement components as well as Directional displacement components The real and imaginary parts of the equation. For acoustic-structure interaction problems, different physical quantities may have significantly different amplitudes. Appropriate scaling parameters can be applied to the network output based on prior information. ,Right now:

[0140] ;

[0141] In the formula, The predicted value is after gain adjustment. For network output, For network output, For trainable network parameters, For network input, It can consist of spatial coordinates, time, and other additional input parameters.

[0142] In this invention, based on prior information about the incident sound pressure amplitude and the target Young's modulus, the scattered sound pressure output is adjusted using the incident sound pressure amplitude, and the displacement output is adjusted using the reciprocal of the Young's modulus. The network weights are initialized using the Xavier method, and except for the last layer which uses a linear activation function, all other hidden layers are configured with the Snake activation function, which is mathematically expressed as follows:

[0143] ;

[0144] In the formula, The expression for the snake activation function. As variables, For frequency parameters, frequency parameters It can be adjusted according to specific problems. In this embodiment of the invention, the frequency parameter... .

[0145] The decoupled parallel model constructs independent sub-networks for the sound pressure field in the fluid domain and the displacement field in the elastic body domain, respectively. and ,like Figure 3 As shown. Among them, The network takes the set of sampling points of fluid domain placement points, far-field absorption radiation boundary and acoustic-structure coupling boundary as input, and outputs the real part and imaginary part of the scattered sound pressure respectively; The network takes the set of locating points in the elastic body domain and the set of sampling points at the acoustic-structure coupling boundary as input, and outputs respectively... The real and imaginary parts of the directional displacement components. The two subnetworks achieve constraints by sharing coupled boundary sampling points and their loss functions, and are updated synchronously using a strategy of minimizing the total loss function. and The network parameters are determined to achieve joint prediction of the sound pressure field and displacement field. The total loss function is defined as the weighted sum of the loss functions of each sub-network, and its expression is:

[0146] ;

[0147] In the formula, For the total loss function, For the residual loss of partial differential equations in the fluid domain, For the boundary condition loss of far-field absorbed radiation, For the residual loss of the partial differential equation in the elastic body domain, For acoustic-structure interaction boundary condition loss, Representing the sound pressure field in the fluid domain and the displacement field of the elastic body domain Network parameters.

[0148] An adaptive weighting method based on a soft attention mechanism is introduced. By designing a trainable weight function for the configuration points, the soft multiplication mask attention mechanism is incorporated into the loss function of PINN. The loss function of adaptive PINN can be expressed as:

[0149] ;

[0150] In the formula, The total loss function for adaptive weights, For the residual loss of fluid domain partial differential equations with adaptive weights, For adaptive weighted far-field absorbed radiation boundary condition loss, For the residual loss of the partial differential equation in the elastic body domain with adaptive weights, For adaptive weighted acoustic-structure coupling boundary condition loss;

[0151] Adaptive weight vector It consists of four components, fluid domain weights Manually truncated boundary weights Elastic domain weights and coupling boundary weights .

[0152] Each sub-loss term corresponds to the residual mean square error of different physical regions:

[0153] ;

[0154] ;

[0155] ;

[0156] ;

[0157] In the formula, Let be the excitation function. , For the region Adaptive weights, Defined over the field of nonnegative real numbers, This indicates that the function is in Differentiable and strictly increasing within the interval, at points with large residuals. Increasing the corresponding weight coefficients guides the model to automatically focus on high-gradient regions during training. The adaptive loss function training strategy involves adjusting the network weights. Execution loss function Minimize, while adjusting the adaptive weights Maximize execution, that is The corresponding parameter updates employ an alternating gradient descent / ascent strategy:

[0158] ;

[0159] In the formula, For the first Neural network parameters for the next iteration. For the first Neural network parameters for the next iteration. For loss function For network parameters gradient, For the first Adaptive weights for the fluid domain in the next iteration. For the first Adaptive weights for the fluid domain in the next iteration. The learning rate for the fluid domain adaptive weights. For loss function For adaptive weights gradient, For the first Adaptive weights for the far-field absorbing radiation boundary in the next iteration. For the first Adaptive weights for the far-field absorbing radiation boundary in the next iteration. The learning rate is the adaptive weight for the far-field absorbing radiation boundary. For loss function For adaptive weights gradient, For the first Adaptive weights for the elastic body domain in the next iteration. For the first Adaptive weights for the elastic body domain in the next iteration. The learning rate is the adaptive weight for the elastic body domain. For loss function For adaptive weights gradient, For the first Adaptive weights for acoustic-structure coupling boundary in the next iteration For the first Adaptive weights for acoustic-structure coupling boundary in the next iteration The learning rate is the adaptive weight of the acoustic-structure coupling boundary. For loss function For adaptive weights gradient, The learning rate is the weight of the neural network.

