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

Abstract

The application relates to a physical information neural network guided complex medium inversion imaging method and system, and the method comprises the following steps: a two-dimensional grid model of a block structure with different medium distribution is constructed, off-plane displacement data at grid points are obtained through staggered grid finite difference, and a wave field full waveform data set is formed; a physical information neural network is constructed, the physical information neural network comprises a first feedforward network for modeling a mapping relationship of a displacement field of a sample, a second feedforward network for modeling a velocity field of the sample and a residual network; based on the wave field full waveform data set, the physical information neural network is trained with the minimum composite loss as the target; and the trained physical information neural network is used to obtain predicted displacement and sound velocity at a position corresponding to a space-time coordinate of the sample with the space-time coordinate of the sample as input, so that inversion imaging of the sound velocity medium distribution is realized. The application can quickly and accurately establish an ultrasonic wave propagation model of a complex medium under the condition of using a small amount of labeled data.

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 additive manufacturing equipment and battery-based energy and power equipment are widely used in industry. They are characterized by complex media and highly inhomogeneous materials. Specifically, due to the rapid heating, cooling and solidification of metal additive manufacturing (AM) processes, the products obtained exhibit strong anisotropy and quality problems caused by metallurgical defects, as well as dynamic changes in the internal inhomogeneous state of the battery, such as electrolyte infiltration, gas generation, lithium precipitation, and changes in interface contact. Accurately assessing its reliability and lifespan puts higher demands on rapid quantitative non-destructive testing technology.

[0003] Ultrasonic waves are an effective physical sensing method. Their propagation characteristics in media include scattering, reflection, and refraction, which can be used to analyze the properties and geometry of unknown materials. In recent decades, many numerical methods have been developed to solve the partial differential equations (PDEs) that describe wave propagation, thereby facilitating 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 huge challenges in many practical scenarios:

[0004] (1) The computational paradigm used is based on meshing, which requires the use of finer meshes and time steps to simulate the propagation of ultrasound in complex materials, thereby increasing the demand for computational resources;

[0005] (2) Numerical simulations are usually time-consuming and impractical for many applications (e.g., inverse problems, optimization design, and uncertainty quantification);

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

[0007] Chinese patent application publication number CN114858919A provides an online detection device and method for additive manufacturing based on transmission laser ultrasound. This method uses a pulsed laser to excite an ultrasonic signal, combined with a laser vibrometer to scan the reflected light from the surface of the additively manufactured part, extracting the ultrasonic signal amplitude for three-dimensional imaging, and achieving real-time defect detection. However, its acoustic path calculation and delay superposition algorithms require processing large amounts of signal data, making real-time detection difficult in practical applications due to limited computing resources. This is particularly true in complex media (such as porous structures or anisotropic materials). Summary of the Invention

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

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

[0010] One aspect of the present invention provides a complex medium inversion imaging method guided by a physical information neural network, comprising the following steps:

[0011] A two-dimensional grid model with a block structure and different medium distribution is constructed. Through staggered grid finite difference, the out-of-plane displacement data at the grid points are obtained to form a full waveform data set of the wave field.

[0012] Constructing a physical information neural network, the physical information neural network including 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;

[0013] Based on the full waveform data set of the wave field, the physical information neural network is trained with the goal of minimizing composite loss;

[0014] 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.

[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, H k represents the output of the k-th layer network, vk-1 represents the output of the k-1 layer network, u θ (v) Characterization of ultrasonic wave fields in complex media, where 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-1th layer network, c θ (η) represents the sound velocity distribution of the complex medium, and L is the number of hidden layers.

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

[0026] Calculate ultrasonic displacement field using feedforward neural network;

[0027] The physical variable value is obtained by automatically differentiating the ultrasonic displacement field, and the composite loss function is calculated.

[0028] As a preferred technical solution, the process of training the physical information neural network includes the following steps:

[0029] According to the preset solution domain boundary, multiple training points in the solution domain, boundary and initial value are obtained by sampling;

[0030] Two different wavefield full waveform datasets obtained based on finite differences are used as label data for 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 and second feedforward networks in a residual network;

[0031] Based on the composite loss function value, backpropagation updates the hyperparameters of the physical information neural network.

[0032] As a preferred technical solution, multiple training points are obtained through LHS sampling, random sampling or Sobol sequence sampling.

[0033] As a preferred technical solution, the composite loss is calculated using the following formula:

[0034]

[0035] In the above formula, is the sampled training point of the solution domain, boundary and initial value, x and t are the space and time coordinates, N r 、N bc 、N ic are the number of training points for the solution domain, boundary, and initial value, respectively. 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.

