Physical information neural network guided complex medium inversion imaging method and system

Abstract

The invention relates to a complex medium inversion imaging method and system guided by a physical information neural network, and the method comprises the steps: constructing a two-dimensional grid model of a block structure with different medium distributions, obtaining out-of-plane displacement data at grid points through staggered grid finite difference, and forming a wave field full-waveform data set; constructing a physical information neural network, wherein the physical information neural network comprises a first feed-forward network for modeling a mapping relation of a displacement field of the sample, a second feed-forward network for modeling a velocity field of the sample, and a residual network; based on the wave field full-waveform data set, training a physical information neural network by taking minimization of compound loss as a target; and taking the space-time coordinates of the sample as input, and utilizing the trained physical information neural network to obtain predicted displacement and sound velocity of the corresponding position of the space-time coordinates, so as to realize inversion imaging of sound velocity medium distribution. According to the method, the ultrasonic propagation model of the complex medium can be quickly and accurately established under the condition that a small amount of marked data is used.

Description

Technical Field

[0001] The present invention relates to the field of ultrasonic imaging technology, and in particular, to a complex medium inversion imaging method and system guided by a physical information neural network. Background Art

[0002] High-end equipment for additive manufacturing and energy power equipment mainly based on batteries are widely used in industry. They are characterized by complex media and highly inhomogeneous materials. Specifically, due to the rapid heating, cooling, and solidification during the metal additive manufacturing (AM) process, the obtained products exhibit strong anisotropy and have quality problems caused by metallurgical defects, as well as dynamic change processes of internal inhomogeneous states of batteries such as electrolyte infiltration, gas generation, lithium plating, and interface contact change. Accurately evaluating their reliability and lifespan poses higher requirements for rapid quantitative non-destructive testing technology.

[0003] Ultrasonic waves are an effective physical sensing method. Their propagation characteristics in a medium include scattering, reflection, and refraction, and can be used to analyze the characteristics and geometry of unknown materials. In recent decades, many numerical methods have been developed to solve the partial differential equations (PDEs) describing wave propagation, thus promoting the detailed analysis of ultrasonic waves in complex media. These methods include the finite element method (FEM), the finite difference time domain method (FDTD), and the boundary element method (BEM). However, using traditional numerical methods to predict and model ultrasonic waves in complex media faces great challenges in many practical scenarios:

[0004] (1) The adopted computational paradigm is based on grid division, and finer grids and time steps are required to simulate the propagation of ultrasonic waves in complex materials, thereby increasing the demand for computing resources;

[0005] (2) Numerical simulations usually take a long time and are not practical for many applications (such as inverse problems, optimization designs, and uncertainty quantification);

[0006] (3) Traditional numerical methods are limited to integrating multi-physical phenomena and deriving equivalent simplified mathematical formulas for convenient implementation.

[0007] Chinese Patent Application Publication No. CN114858919A provides an online detection device and method for additive manufacturing based on transmissive laser ultrasound. It uses a pulsed laser to excite ultrasonic signals, combines a laser vibrometer to scan the reflected light on the surface of the additive manufacturing part, and extracts the ultrasonic signal amplitude for three-dimensional imaging to achieve real-time defect detection. However, its sound path calculation and delay superposition algorithms need to process a large amount of signal data, and it may be difficult to achieve real-time detection due to computing resource limitations in practical applications, especially more significant in complex media (such as porous structures or anisotropic materials). Summary of the Invention

[0008] The objective of the present invention is to overcome the defects existing in the above-mentioned prior art and provide a physical-information neural network-guided complex medium inversion imaging method and system, so as to solve or partially solve the problems that it is difficult to analyze the ultrasonic propagation characteristics of complex media, the calculation speed of numerical calculation methods is slow, and it is difficult to obtain sufficient data in data-driven methods.