[0160] The update step size is represented as follows:

[0161] ;

[0162] In the formula, For the first In this iteration, the loss function is used to calculate the gradient of the stream neural network parameters. For the k-th iteration, the fluid domain is... Gradient scaling factor for adaptive weights at each sampling point;

[0163] The network architecture of the decoupled parallel model allows for independent optimization of the network structure and hyperparameters of the fluid domain and the elastic domain.

[0164] S4, Generate training data, which includes a set of configuration points collected in the fluid domain, the elastic body domain, the artificially truncated boundary, and the acoustic-structure coupling boundary;

[0165] Assuming the speed of sound in water Incident sound wave frequency Wavelength of sound waves The maximum feature length of the geometric domain Each wavelength requires at least The total number of sampling points in the geometric domain for a two-dimensional solution domain. The expression is:

[0166] ;

[0167] Let the perimeter of the boundary be... Each wavelength requires at least Number of sampling points, total number of sampling points on the boundary Represented as:

[0168] ;

[0169] In the formula, For wavelength, The maximum feature length of the domain. This indicates rounding up to the nearest integer.

[0170] S5. Using the set of configuration points and environmental parameters, the decoupled parallel physical information neural network is iteratively trained to minimize the loss function, thereby obtaining a trained model for calculating the scattered sound pressure field outside the target and the displacement field inside the elastic body.

[0171] Example 2: The underwater target acoustic scattering modeling system based on physical information neural networks provided in this embodiment of the invention includes:

[0172] A network architecture building module is used to construct the decoupled and parallel physical information neural network architecture;

[0173] The loss function construction module is used to construct and embed the loss function of the physical constraints in the physical information neural network based on the acoustic-structure coupling mathematical model.

[0174] The training data generation module is used to generate the initial set of input configuration points for the fluid domain, elastic body domain, artificially truncated boundary, and acoustic-structure coupling boundary;

[0175] The network prediction module is used to load the trained model and calculate the sound pressure value at any coordinate point in the fluid domain and / or the displacement value at any coordinate point in the elastic body.

[0176] The network architecture building module, loss function construction module, training data generation module, and network prediction module are implemented by the processor executing computer program instructions stored in the memory.

[0177] To further demonstrate the positive effects of the above embodiments, the present invention conducts the following experiments based on the above technical solutions.

[0178] 1. Validation experiment on the effectiveness of the initial input configuration point number calculation method.

[0179] This example considers the acoustic scattering problem of a two-dimensional elastic circular target in an infinitely homogeneous medium, specifically the typical acoustic scattering case of an infinitely long cylinder. The computational domain is set as a circular region with a radius of 2m, and the target is located at the center of the geometric model with a radius of 0.5m. Its material parameter is Young's modulus of 2.1 × 10⁻⁶. 11 Pa, Poisson's ratio 0.3. Background fluid medium is seawater, sound velocity 1500 m / s. f =954.93Hz, incident plane wave along x Propagation occurs in the positive direction of the axis. The number of placement points for each wavelength on the fluid domain, elastic domain, absorbing radiation boundary, and coupling boundary are respectively denoted as: This indicates the configuration point setting scheme during training. Using the controlled variable method, the impact of changing the number of configuration points in the area under analysis on the prediction results was analyzed when there were many configuration points in other areas. The range of configuration point numbers is shown in Table 1.