[0036] As a preferred technical solution, during the training process of the physical information neural network, the training data is standardized and the scale of the partial differential equation in the loss function is scaled to a sound speed between (0,1).

[0037] As a preferred technical solution, the process of constructing the two-dimensional grid model includes:

[0038] Establish a linear block grid model corresponding to different sound speeds;

[0039] Configure the position of a single excitation array element in the block grid model and symmetrically load the out-of-plane displacement signal at the position of the excitation array element;

[0040] Configure the mesh size to 3e-4m and the time step to 5e-6s;

[0041] Under the premise that the excitation array element positions are fixed and the number is unique, the time domain signal of each grid point is obtained as the off-plane displacement data to form a full waveform data set of the wavefield.

[0042] Another aspect of the present invention provides a complex medium inversion imaging system guided by a physical information neural network, which is used to implement the aforementioned complex medium inversion imaging method, comprising:

[0043] The staggered grid finite difference construction module is used to construct a two-dimensional grid model with a block structure of different media distributions. Through staggered grid finite differences, the out-of-plane displacement data at the grid points are obtained to form a full waveform data set of the wave field;

[0044] A physical information neural network construction module is 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;

[0045] A physical information neural network training module is used to train the physical information neural network based on the wavefield full waveform data set with the goal of minimizing composite loss;

[0046] 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.

[0047] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0048] (1) High computational efficiency: This paper uses a staggered grid finite difference algorithm to establish a two-dimensional model of complex media and generate a full waveform data set of the wave field. Two feedforward neural networks (approximating the displacement field and velocity field, respectively) and a residual network are constructed and connected through automatic differentiation technology to form a closed-loop physical information neural network framework. Compared with traditional numerical methods (such as FDTD and FEM), this method significantly improves the computational speed and does not rely on high-precision meshing, reducing the demand for computing resources.

[0049] (2) Reduce data requirements: The residual network of the present invention uses automatic differentiation technology to calculate the partial derivatives of the displacement field and construct a composite loss function in the form of a wave equation operator. In addition, the loss function is optimized by a scaling factor, which significantly accelerates the training convergence speed. Only two time segments of wave field data 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 massive labeled data. It is particularly suitable for scenarios where experimental data is scarce.

[0050] (3) High modeling accuracy: The present invention only requires wave field data at two initial moments as labels, and combines them with unlabeled spatiotemporal coordinate sampling data (LHS, Sobol sequence, etc.) for training. By accelerating calculations with a graphics card, the efficiency of the staggered grid finite difference method is improved, and high-quality training data is quickly generated. The fast data generation capability of the staggered grid finite difference method and graphics card acceleration technology are combined to optimize the computational efficiency of the entire process.

[0051] (4) Strong flexibility and versatility: The present invention uses the sound velocity distribution as a trainable variable of the neural network, directly defines the defect shape and position through the difference in sound velocity assignment, uses the Tanh activation function and the Adam optimization algorithm to improve the nonlinear mapping capability and training stability, and uses the sound velocity as a trainable variable to directly invert the medium defects, simplifying the imaging process and improving the positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of a complex medium inversion imaging method guided by a physical information neural network in an embodiment;

[0053] Figure 2 A schematic diagram of a physical information neural network in an embodiment;

[0054] Figure 3 Schematic diagram of the finite difference sound velocity model in the embodiment;

[0055] Figure 4 A comparison diagram of the PINN ultrasound modeling prediction results and the FDTD results in the embodiment;

[0056] Figure 5 A comparison diagram of the sensor receiving signal and the reference solution in the embodiment;

[0057] Figure 6 Schematic diagram of the prediction results of the test set in the embodiment;

[0058] Figure 7 Schematic diagram of a complex medium inversion imaging system guided by a physical information neural network in an embodiment;

[0059] Figure 8 Schematic diagram of an electronic device in an embodiment. DETAILED DESCRIPTION

[0060] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0061] Example 1

[0062] To address the problems of difficulty in analyzing the ultrasonic propagation characteristics of complex media, slow calculation speed of numerical calculation methods, and difficulty in obtaining sufficient data in data-driven methods, this embodiment provides a complex media inversion imaging method guided by a physical information neural network using a small amount of labeled data to quickly and accurately establish an ultrasonic propagation model of complex media. At the same time, quantitative inversion imaging of the sound velocity distribution of complex media can be achieved by parameterizing the velocity term of the damage function through a feedforward neural network.