[0009] The objective of the present invention can be achieved by the following technical solutions:

[0010] In one aspect of the present invention, a physical-information neural network-guided complex medium inversion imaging method is provided, including the following steps:

[0011] Construct a two-dimensional grid model of a block structure with different medium distributions, and through staggered-grid finite difference, obtain the out-of-plane displacement data at the grid points to form a full waveform data set of the wave field;

[0012] Construct a physical-information neural network, which includes a first feedforward network for modeling the mapping relationship of the displacement field of the specimen, a second feedforward network for modeling the velocity field of the specimen, and a residual network;

[0013] Based on the full waveform data set of the wave field, train the physical-information neural network with the objective of minimizing the composite loss;

[0014] Using the spatio-temporal coordinates of the specimen as the input, and utilizing the trained physical-information neural network, obtain the predicted displacement and sound speed at the positions corresponding to the spatio-temporal coordinates, and realize the inversion imaging of the sound speed medium distribution.

[0015] As a preferred technical solution, the first feedforward network is modeled as:

[0016] H 1 (v) = σ(w 1 v 0 + b 1 ),

[0017] H k (v) = σ(w k v k-1 + b k ), k = 2,..., L - 1,

[0018] u θ (v) = w L v L-1 + b L ),

[0019] In the above formula, {w k , b k} represents the learnable hyperparameters of the k-th layer network, and H k represents the output of the k-th layer network, and vk-1 represents the output of the (k - 1)-th layer network, u θ (v) characterizes the ultrasonic wave field of the complex medium, and L is the number of hidden layers.

[0020] As a preferred technical solution, the second feedforward network is modeled as:

[0021] H 1 (η) = σ(w 1 η 0 + b 1 ),

[0022] H k (η) = σ(w k η k-1 + b k ), k = 2, …, L - 1,

[0023] c θ (η) = w L η L-1 + b L ,

[0024] In the above formula, {w k , b k} represents the learnable hyperparameters of the k-th layer network, H k represents the output of the k-th layer network, η k-1 represents the output of the (k - 1)-th layer network, and c θ (η) characterizes the sound speed distribution of the complex medium, and L is the number of hidden layers.

[0025] As a preferred technical solution, the residual network is modeled as:

[0026] Use the feedforward neural network to calculate the ultrasonic displacement field;

[0027] Obtain the physical variable values by automatically differentiating the ultrasonic displacement field, and calculate the complex loss function.

[0028] As a preferred technical solution, the process of training the physics-informed neural network includes the following steps:

[0029] According to the preset boundary of the solution domain, obtain multiple training points in the solution domain, boundary, and initial values by sampling;

[0030] According to the preset boundary of the solution domain, obtain multiple training points in the solution domain, boundary, and initial values by sampling;

[0031] Two different full waveform datasets of wave fields obtained based on finite differences are used as the label data for the first feedforward network in the physics-informed neural network. The hyperparameters of the second feedforward network are randomly initialized, and the composite loss value is calculated by automatic differentiation based on the outputs of the first feedforward network and the second feedforward network in the residual network.

[0032] Based on the composite loss function value, the hyperparameters of the physics-informed neural network are updated by backpropagation.

[0033] As a preferred technical solution, multiple training points are obtained by LHS sampling, random sampling, or Sobol' sequence sampling.

[0034] As a preferred technical solution, the composite loss is calculated by the following formula:

[0035]

[0036] In the above formula, are the training points of the solution domain, boundary, and initial values obtained by sampling, x and t are the spatial and temporal coordinates, N r 、N bc 、N ic are the numbers of training points of the solution domain, boundary, and initial values respectively, are the differential equation loss, boundary condition loss, and initial value loss respectively, represents the differential operator, and represent the boundary operator and initial operator, u θ () is the output of the first feedforward network, and f(), g(), h() are the functions to be fitted.

[0037] As a preferred technical solution, during the training process of the physics-informed neural network, the training data is standardized, and the partial differential equation in the loss function is scaled so that the sound speed is between (0,1).