[0180] Table 1 Number of points per wavelength in each region at 1kHz

[0181]

[0182] The model was trained using the configuration points in Table 1 for each region. The model structure adopted the traditional single neural network PINN (Unified 1-network, U1net), meaning the entire model uses only one unified network to complete the task, with no structural decoupling; this is the most basic PINN architecture. U1net is set to 4 hidden layers by default, with 30 neurons per layer. If the number of neurons in each layer changes, then... Indicates each layer There are [number] neurons. Adam and LBFGS are used to optimize network parameters, with learning rates of 0.001 and 1, and training iterations of 5000 and 20000, respectively. For example... Figure 4 As shown, Figure 4 Figures (a) to (d) show the variation of the L2 relative error between the predicted scattered sound pressure and the analytical solution for 5000 randomly selected points in the fluid domain, depending on the number of points configured in the fluid domain, elastic body domain, absorbing radiation boundary, and coupling boundary. The results indicate that the number of points configured in the fluid and elastic body domains has the greatest impact on the model's prediction results. Insufficient points in the solution domain of the governing equations make it difficult to accurately describe the problem and hinder the model from achieving accurate convergence. At that time, the L2 relative error had already stabilized; As the number of configuration points in the elastic body domain increases, the L2 relative error decreases slowly and tends to stabilize overall. However, when the number of configuration points in the fluid domain and elastic body domain is sufficient, the increase in the number of configuration points for the circular boundary has little impact on the model prediction results, meaning that a smaller number of configuration points can also describe the circular shape. Figures 5-10 The prediction results of the decoupled parallel model for the real and imaginary parts of the scattered sound pressure and the x and y components of the displacement field are presented, along with their absolute errors compared to the COMSOL reference solution. The results demonstrate that the PINN method can effectively capture the complex physical characteristics of acoustic-structure interaction fields, achieving high-precision prediction of the acoustic scattering field of underwater elastic targets.

[0183] To verify the applicability of the conclusion regarding the influence of the number of initial placement points on the predicted solution at different frequencies, one non-resonant frequency was selected. Simulation verification was conducted using three resonant frequencies. The acoustic scattering waveform of an infinitely long cylindrical target was analyzed. By subtracting the corresponding rigid wavelet shape function from the elastic wavelet shape function, the target's purely elastic acoustic scattering wavelet shape functions of different orders are obtained. The index of the resonance peaks is represented by... Indicates, that is For the acoustic scattering problem of a two-dimensional elastic circular target in an infinitely homogeneous medium, given above, its order... Serial Number The corresponding resonant frequencies are approximately: To avoid the influence of random distribution of configuration point locations, the location of the L2 relative error is chosen when its variation is relatively stable. The number of boundary configuration points is set to The environmental and target parameters remain unchanged, using the traditional U1net network with a 4-layer hidden layer structure and 30 neurons per layer by default. Figure 11 As shown in Figures (a) and (b), the captions are as follows: Indicates each layer For example, (100) represents 100 neurons per layer. The training loss and test loss curves of the model at different frequencies all show a monotonically decreasing characteristic as the number of iterations increases, indicating that the current configuration number of points This solution meets the requirements for solving acoustic-structure interaction problems that vary with frequency. It's important to note that when the incident radio frequency is 477Hz, the computational domain radius of both the model and COMSOL is set to 4m, ensuring the distance to the far-field absorption radiation boundary is greater than one wavelength, thus avoiding significant errors caused by boundary reflection interference. To accelerate model convergence at higher frequencies, the 4055Hz calculation result is based on a model trained at 2049Hz, achieved using a transfer learning strategy. Figure 12 As shown in Table 2, the target echo intensity distribution characteristics of the PINN predicted solution, COMSOL numerical solution, and analytical solution are compared at the boundary of the unit circle. To quantify the accuracy of the PINN solution, the L2 relative error between the predicted solution and the numerical solution and the analytical solution is calculated at both grid nodes and non-grid nodes in COMSOL. As shown in Table 2, the L2 relative error index based on grid nodes verifies the consistency of the accuracy between the predicted solution and the numerical solution, with a maximum error of <0.6%. For non-grid nodes, 360 points are uniformly sampled on a unit circle, and it is found that the accuracy of the predicted solution is improved by about 1% compared to the interpolation result of the numerical solution. In addition, when the incident radio frequency is 1500-4055Hz, Table 2 shows that the relative error is smaller at higher frequencies. Analysis shows that this is because the radius of the computational domain is set to 2m. The higher the frequency, the larger the computational domain is relative to the wavelength, which better meets the absorption radiation conditions and reduces boundary reflection interference. The above results indicate that PINN can effectively capture the complex physical characteristics of acoustic-structure coupling fields and accurately solve the acoustic scattering problem of two-dimensional elastic circular targets.

