Underwater flow field multi-parameter inversion method and system based on physical information neural network

Abstract

The underwater flow field multi-parameter inversion method based on the physical information neural network uses full waveform information of multiple groups of measured pulse responses for river sound tomography inversion, improves data utilization, and significantly improves inversion resolution; joint inversion of river section sound velocity field and vector flow velocity field is adopted to eliminate system error caused by the assumption of uniform sound velocity in traditional methods, and the inversion accuracy can be improved by more than 15%; frequency domain modeling is adopted to eliminate the dependence of traditional time domain PINN on initial conditions, adapt to long propagation time scenarios of large-scale rivers, and improve training stability and efficiency; the physical control equation is used as a natural regularization term, without manual adjustment of the regularization parameter, and the adaptability to complex flow fields is stronger; boundary constraints are integrated into the inversion process, which is more consistent with the topographic characteristics of actual rivers, and improves the inversion accuracy of complex terrain river sections; without grid division of the calculation area, it can flexibly adapt to any complex riverbed topography, and has higher deployment and calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of underwater flow field multi-parameter inversion technology, specifically to an underwater flow field multi-parameter inversion method and system based on physical information neural networks. Background Technology

[0002] River fluxes (flow rate, velocity, mass transport flux, etc.) are core monitoring indicators for water resource management, flood control and disaster reduction, and ecological environmental protection. Traditional river monitoring methods, such as ADCP mobile flow measurement and time-of-flight ultrasonic flow measurement, have limitations such as complex deployment, inability to cover the entire cross section, and difficulty in obtaining real-time three-dimensional flow field structure.

[0003] River acoustic tomography originated from ocean acoustic tomography. By deploying multiple acoustic base stations on both banks of a river cross section, the flow field and environmental parameters within the cross section are retrieved using the propagation information of sound waves in the water. This enables full-section, non-contact, real-time online monitoring, and has been widely used in the field of hydrological monitoring in recent years.

[0004] Currently, the mainstream inversion methods for river acoustic tomography are mainly based on ray travel-time tomography. Traditional travel-time inversion methods extract the propagation time of sound waves and, based on ray theory, use methods such as Tikhonov regularization to invert the velocity distribution within the cross-section. These methods only utilize the time information of sound wave propagation, ignoring the full waveform (impulse response) information of the received signal, resulting in low data utilization and limited inversion resolution.

[0005] Existing technologies typically assume that the sound velocity in water is a uniform constant, neglecting the changes in the sound velocity field caused by the spatial heterogeneity of parameters such as temperature, sediment concentration, and salinity in rivers. This introduces significant flow velocity inversion errors, especially in areas with drastic changes in environmental parameters, such as tidal river sections and estuaries, where the error can reach more than 10%.

[0006] Traditional linear inversion methods require manual selection of regularization parameters to stabilize the solution. Parameter selection depends on experience and has poor adaptability to complex non-uniform flow fields, making it difficult to simultaneously invert two high-dimensional unknown fields: the sound velocity field and the flow velocity field.

[0007] In recent years, Physical-Informed Neural Networks (PINN), as a novel deep learning framework, has shown great potential in solving high-dimensional inversion problems by incorporating physical governing equations as regularization constraints into neural network training. It has demonstrated significant promise in fields such as flow field reconstruction and wave field inversion. However, the application of PINN technology in river acoustic tomography remains unexplored.

[0008] The present invention aims to solve the above-mentioned technical problems by using a physical information neural network based on multiple sets of measured impulse responses to jointly invert the three-dimensional sound velocity field and vector flow velocity field of a river profile. Summary of the Invention

[0009] This invention provides a method and system for multi-parameter inversion of underwater flow fields based on physical information neural networks. It utilizes physical information neural networks to jointly invert the three-dimensional sound velocity field and vector velocity field of a river profile based on multiple sets of measured impulse responses, thereby solving the technical problems mentioned in the background.