[0038] As a preferred technical solution, the construction process of the two-dimensional grid model includes:

[0039] Establish a linear block grid model corresponding to different sound speeds;

[0040] Configure the positions of single excitation array elements in the block grid model, and symmetrically load out-of-plane displacement signals at the positions of the excitation array elements;

[0041] Configure the single body size of the grid division to be 3e-4m and the time step to be 5e-6s;

[0042] On the premise that the position of the excitation array element is fixed and the quantity is unique, the time-domain signals of each grid point are obtained as the out-of-plane displacement data to form a full waveform dataset of the wave field.

[0043] Another aspect of the present invention provides a physical information neural network-guided complex medium inversion imaging system for implementing the foregoing complex medium inversion imaging method, including:

[0044] An interleaved grid finite difference construction module for constructing a two-dimensional grid model of a block structure with different medium distributions, obtaining out-of-plane displacement data at grid points through interleaved grid finite difference, and forming a full waveform data set of the wave field;

[0045] A physical information neural network construction module for constructing a physical information neural network, where the physical information neural network includes a first feedforward network for modeling the mapping relationship of the displacement field of the specimen, a second feedforward network for modeling the velocity field of the specimen, and a residual network;

[0046] A physical information neural network training module for training the physical information neural network based on the full waveform data set of the wave field with the goal of minimizing the composite loss;

[0047] A complex medium inversion imaging module for taking the spatio-temporal coordinates of the specimen as input, and using the trained physical information neural network to obtain the predicted displacement and sound velocity at the position corresponding to the spatio-temporal coordinates, and realizing the inversion imaging of the sound velocity medium distribution.

[0048] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0049] (1) High computational efficiency: The present invention uses the interleaved grid finite difference algorithm to establish a two-dimensional model of complex media, generates a full waveform data set of the wave field, constructs two feedforward neural networks (approximating the displacement field and the velocity field respectively) and a residual network, and connects them through automatic differentiation technology to form a closed-loop physical information neural network framework. Compared with traditional numerical methods (such as FDTD, FEM), the computational speed is effectively improved, and there is no need to rely on high-precision grid division, reducing the computational resource requirements.

[0050] (2) Reduced data requirements: The residual network of the present invention uses automatic differentiation technology to calculate the partial derivatives of the displacement field, constructs a composite loss function in the form of a wave equation operator, and optimizes the loss function through a scaling factor, significantly accelerating the training convergence speed. Only the wave field data of two time segments are needed to accurately and quickly predict the propagation of ultrasonic waves and invert the sound velocity distribution of the medium, breaking the dependence of traditional data-driven methods on a large amount of labeled data, and is especially suitable for scenarios where experimental data is scarce.

[0051] (3) High modeling accuracy: The present invention only requires wave field data at two initial moments as labels, combines unlabeled spatio-temporal coordinate sampling data (LHS, Sobol sequence, etc.) for training, accelerates the calculation through the graphics card, improves the efficiency of the staggered grid finite difference method, quickly generates high-quality training data, combines the fast data generation ability of the staggered grid finite difference method with the graphics card acceleration technology, and optimizes the overall calculation efficiency.

[0052] (4) Strong flexibility and versatility: The present invention takes the sound speed distribution as a trainable variable of the neural network, directly defines the defect shape and position through the difference in sound speed assignment, uses the Tanh activation function and the Adam optimization algorithm to improve the non-linear mapping ability and training stability, directly inverses the medium defect by taking the sound speed as a trainable variable, simplifies the imaging process and improves the positioning accuracy. Brief Description of the Drawings

[0053] Figure 1 It is a flow chart of the physical information neural network-guided complex medium inversion imaging method in the embodiment;

[0054] Figure 2 It is a schematic diagram of the physical information neural network in the embodiment;

[0055] Figure 3 It is a schematic diagram of the finite difference sound speed model in the embodiment;

[0056] Figure 4 It is a comparison diagram of the PINN ultrasonic modeling prediction result and the FDTD result in the embodiment;

[0057] Figure 5 It is a comparison diagram of the sensor received signal and the reference solution in the embodiment;