[0184] Table 2. L2 relative errors of predicted solutions, numerical solutions, and analytical solutions.

[0185]

[0186] 2. Conduct ablation experiments to verify the performance of the decoupled parallel model.

[0187] The environmental parameters for this example are consistent with those in Experiment 1, including the wavenumber. k =4, the number of points configured for each wavelength in each region is: .

[0188] First, we verify the performance of the decoupled parallel network. We denote the traditional single network, the decoupled parallel network, and the decoupled sequential network PINN as U1net (Unified 1-network), UP2net (Unified Parallel 2-network), and US2net (Unified Sequential 2-network), respectively. The decoupled parallel network PINN (UP2net) model contains two sub-networks that run in parallel, compute independently, and output simultaneously, achieving structural decoupling. The decoupled sequential network (US2net) model contains two sub-networks that run sequentially, with the output of the previous sub-network serving as the input of the next, completing the task according to the flow.

[0189] In terms of model architecture and training parameter settings, the subnetworks in U1net, UP2net, and US2net all adopt a 4-layer hidden layer structure, with 30 neurons in each layer. U1net ( This represents a traditional single network with a 4-layer hidden layer structure, each layer... 100 neurons. Among them, UP2net and US2net contain 100 neurons. The two sub-networks are shown in Table 3. A hybrid optimization strategy combining Adam and LBFGS is used to optimize the network parameters. The learning rate of the Adam optimizer is 0.001, and the learning rate of the LBFGS optimizer is 1. The training iterations are 5000 and 25000, respectively. When the training loss is less than a threshold of 1×10... -4 The training process was terminated prematurely.

[0190] Table 3 Network Structure Information

[0191]

[0192] like Figure 13 The comparison of training / test loss curves shows that U1net can improve convergence efficiency by 25.4% by increasing the network size (U1net(45)). Compared with U1net(45) which has more network parameters, UP2net and US2net, which adopt the physical field decoupling strategy, show better convergence efficiency and generalization ability. Based on U1net, other models achieve convergence acceleration of 70.4% and 62.6% respectively when reaching the same test loss (0.001), as shown in Table 4. To further examine the decoupling model at higher frequencies... Under the unified sub-network architecture (4 hidden layers × 68 neurons), the total number of parameters of UP2net and US2net (38358) is reduced by 7.1% compared to the total number of parameters of U1net (100) (41306). Figure 13As shown, US2net experiences gradient explosion as the frequency increases, leading to excessive weight updates and a sudden, abnormal increase in the training loss function during training. Therefore, gradient clipping is used to control the gradient of US2net_GC within a reasonable range, but its convergence speed is limited. UP2net's convergence efficiency advantage, however, shows a significant amplification effect with increasing frequency. With the same test loss (0.001), UP2net and U1net (100) require 29414 and 91429 training iterations respectively, with UP2net achieving a 67.8% improvement in convergence efficiency.

[0193] Table 4 shows the performance comparison between the U1net model and the test loss model (test loss = 0.001).

[0194]

[0195] Verify the performance of the Snake activation function. Using the UP2net model, compare the performance differences of four activation functions—ReLU, Tanh, Sin, and Snake—in the acoustic scattering problem of a two-dimensional elastic circular target. Figure 14 The results show that the ReLU activation function, due to its constant second derivative and gradient discontinuity, causes the model to lack information about the second derivative of the output variables, thus failing to achieve convergence. While the Tanh activation function maintains training stability, its saturated nonlinearity limits its ability to express complex sound pressure field features. The Sin activation function, by introducing global periodic continuity, theoretically possesses the potential to represent complex nonlinear relationships, but its convergence efficiency and generalization performance are significantly lower than those of the Snake activation function.