[0010] This invention provides the following technical solution: a multi-parameter inversion method for underwater flow fields based on a physical information neural network, comprising: S1, data acquisition and preprocessing: acquiring measured impulse response data based on preset base stations in river acoustic tomography, the measured impulse response data including the impulse response time of any pair of transceiver base stations; S2, constructing a neural network: constructing a physical information neural network model, the input of which includes the spatial coordinates, frequency, and sound source location encoding of any point within the river cross-section, and the output including the sound velocity field and flow velocity field of the flow field; S3, frequency response prediction: using the sound velocity field and flow velocity field obtained in step S2. Calculate the frequency response and transform it to obtain the predicted impulse response; S4, Response Comparison: Compare the predicted impulse response with the measured impulse response, and adjust the sound velocity field and flow velocity field based on the comparison results to output the final sound velocity field and flow velocity field; Among them, the comparison between the predicted impulse response and the measured impulse response is based on the constraint cost function, which is a joint cost function that includes data fitting terms, physical constraint terms, and boundary constraints; use the constraint cost function to calculate the gradient of any parameter of the neural network to update the network parameters until the function converges, and output the final sound velocity field and flow velocity field to complete the inversion.

[0011] This multi-parameter inversion method for underwater flow fields based on physical information neural networks (PINNs) utilizes full waveform information from multiple sets of measured impulse responses for river acoustic tomography inversion. Compared to traditional travel-time tomography, it improves data utilization by an order of magnitude and significantly enhances inversion resolution. The joint inversion of the river cross-section sound velocity field and vector velocity field eliminates the systematic errors caused by the assumption of uniform sound velocity in traditional methods. In river sections with drastically changing environmental parameters, the inversion accuracy can be improved by more than 15%. Frequency domain modeling completely eliminates the dependence of traditional time-domain PINNs on initial conditions, adapting to the long propagation time scenarios of large-scale rivers and significantly improving training stability and efficiency. Utilizing PINNs to use physical control equations as natural regularization terms eliminates the need for manual adjustment of regularization parameters, making it more adaptable to complex flow fields. Incorporating boundary constraints into the inversion process better reflects the actual terrain characteristics of rivers, significantly improving the inversion accuracy of river sections with complex terrain. The method eliminates the need for gridding of the computational domain, flexibly adapting to arbitrarily complex riverbed terrain, resulting in higher deployment and computational efficiency.

[0012] As an optional scheme of the underwater flow field multi-parameter inversion method based on physical information neural network described in this invention, the data fitting term constraint on the matching degree between the predicted result and the measured data is constructed using the mean square error between the measured impulse response and the predicted impulse response. The data fitting term constraint includes: ,in, Let i be the measured impulse response of the i-th transmit / receive pair. To predict the impulse response, M represents the total number of transmit and receive pairs, and T represents the number of time sampling points. Physical constraints include frequency-domain motion medium wave equation constraints and fluid continuity equation constraints. The frequency-domain motion medium wave equation constraints are based on the acoustic Helmholtz equations for moving fluids in the frequency domain. The sound velocity field, flow velocity field, and predicted impulse response output by the neural network are substituted into the Helmholtz equations to calculate the residual constraint loss. The fluid continuity equation constraints ensure that the flow velocity field satisfies the continuity equations for incompressible fluids. The Helmholtz equations include: ,in, Angular frequency, For the unit direction vector formed by the transducer pairs, the frequency domain motion medium wave equation constraint requires no initial conditions, only spatial constraints; substituting the sound velocity field, flow velocity field, and predicted impulse response output by the neural network into the Helmholtz equation, the residual constraint loss of the equation is calculated, including: ,in, These are the predicted frequency response, sound velocity field, and flow velocity field, respectively. These are the spatial coordinates within the river cross-section. The continuity equation includes: The corresponding loss term is: The physical constraints are the sum of the constraints from the wave equation of the moving medium in the frequency domain and the fluid continuity equation. Boundary constraints are based on the surveyed three-dimensional topographic model of the riverbed, applying solid-wall boundary conditions, including that the normal flow velocity at the riverbed boundary satisfies the impermeable boundary condition and that the sound pressure at the riverbed boundary satisfies the reflection boundary condition of the solid-liquid interface. The normal flow velocity at the riverbed boundary satisfies the impermeable boundary condition as follows: ,in, The unit vector normal to the riverbed boundary. The velocity field is given; the sound pressure at the riverbed boundary satisfies the reflection boundary condition of the solid-liquid interface as follows: This indicates that the rate of change of the frequency response along the normal direction is zero; the loss term is defined as: ,in, This indicates the boundary area of ​​the riverbed.