[0058] Figure 6 It is a schematic diagram of the prediction result of the test set in the embodiment;

[0059] Figure 7 It is a schematic diagram of the physical information neural network-guided complex medium inversion imaging system in the embodiment;

[0060] Figure 8 It is a schematic diagram of the electronic device in the embodiment. Detailed Embodiments

[0061] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] Embodiment 1

[0063] Aiming at the problems that it is difficult to analyze the ultrasonic propagation characteristics in complex media, the calculation speed of numerical calculation methods is slow, and it is difficult to obtain sufficient data in data-driven methods, in this embodiment, a physical-information neural network-guided complex medium inversion imaging method is provided under the condition of using a small amount of labeled data, so as to quickly and accurately establish an ultrasonic propagation model of complex media, and at the same time, the quantitative inversion imaging of the sound velocity distribution of complex media can be realized by parameterizing the velocity term of the damage function through a feedforward neural network.

[0064] See Figure 1 , this method mainly includes the following steps:

[0065] Step S1, staggered-grid finite-difference construction. Specifically, step S1 includes steps S101 - S104:

[0066] Step S101, setting model structure parameters.

[0067] A grid model of a block (30×30mm 2 , with sound velocities of 1400m / s, 1200m / s, and 1000m / s) established using python software, the schematic diagram is as Figure 3 shown. The control equation to be solved is the linear acoustic wave equation, and material nonlinearity and geometric nonlinearity are not considered during the simulation process.

[0068] Step S102, setting excitation signal parameters.

[0069] In the simulation, the excitation array element is single and the position is fixed. An out-of-plane displacement signal is symmetrically loaded at the position of the excitation array element. The excitation signal is a 1-cycle Ricker wavelet time-domain pulse signal. Among them, the amplitude of the displacement signal is taken as 1e-8m, and the excitation frequency is set to 30kHz.

[0070] Step S103, setting grid parameters.

[0071] Taking into account factors such as the calculation accuracy and efficiency of the model, the size of the unit cell is set to 3e-4m during grid division, the time step is 5e-6s, and the ultrasonic propagation for 1.4ms is simulated.

[0072] Step S104, obtaining complete data.

[0073] The number of excitation array elements in the model is unique and the position is fixed. Receivers are placed at all grid points to extract the full-field time-domain signal. The dimension of the full-wavefield data is 101×101×280.

[0074] Step S2, constructing a physical-information neural network (PINN).

[0075] As Figure 2As shown, the PINN of this embodiment includes two parts: a feedforward neural network and a residual network. The two parts of the network are integrated together through a feedback mechanism to form the PINN dynamics. Specifically, step S2 may include steps S201 - S203.

[0076] Step S201, establish a feedforward neural network.

[0077] The physical phenomena of complex systems can be described by partial differential equations (PDEs). Essentially, the partial differential equations on a bounded domain can be expressed in the following general form

[0078]

[0079] where u(x, t) is the potential physical field corresponding to the solution of the PDE, x and t are the spatial and temporal coordinates, represents the differential operator, and represent the boundary operator and the initial operator.

[0080] In PINN, according to the universal approximation theorem, a fully connected feedforward neural network is considered, which has an input layer and L hidden layers, and is used to approximate the unknown physical field u. Among them, the input layer v = [x, t] includes the spatial coordinate x and the temporal coordinate t. The number of neurons in the k-th hidden layer is denoted as N k , and the feedforward process is expressed as:

[0081] H 1 (v) = σ(w 1 v 0 + b 1 ),

[0082] H k (v) = σ(w k v k-1 + b k ), k = 2,..., L - 1,

[0083] u θ (v) = w L v L-1 + b L ,

[0084] where {w k , b k} represents the learnable hyperparameters of the k-th layer network. u θ (v) can be used to approximate the ultrasonic wave field of complex media.