[0196] Based on the UP2net and Snake activation functions, an adaptive weight optimization strategy (denoted as SA-UP2net) based on a soft attention mechanism is introduced to optimize the weights of the configuration points in each region. According to preliminary simulation results, the mask function is set as follows: ,like Figure 15 As shown in Figure (a), Defined over the field of nonnegative real numbers, This indicates that the function is in Differentiable and strictly increasing within the interval, at points with large residuals. Increase the corresponding weight coefficients to guide the model to automatically focus on high gradient regions during training. All adaptive weights are initially set to 1 and dynamically updated using the Adam optimizer, which is synchronized with the network parameters. Incident frequency is considered. f = 954.93Hz and 2409Hz correspond to 4 hidden layers × 30 neurons and 4 hidden layers × 68 neurons in the sub-network structure, respectively, while the other parameters remain the same. Figure 15Figures (b) and (c) show the training and testing loss curves of UP2net and SA-UP2net at two frequencies, where the solid and dashed lines represent the training and testing losses, respectively. f =954.93Hz, dots and dotted lines are f The calculated result is 2409Hz. When reaching the equivalent test loss threshold of 0.001, f At 2409Hz, the number of convergence iterations decreased from 29414 for UP2net to 19397 for SA-UP2net, and the adaptive weight method improved the model convergence efficiency by approximately 34.1%. Compared with the baseline model U1net(100) which required 91429 iterations, SA-UP2net achieved a convergence efficiency improvement of 78.8%.

[0197] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for underwater target acoustic scattering modeling based on physical information neural network, characterized in that, The method constructs a physical information neural network model suitable for solving the underwater target sound scattering problem, adopts a decoupled parallel double network architecture, including a fluid domain neural network and an elastic body domain neural network, and specifically includes the following steps: S1, an acoustic-solid coupling mathematical model representing the acoustic scattering physical process of an underwater elastic target is established, the model includes a Helmholtz equation of the fluid domain, a Navier-Cauchy equation of the elastic body domain, a far-field radiation condition, and normal displacement and stress continuity conditions on the acoustic-solid coupling boundary; S2, constructing a loss function of the physical information neural network, the loss function being composed of fluid domain partial differential equation residuals elastomer domain partial differential equation residuals far-field radiation condition loss and acoustic-structure coupling boundary condition loss are weighted and summed up; S3, a decoupled parallel physical information neural network architecture is built, the fluid domain neural network is used to learn and output the scattered sound pressure field of the fluid domain, and the elastic body domain neural network is used to learn and output the displacement field of the elastic body domain, and the two networks are physically coupled by sharing sampling points and corresponding boundary condition loss functions on the acoustic-solid coupling boundary; S4, training data is generated, the training data includes a set of configuration points collected on the fluid domain, the elastic body domain, the artificial truncation boundary and the acoustic-solid coupling boundary; S5, the decoupled parallel physical information neural network is iteratively trained using the set of configuration points and environmental parameters to minimize the loss function, thereby obtaining a trained model for calculating the scattered sound pressure field outside the target and the displacement field inside the elastic body; The fluid domain neural network and the elastic body domain neural network adopt a full connection structure, and the hidden layer adopts a Snake activation function; In the loss function, an adaptive weight based on a soft attention mechanism is introduced, a trainable weight coefficient is given to the loss term of the configuration point of different physical regions, and the network parameters and the weight coefficient are jointly optimized in the training process; The training process of the adaptive weight based on the soft attention mechanism includes: performing minimization of the loss function on the network weight, and performing maximization on the adaptive weight, and adopting an alternating strategy of gradient descent and gradient ascent to update the parameters.