[0013] As an optional scheme of the underwater flow field multi-parameter inversion method based on physical information neural network described in this invention, the inversion and network parameter update include:

[0014] 1. Initialization: Initialize the neural network parameters;

[0015] 2. Sampling: Randomly sample spatial points (x, y, z) within the cross-section, randomly sample frequency points f within the working frequency band, traverse all sound source indices S, and construct training batches;

[0016] 3. Forward prediction: Input the sampled signal into the network to obtain the predicted sound velocity field c(x,y,z), the flow velocity field v(x,y,z), and the predicted frequency response p(x,y,z,f,S);

[0017] 4. Loss Calculation: For each sound source S, extract the predicted frequency response of the receiving point, perform inverse Fourier transform to obtain the predicted impulse response, and calculate the data fitting loss; automatically differentiate to calculate the residual between the frequency domain wave equation and the fluid continuity equation to obtain the physical constraint loss; calculate the boundary constraint loss for the sampling points of the riverbed boundary; and summarize to obtain the total cost function.

[0018] 5. Parameter Update: The gradient of the total cost function with respect to all network parameters is calculated using the backpropagation algorithm, and the network parameters are updated. Training stops when the change in total loss is less than a threshold or the number of iterations reaches a preset value.

[0019] 6. Output Results: Once training is complete, the network outputs the three-dimensional sound velocity field and vector flow velocity field of the entire cross section, thus completing the inversion.

[0020] Systems employing the aforementioned multi-parameter inversion method for underwater flow fields based on physical information neural networks include:

[0021] Data acquisition and preprocessing module: used to acquire measured impulse response data based on preset base stations in river acoustic tomography;

[0022] Neural network module: used to predict the sound velocity field and flow velocity field. The input of the model includes the spatial coordinates, frequency and sound source location code of any point in the river cross section. The output includes the sound velocity field and flow velocity field of the flow field.

[0023] Frequency response prediction module: The frequency response is calculated using the sound velocity field and flow velocity field obtained by the neural network module, and the frequency response is transformed to obtain the predicted impulse response;

[0024] Response Comparison Module: After comparing the predicted impulse response with the measured impulse response, the sound velocity field and flow velocity field are adjusted based on the comparison results, and the final sound velocity field and flow velocity field are output.

[0025] Among them, the predicted impulse response is compared with the measured impulse response based on the constraint cost function, which is a joint cost function that includes data fitting terms, physical constraint terms and boundary constraints.

[0026] The gradient of any parameter of the neural network is calculated using the constraint cost function to update the network parameters until the function converges, and the final sound velocity field and flow velocity field are output to complete the inversion.

[0027] The present invention has the following beneficial effects:

[0028] 1. This multi-parameter inversion method for underwater flow fields based on physical information neural networks (PINNs) utilizes full waveform information from multiple sets of measured impulse responses for river acoustic tomography inversion. Compared to traditional travel-time tomography, data utilization is increased by an order of magnitude, and inversion resolution is significantly improved. The joint inversion of the river cross-section sound velocity field and vector velocity field eliminates the systematic errors caused by the assumption of uniform sound velocity in traditional methods. In river sections with drastically changing environmental parameters, inversion accuracy can be improved by more than 15%. Frequency domain modeling completely eliminates the dependence of traditional time-domain PINNs on initial conditions, adapting to the long propagation time scenarios of large-scale rivers, and significantly improving training stability and efficiency. Using PINNs to apply physical control equations as natural regularization terms eliminates the need for manual adjustment of regularization parameters, making it more adaptable to complex flow fields. Incorporating boundary constraints into the inversion process better reflects the actual terrain characteristics of rivers, significantly improving the inversion accuracy for river sections with complex terrain. No gridding of the computational domain is required, allowing for flexible adaptation to arbitrarily complex riverbed terrain, resulting in higher deployment and computational efficiency.

[0029] 2. The boundary constraints of this underwater flow field multi-parameter inversion method based on physical information neural network utilize the three-dimensional riverbed model obtained by surveying as a hard boundary constraint and integrate it into the inversion process. It uses actual terrain features as constraint conditions, making it applicable to all complex river sections and more realistic and adaptable. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the steps of the underwater flow field multi-parameter inversion method based on physical information neural network in Embodiment 1 of the present invention.