[0063] See also Figure 1 , this method mainly includes the following steps:

[0064] Step S1, staggered grid finite difference construction. Specifically, step S1 includes steps S101-S104:

[0065] Step S101: setting model structure parameters.

[0066] The block (30×30mm) created using Python software 2 , the grid model with sound speed of 1400m / s, 1200m / s, 1000m / s) is shown in the following diagram. Figure 3 As shown in the figure, 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.

[0067] Step S102: setting excitation signal parameters.

[0068] In the simulation, the excitation array element is single and fixed in position. The off-plane displacement signal is symmetrically loaded at the position of the excitation array element. The excitation signal is a 1-cycle Riker wavelet time domain pulse signal, where the displacement signal amplitude is 1e-8m and the excitation frequency is set to 30kHz.

[0069] Step S103: grid parameter setting.

[0070] Taking into account factors such as model calculation accuracy and efficiency, the unit size is set to 3e-4m during mesh division, and the time step is 5e-6s to simulate ultrasonic propagation of 1.4ms.

[0071] Step S104: complete data acquisition.

[0072] The number of excitation array elements in the model is unique and their positions are fixed. Receivers are placed at all grid points to extract the time domain signal of the entire field. The dimension of the full wavefield data is 101×101×280.

[0073] Step S2, construction of physical information neural network (PINN).

[0074] like Figure 2As shown, the PINN of this embodiment includes two parts: a feedforward neural network and a residual network. The two networks are integrated together through a feedback mechanism to form the PINN dynamics. Specifically, step S2 may include steps S201-S203.

[0075] Step S201: Establish a feedforward neural network.

[0076] The physical phenomena of complex systems can be described by partial differential equations (PDEs). The partial differential equation on can be expressed in the following general form

[0077]

[0078] where u(x,t) is the underlying physics corresponding to the solution of the PDE, x and t are the space and time coordinates, represents the differential operator, and Represents the boundary operator and the initial operator.

[0079] 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 to approximate the unknown physical field u, where the input layer v = [x, t] includes the spatial coordinate x and the time coordinate t. The number of neurons in the kth hidden layer is denoted by N k , the feedforward process is expressed as:

[0080] H 1 (v)=σ(w 1 v 0 +b 1 ),

[0081] H k (v)=σ(w k v k-1 +b k ),k=2,…,L-1,

[0082] u θ (v) = w L v L-1 +b L ,

[0083] where {w k , b k} represents the learnable hyperparameters of the k-th layer network. θ (v) It can be used to approximate ultrasonic wave fields in complex media.

[0084] When the task is to characterize the sound velocity distribution of a complex medium by collecting ultrasonic full-field time domain signals from an unknown complex medium, it is necessary to construct another fully connected feedforward neural network to approximate the sound velocity distribution c θ (η). Its input layer η = [x] only includes spatial coordinates, and its feedforward process is expressed as

[0085] H 1 (η)=σ(w 1 η 0 +b 1 ),

[0086] H k (η)=σ(w k η k-1 +b k ), k = 2, ..., L-1,

[0087] c θ (η)=w L η L-1 +b L .

[0088] Step S202: constructing a residual network.

[0089] In residual networks, automatic differentiation (AD) is used to calculate the derivatives of PDEs. For example, if y is an equation that can be represented by multiple basic functions such as A, B, and C, as shown below, AD calculates the derivative of a physical quantity by applying the chain rule to these basic arithmetic operations.

[0090] y=A(B(C(x)))=A(B(z0))=A(z1)

[0091] Among them, z0=C(x), z1=B(z0), y=A(z1).

[0092] Automatic differentiation, also known as computational differentiation or algorithmic differentiation, is a key difference between PINN and traditional methods such as FDM / FEM, as shown below.

[0093]

[0094] This embodiment uses a feedforward network to obtain the displacement field u. Various other physical variables such as stress and strain are obtained by automatically differentiating the displacement field u in the residual network through PyTorch, and then calculating the composite loss function.

[0095] The physical information model can be trained by minimizing the following composite loss function:

[0096]

[0097]

[0098] Where, is the partial differential equation term, which in this case is

[0099] represents the boundary condition term, represents the initial condition term. These are training points for the solution domain, boundaries, 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 domain, boundary, and initial value respectively, and then use the sampling algorithm to solve the domain and take a set number of training points The wave field data at t = 0.5 ms and t = 0.75 ms obtained by finite difference are used as 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] In order to improve the accuracy of the model and the convergence speed of the model training, the training data is standardized and the scale of the partial differential equation in the loss function is scaled to the speed of sound between (0,1).