2. The method of claim 1, wherein, In step S1, the model includes the Helmholtz equation of the fluid domain, the Navier-Cauchy equation of the elastic body domain, the far-field radiation condition, and the normal displacement and stress continuity conditions on the acoustic-solid coupling boundary, including: In the fluid domain Ω f The scattered sound pressure field satisfies the Helmholtz equation: wherein is the Laplacian operator, p s is the scattered sound pressure in the fluid domain, Ω f is the fluid domain, k is the wave number, k = e k 2πf / c f , c f is the speed of sound wave propagation in the fluid, e k is the unit normal vector of the incident sound wave direction, represents the incident sound wave direction, f is the frequency of the incident sound wave; The displacement field u(x) in the elastic body satisfies the elastic dynamics Navier-Cauchy equation: σ ij,j +ρ s ω 2 u i = 0, in Ω s where σ ij is the Cauchy stress tensor, σ ij,j is the partial derivative of the stress tensor with respect to the coordinate x j , u i is the i-th component of the elastic displacement field, in Ω s denotes the domain of the elastic body; the indices i, j = 1,..., d, repeated indices are subject to Einstein's summation convention; the symbol j indicates the derivative with respect to the coordinate, i.e. ρ s is the solid density, ω is the angular frequency; At the acoustic-solid coupling boundary, the total sound pressure field and the displacement field should satisfy the transmission condition: where p is the density of the fluid, u is the displacement of the elastic body, p is the total sound pressure in the fluid domain, n is the unit normal vector of the acoustic-structure coupling boundary, n is the i / j direction component of the unit normal vector n, and n is the k direction component of the unit normal vector n. f n t i j is represented on the acoustic-structure coupling boundary.​​​​​ 3. The method of claim 1, wherein, In step S2, when constructing the loss function with physical constraints, the real part and the imaginary part of the fluid domain scattered sound pressure field and the elastic body domain displacement field are evaluated and the residual is calculated respectively; considering the complex-valued nature of the sound pressure field and the displacement field the loss functions need to be evaluated separately for the real and imaginary parts of the predicted values, being the real part of the predicted scattered sound pressure, being the imaginary part of the predicted scattered sound pressure, being the real part of the predicted elastomer displacement, being the imaginary part of the predicted elastomer displacement; The specific mathematical expression of each loss function is defined as follows: where x j is the coordinate of the i-th sampling point, 2 is the square of the absolute value, i is the sampling point number, j is the direction component, is the real part of the x-direction stress derivative, p s is the solid density, is the real part of the x-direction displacement, is the imaginary part of the x-direction stress derivative, is the imaginary part of the x-direction displacement, is the real part of the y-direction stress derivative, is the real part of the y-direction displacement, is the imaginary part of the y-direction stress derivative, is the imaginary part of the y-direction displacement, is the real part of the displacement vector, is the real part of the total sound pressure prediction, s Re is the real part of the Cauchy stress tensor vector, is the imaginary part of the displacement vector, is the imaginary part of the total sound pressure prediction, is the imaginary part of the Cauchy stress tensor vector; Re and Im represent the real part and the imaginary part, respectively, are the total number of fluid domain collocation points, elastic body domain collocation points, far-field absorbing radiation boundary condition sampling points, and acoustic-structure coupling boundary condition sampling points, respectively.

4. The method of claim 1, wherein, In step S3, in the decoupled parallel physical information neural network architecture, gain adjustment based on prior knowledge is applied to the network output; Specifically, the amplitude of the incident sound pressure is used to adjust the scattered sound pressure output by the fluid domain neural network, and the inverse of the Young's modulus of the target is used to adjust the displacement output by the elastic body domain neural network.