[0085] When the task is to characterize the sound speed distribution of a complex medium through the full-field time-domain ultrasonic signals collected in an unknown complex medium, another fully connected feedforward neural network needs to be constructed to approximate the sound speed distribution c θ (η). Its input layer η = [x] only includes spatial coordinates, and its feedforward process is expressed as

[0086] H 1 (η) = σ(w 1 η 0 +b 1 ),

[0087] H k (η) = σ(w k η k-1 +b k ), k = 2,..., L-1,

[0088] c θ (η) = w L η L-1 +b L .

[0089] Step S202, construction of the residual network.

[0090] In the residual network, automatic differentiation (AD) is used to calculate the derivative of the PDE. For example, if y is an equation that can be represented by multiple basic functions such as A, B, C, etc., as shown in the following formula, AD calculates the derivative of a physical quantity by applying the chain rule to these basic arithmetic operations.

[0091] y = A(B(C(x))) = A(B(z0)) = A(z1)

[0092] where z0 = C(x), z1 = B(z0), and y = A(z1).

[0093] Automatic differentiation, that is, calculating the difference or algorithmic difference, is a key difference between PINN and traditional methods such as FDM / FEM, as shown below.

[0094]

[0095] In this embodiment, a feedforward network is used to obtain the displacement field u, and various other physical variables such as stress and strain are obtained by automatically differentiating the displacement field u through PyTorch in the residual network, and then the composite loss function is calculated.

[0096] The physical information model can be trained by minimizing the following composite loss function:

[0097]

[0098]

[0099] In the formula, is the partial differential equation term, and in this case, it is specifically represents the boundary condition term, represents the initial condition term. are the training points of the solution domain, boundary, and initial values calculated using sampling algorithms such as LHS, random sampling, and Sobol′ sequence.

[0100] Step S203, data set preprocessing.

[0101] Set the size of the solution domain (x, y, t) to determine the boundary range, solve the interior of the domain, boundary, and initial values respectively, and then take a set number of training points in the solution domain through the sampling algorithm Use the wave field data at t = 0.5 ms and t = 0.75 ms obtained by finite difference as the initial condition constraints. The first time snapshot is used to constrain the position and shape of the excitation source, and the second time snapshot is used to constrain the propagation direction of the excitation source.

[0102] To improve the model accuracy and the convergence speed of model training, perform standardization processing on the training data, and scale the partial differential equation in the loss function so that the sound speed is between (0, 1).

[0103]

[0104] Using the scaling factors α = 1 / max(c) and β = 1 / max(|u i |), the scaled partial differential equation damage term is:

[0105]

[0106] Step S3, training and prediction of the physics-informed neural network.

[0107] After establishing the complete framework of the physics-informed neural network through the above description, extract features from the wave field data of the multi-layer heterogeneous structure obtained by finite difference, and predict the true sound speed distribution under the guidance of the wave equation operator (i.e., the residual of the partial differential equation, corresponding to the F operator - f(x)).

[0108] First, the wave field data at t = 0.5 ms and t = 0.75 ms obtained by finite difference are used as the input of a feedforward neural network. After calculation through the fully connected layer, the mapping relationship between its spatio-temporal coordinates and ultrasonic displacement is established. Another feedforward neural network establishes the mapping relationship between the spatial coordinates and the sound speed of the medium after calculation through the fully connected layer based on the training points obtained by the sampling algorithm in the spatial domain. Then, the automatic differentiation of Pytorch is used to calculate the derivatives of each order of the displacement, and further calculate the value of the loss function. By minimizing the composite loss function, the hyperparameters of the two feedforward neural networks are updated by backpropagation to predict the correct displacement field and velocity field. In addition, the Tanh activation function is used to realize the non-linear mapping of features. The Adam optimization algorithm is selected during the network training process, the learning rate is set to 0.0005, the loss function is selected as MSE, and the number of iterations is set to 20,000.