[0103]

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

[0105]

[0106] Step S3: physical information neural network training and prediction.

[0107] After establishing the complete framework of the physical information neural network through the above instructions, feature extraction is performed on the wave field data of the multi-layer heterogeneous structure obtained by finite difference, and the real sound speed distribution is predicted 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 wavefield data at t = 0.5ms and t = 0.75ms, obtained by finite difference, were fed into a feedforward neural network. After computation in a fully connected layer, a mapping relationship between the spatial coordinates and the ultrasonic displacement was established. Another feedforward neural network, based on training points obtained from the spatial domain via a sampling algorithm, was then computed in a fully connected layer to establish a mapping relationship between the spatial coordinates and the medium's acoustic velocity. Next, automatic differentiation in PyTorch was used to calculate the derivatives of the displacements and further calculate the loss function. By minimizing the composite loss function, backpropagation was used to update the hyperparameters of the two feedforward neural networks to accurately predict the displacement and velocity fields. Furthermore, the Tanh activation function was used to implement nonlinear feature mapping. The Adam optimization algorithm was used for network training, with a learning rate of 0.0005, the mean square error (MSE) loss function, and 20,000 iterations.

[0109] After the neural network model training is completed, the three-layer heterogeneous model test set data with t = 0.75ms, t = 1ms, t = 1.25ms, and t = 1.4ms are predicted and compared with the actual wave field data obtained by finite difference. The results are as follows: Figure 4 As shown in Figure 2, the PINN wavefield prediction results are consistent with those of FDTD. Figure 5 In order to place four receiving sensors at equal intervals from (0.12, 0.12) to (0.12, 0.21) in the three-layer heterogeneous model, and compare them with the results solved by FDTD, the sensor receiving signals show that there is a high consistency between the predicted value and the true value, and the prediction result is accurate. The inversion result of the sound velocity medium distribution is predicted by the feedforward neural network approximating the sound velocity, and the results are as follows Figure 6 As shown, there is an obvious three-layer medium stratification, and its sound speed is roughly the same as the true velocity model.

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

[0111] (1) Only two time-segment wavefield data are needed to accurately and quickly predict the propagation of ultrasonic waves and invert the sound velocity distribution of the medium, which has stronger generalization ability than traditional neural networks;

[0112] (2) Ultrasonic modeling of complex media can be achieved without expensive numerical solutions;

[0113] (3) Improved the application of neural network models with a small amount of labeled data.

[0114] Example 2

[0115] Based on Example 1, see Figure 7This embodiment provides a complex medium inversion imaging system guided by a physical information neural network, which is used to implement 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 with a block structure of 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.

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

[0118] (3) A physical information neural network training module, which 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) Complex medium inversion imaging module, which 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 position corresponding to the space-time coordinates, and realize the inversion imaging of the sound speed medium distribution.

[0120] Example 3

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

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

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

[0124] Computer-readable media includes permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. 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 technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0125] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection 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 a block structure and different medium distribution is constructed. Through staggered grid finite difference, the out-of-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 including 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 full waveform data set of the wave field, 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 displacement and sound velocity predicted at the corresponding position of the space-time coordinates, thus realizing the inversion imaging of the sound velocity medium distribution. 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 datasets obtained based on finite differences are used as label data for 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 and second feedforward networks in a residual network; Based on the composite loss function value, backpropagation updates the hyperparameters of the physical information neural network.

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-1 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, characterized in that: The second feedforward network is modeled as: H 1 (η)=σ(w 1 or 0 +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 the complex medium, 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 composite 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: Multiple training points are obtained through LHS sampling, random sampling or Sobol sequence sampling.

6. 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, is the sampled training point of the solution domain, boundary and initial value, x and t are the space and time coordinates, N r 、N bc 、N ic are the number of training points for the solution domain, boundary, and initial value, respectively. 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.

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

8. The complex medium inversion imaging method guided by a physical information neural network according to claim 1, characterized in that: The process of constructing 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 out-of-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 excitation array element positions are fixed and the number is unique, the time domain signal of each grid point is obtained as the off-plane displacement data to form a full waveform data set of the wavefield.

9. A complex medium inversion imaging system guided by a physical information neural network, characterized in that: A method for implementing complex medium inversion imaging according to any one of claims 1 to 8, comprising: The staggered grid finite difference construction module is used to construct a two-dimensional grid model with a block structure of different media distributions. Through staggered grid finite differences, the out-of-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 is 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 is used to train the physical information neural network based on the wavefield 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