5. The method of claim 1, wherein, In step S3, the two networks are physically coupled by sharing the sample points and their corresponding boundary condition loss functions at the acoustic-structure coupling boundary, including: the total loss function is defined as the weighted sum of the loss functions of each sub-network, expressed as: where L(θ p ,θ u ) is the total loss function, is the fluid domain partial differential equation residual loss, is the far-field absorbing radiation boundary condition loss, is the elastomer domain partial differential equation residual loss, is the acoustic-structure coupling boundary condition loss, θ p ,θ u represent the network parameters of the fluid domain acoustic pressure field NN p and the elastomer domain displacement field NN u , respectively; An adaptive weight method based on soft attention mechanism is introduced, and a trainable weight function is designed for the configuration points. The soft multiplication mask attention mechanism is introduced into the loss function of PINN. The adaptive PINN loss function can be expressed as: where L(θ, λ) is the total loss function of adaptive weights, is the fluid domain partial differential equation residual loss of adaptive weights, is the far-field absorbing radiation boundary condition loss of adaptive weights, is the elastomer domain partial differential equation residual loss of adaptive weights, is the acoustic-structure coupling boundary condition loss of adaptive weights; Adaptive weight vector Fluid domain weight Artificial truncated boundary weight Elastomer domain weight And coupled boundary weight Each sub-loss term corresponds to the residual mean square error of different physical regions: where m(λ i ) is the excitation function, λ i is the adaptive weight of region i, m(λ) is defined on the non-negative real number domain, m'(λ) indicates that the function is differentiable and strictly increasing in the interval [0, ∞), m(λ) increases the corresponding weight coefficient at the configuration point with large residual, guiding the model to automatically focus on the high gradient area in the training process; the adaptive loss function training strategy is to perform the minimization of the loss function L(θ, λ) on the network weight θ, while performing the maximization on the adaptive weight λ, that is The corresponding parameter update adopts the gradient descent / gradient ascent alternating strategy: where θ k+1 is the neural network parameter at the k+1th iteration, θ k is the neural network parameter at the kth iteration, is the gradient of the loss function L with respect to the network parameter θ, is the fluid domain adaptive weight at the k+1th iteration, is the fluid domain adaptive weight at the kth iteration, is the learning rate of the fluid domain adaptive weight, is the gradient of the loss function L with respect to the adaptive weight , is the far-field absorbing radiation boundary adaptive weight at the k+1th iteration, is the far-field absorbing radiation boundary adaptive weight at the kth iteration, is the learning rate of the far-field absorbing radiation boundary adaptive weight, is the gradient of the loss function L with respect to the adaptive weight , is the elastodynamics domain adaptive weight at the k+1th iteration, is the elastodynamics domain adaptive weight at the kth iteration, is the learning rate of the elastodynamics domain adaptive weight, is the gradient of the loss function L with respect to the adaptive weight , is the acoustic-structure coupling boundary adaptive weight at the k+1th iteration, is the acoustic-structure coupling boundary adaptive weight at the kth iteration, is the learning rate of the acoustic-structure coupling boundary adaptive weight, is the gradient of the loss function L with respect to the adaptive weight , l r is the learning rate of the neural network weight; The update step is expressed as: wherein is the gradient of the loss function with respect to the parameters of the flow neural network at the kth iteration, is the gradient scaling factor for the adaptive weights of the i-th sample point in the fluid domain at the kth iteration. The network architecture of the decoupled parallel model allows the network structure and hyperparameters of the fluid domain and the elastic domain to be optimized independently.

6. The method of claim 1, wherein, The input configuration points of the physical information neural network include the input of the fluid domain neural network and the input of the elastic domain neural network. The input of the fluid domain neural network is the set of fluid domain configuration points, artificial truncated boundary sample points and acoustic-structure coupling boundary sample points. The input of the elastic domain neural network is the set of elastic domain configuration points and acoustic-structure coupling boundary sample points. The environmental parameters of the calculation problem include the incident sound wave frequency, the sound speed and density of seawater medium, the target radius, density, Young's modulus and Poisson's ratio; The number of fluid domain configuration points, elastic domain configuration points, artificial truncated boundary sample points and acoustic-structure coupling boundary sample points is determined according to the principle of at least n points per wavelength; For a two-dimensional solution domain, the total number of sample points N in the geometric domain is expressed as: Let the perimeter of the boundary be P, and each wavelength requires at least q sample points. The total number of sample points Q on the boundary is expressed as: where λ is the wavelength and L is the largest characteristic length of the domain, denotes the ceiling function.

7. The method of claim 1, wherein, The iterative training of the decoupled parallel fully connected physical information neural network uses the Adam and LBFGS hybrid optimizer to train the model.

8. The method of claim 1, wherein, The scattered sound pressure field outside the target and the displacement field inside the elastic body represent the real and imaginary parts of the fluid domain neural network output scattered sound pressure field and the real and imaginary parts of the elastic domain neural network output displacement field components, respectively.

9. A physical information neural network based underwater target acoustic scattering modeling system, characterized in that, A system for implementing the underwater target acoustic scattering modeling method based on the physical information neural network of any one of claims 1 to 8, the system comprising: A network architecture building module for building the decoupled parallel physical information neural network architecture; A loss function building module for building and embedding the loss function of the physical constraint in the physical information neural network according to the acoustic-structure coupling mathematical model; A training data generation module for generating the configuration point set of the fluid domain, elastic domain, artificial truncated boundary and acoustic-structure coupling boundary; A network prediction module for loading the trained model to calculate the sound pressure value of any coordinate point in the fluid domain and / or the displacement value of any coordinate point in the elastic body; Any one or more of the network architecture building module, loss function building module, training data generation module and network prediction module is implemented by a processor executing computer program instructions stored in a memory.

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