[0109] After the neural network model training is completed, the test set data of the three-layer heterogeneous model at t = 0.75 ms, t = 1 ms, t = 1.25 ms, and t = 1.4 ms are predicted and compared with the wave field data obtained by actual finite difference. The results are as Figure 4 shown, and the PINN wave field prediction results are consistent with FDTD. Figure 5 Four receiving sensors are evenly placed at equal intervals from (0.12, 0.12) to (0.12, 0.21) in the three-layer heterogeneous model and compared with the results obtained by FDTD solution. The sensor received signals show a high degree of consistency between the predicted values and the true values, and the prediction results are accurate. The inversion results of the sound speed medium distribution are predicted by the feedforward neural network approaching the sound speed, and the results are as Figure 6 shown, and it can be seen that there is an obvious three-layer medium stratification, and its sound speed is roughly the same as the true speed model.

[0110] In summary, this method provides an effective and novel means, which has important application value for the non-destructive testing, damage identification and interface simulation of complex materials. This method has the following characteristics:

[0111] (1) Only the wave field data of two time segments are needed to accurately and quickly predict the propagation of ultrasonic waves and invert the sound speed distribution of the medium, and it has stronger generalization ability compared with traditional neural networks;

[0112] (2) The ultrasonic modeling of complex media can be realized without expensive numerical schemes;

[0113] (3) It improves the universality of the application of the neural network model under a small amount of labeled data.

[0114] Example 2

[0115] On the basis of Example 1, see Figure 7, this embodiment provides a complex medium inversion imaging system guided by a physical information neural network for implementing the complex medium inversion imaging method of Embodiment 1. The system includes:

[0116] (1) The staggered grid finite difference construction module is used to construct a two-dimensional grid model of a block structure with different medium distributions, and through staggered grid finite difference, obtain the out-of-plane displacement data at the grid points to form a full waveform data set of the wave field.

[0117] (2) The physical information neural network construction module is used to construct a physical information neural network, and the physical information neural network includes a first feedforward network for modeling the mapping relationship of the displacement field of the specimen, a second feedforward network for modeling the velocity field of the specimen, and a residual network.

[0118] (3) The physical information neural network training module is used to train the physical information neural network based on the full waveform data set of the wave field with the goal of minimizing the composite loss.

[0119] (4) The complex medium inversion imaging module is used to take the spatio-temporal coordinates of the specimen as input, and use the trained physical information neural network to obtain the predicted displacement and sound speed at the position corresponding to the spatio-temporal coordinates, and realize the inversion imaging of the sound speed medium distribution.

[0120] Embodiment 3

[0121] Based on the foregoing embodiments, this embodiment provides an electronic device, including: one or more processors and a memory, and the memory stores one or more programs, and the one or more programs include instructions for executing the complex medium inversion imaging method of Embodiment 1.

[0122] As Figure 8 described, at the hardware level, the electronic device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for other services. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the above Figure 1 described method. Of course, in addition to the software implementation method, the present invention does not exclude other implementation methods, such as logical devices or a combination of software and hardware, etc. That is to say, the execution subject of the following processing flow is not limited to each logical unit, and can also be hardware or a logical device.

[0123] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of, for example, read-only memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.

[0124] A computer-readable medium includes permanent and non-permanent, removable and non-removable media that can implement information storage by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer-readable medium does not include transitory computer-readable media, such as modulated data signals and carrier waves.

[0125] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A complex medium inversion imaging method guided by a physical information neural network, characterized in that: The steps include: A two-dimensional grid model with block structures and different medium distributions is constructed. Through staggered grid finite difference, the off-plane displacement data at the grid points are obtained to form a full waveform data set of the wave field. Constructing a physical information neural network, the physical information neural network comprising a first feedforward network for modeling a mapping relationship of a displacement field of the sample, a second feedforward network for modeling a velocity field of the sample, and a residual network; Based on the wavefield full waveform data set, the physical information neural network is trained with the goal of minimizing composite loss; Taking the space-time coordinates of the sample as input, the trained physical information neural network is used to obtain the predicted displacement and sound speed of the position corresponding to the space-time coordinates, thereby realizing the inversion imaging of the sound speed medium distribution.

2. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: The first feedforward network is modeled as: H 1 (v)=σ(w 1 v 0 +b 1 ), H k (v)=σ(w k v k-1 +b k ),k=2,...,L-1, u θ (v)=w L v L-1 +b L , In the above formula, {w k , b k } represents the learnable hyperparameters of the k-th layer network, H k represents the output of the k-th layer network, v k-1 represents the output of the k-1th layer network, u θ (v) Characterization of ultrasonic wave fields in complex media, where L is the number of hidden layers.

3. The complex medium inversion imaging method guided by a physical information neural network according to claim 1 is characterized in that: The second feedforward network is modeled as: H 1 (η)=σ(w 1 η0 + b 1 ), H k (η)=σ(w k or k-1 +b k ), k=2,…, L-1, c θ (h)=w L or L-1 +b L , In the above formula, {w k , b k } represents the learnable hyperparameters of the k-th layer network, H k represents the output of the k-th layer network, η k-1 represents the output of the k-1th layer network, c θ (η) represents the sound velocity distribution of complex media, and L is the number of hidden layers.

4. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: The residual network model is: Calculate ultrasonic displacement field using feedforward neural network; The physical variable value is obtained by automatically differentiating the ultrasonic displacement field, and the complex loss function is calculated.

5. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: The process of training the physical information neural network includes the following steps: According to the preset solution domain boundary, multiple training points in the solution domain, boundary and initial value are obtained by sampling; Two different wavefield full waveform data sets obtained based on finite differences are used as label data of a first feedforward network in the physical information neural network, hyperparameters of a second feedforward network are randomly initialized, and a composite loss value is calculated by automatic differentiation based on the outputs of the first feedforward network and the second feedforward network in the residual network; Based on the value of the loss function, back propagation updates the hyperparameters of the physical information neural network.

6. The complex medium inversion imaging method guided by a physical information neural network according to claim 5, characterized in that: Multiple training points are obtained through LHS sampling, random sampling or Sobol' sequence sampling.

7. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: The composite loss is calculated using the following formula: In the above formula, are the sampled training points for the solution domain, boundary, and initial value, x and t are the spatial and time coordinates, N r 、N bc 、N ic are the number of training points for the solution domain, boundary and initial value, respectively. They are differential equation loss, boundary condition loss and initial value loss respectively. represents the differential operator, and represents the boundary operator and the initial operator, u θ () is the output of the first feedforward network, and f(), g(), and h() are the functions to be fitted.

8. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: In the training process of physical information neural network, the training data is standardized and the scale of partial differential equation in the loss function is scaled to the speed of sound between (0,1).

9. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: The construction process of the two-dimensional grid model includes: Establish a linear block grid model corresponding to different sound speeds; Configure the position of a single excitation array element in the block grid model, and symmetrically load the off-plane displacement signal at the position of the excitation array element; Configure the mesh size to 3e-4m and the time step to 5e-6s; Under the premise that the positions of the excitation array elements are fixed and the number is unique, the time domain signals of each grid point are obtained as the off-plane displacement data to form a full waveform data set of the wave field.

10. A complex medium inversion imaging system guided by a physical information neural network, characterized in that: A method for implementing complex medium inversion imaging as claimed in any one of claims 1 to 9, comprising: The staggered grid finite difference construction module is used to construct a two-dimensional grid model with a block structure with different medium distributions. Through the staggered grid finite difference, the off-plane displacement data at the grid points are obtained to form a full waveform data set of the wave field; A physical information neural network construction module, used to construct a physical information neural network, wherein the physical information neural network includes a first feedforward network for modeling a mapping relationship of a displacement field of the sample, a second feedforward network for modeling a velocity field of the sample, and a residual network; A physical information neural network training module, used for training the physical information neural network based on the wave field full waveform data set with the goal of minimizing composite loss; The complex medium inversion imaging module is used to take the space-time coordinates of the sample as input, use the trained physical information neural network to obtain the predicted displacement and sound speed of the corresponding position of the space-time coordinates, and realize the inversion imaging of the sound speed medium distribution.

Images