[0031] Figure 2 This is a screenshot of a river channel profile used in Embodiment 1 of the present invention for applying the underwater flow field multi-parameter inversion method based on physical information neural network, taking two-dimensional inversion as an example.

[0032] Figure 3 This is a diagram showing the measurement point setup for the underwater flow field multi-parameter inversion method based on physical information neural network in Embodiment 1 of the present invention.

[0033] Figure 4 This is the expected sound velocity profile obtained by the underwater flow field multi-parameter inversion method based on physical information neural network in Embodiment 1 of the present invention.

[0034] Figure 5 This is the expected inversion profile vector flow field diagram obtained by the underwater flow field multi-parameter inversion method based on physical information neural network in Embodiment 1 of the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Example 1

[0037] Please see Figure 1 One method for multi-parameter inversion of underwater flow fields based on physical information neural networks includes:

[0038] S1. Data Acquisition and Preprocessing: Based on river acoustic tomography, base stations were deployed in a tidal section of the lower Yangtze River. This section has a significantly undulating riverbed with a maximum depth of 5.2m. In this embodiment, three sets of left-bank acoustic base stations and two sets of right-bank acoustic base stations were deployed, totaling five base stations. The base stations support synchronous clock and alternating excitation modes, operating at frequencies of 10-40kHz. The five base stations sequentially transmit coded pulse signals as sound sources, while the remaining base stations act as receivers, acquiring the acoustic signals transmitted from the opposite bank. Based on the reciprocal propagation principle of FAT (Frequency of Atlas), bidirectional acoustic propagation signals can be acquired for each pair of transceiver base stations. The measured impulse response (pulse response) of this path is extracted through signal cross-correlation, ultimately yielding ten sets of measured impulse response time series for all transceiver pairs, with a sampling rate of 100kHz.

[0039] The three-dimensional topography of the riverbed at this cross section is obtained by multibeam bathymetry and used as the boundary constraint input for inversion.

[0040] Bandpass filtering was performed on 10 sets of measured impulse response time series to remove environmental noise and high-frequency interference. At the same time, Fourier transform was performed on the signals to extract 100 frequency points in the range of 10-40kHz, in preparation for frequency domain inversion.

[0041] S2. Constructing the Neural Network: A physical information neural network model is constructed. This invention abandons the traditional time-domain PINN architecture; the frequency-domain PINN network adopts a 5-layer fully connected network with 128 hidden layers and the Tanh activation function. By using a frequency-domain physical information neural network, the constraints of initial conditions are completely eliminated. The network's input and output design is as follows:

[0042] The model input vector is (x,y,z,f,S), where S is the sound source index from 0 to 4, used to distinguish different transmitting base stations, adapting to the working mode of the FAT system where multiple base stations are excited sequentially, realizing unified modeling of multi-source data, corresponding to 5 base stations, x,y,z are the spatial coordinates within the river cross section, used to characterize the spatial position of the medium; f is the frequency point of the current simulation, covering the 20-80kHz frequency band of the system, used for frequency domain wave field modeling.

[0043] The output includes the sound velocity field and the flow velocity field of the flow field;

[0044] S3. Frequency Response Prediction: The frequency response is calculated using the sound velocity field and flow velocity field obtained in step S2. The frequency response is then transformed to obtain the predicted impulse response. The sound velocity field and flow velocity field are the core unknowns to be inverted. The sound velocity field c(x,y,z) is only related to spatial location and characterizes the inherent sound velocity of the local water body. It is used to describe the spatial heterogeneity of parameters such as temperature, salinity, and sediment concentration, and is the core environmental parameter to be inverted in this invention. The spatially related vector flow velocity field v(x,y,z) = v x (x,y,z),v y (x,y,z),v z (x,y,z) is only related to the spatial location and represents the two-dimensional velocity distribution within the cross section. It is the core flow field parameter to be inverted in this invention. The frequency domain sound pressure (frequency response) p(x,y,z,f,S) is related to all input dimensions and represents the sound pressure frequency response under the current spatial location, current frequency point, and current sound source excitation. It is used to describe the frequency domain propagation characteristics of sound waves.

[0045] S4. Response Comparison: After comparing the predicted impulse response with the measured impulse response, the sound velocity field and flow velocity field are adjusted based on the comparison results, and the final sound velocity field and flow velocity field are output. For each excitation sound source S, the network can predict the frequency response of all receiving base station locations. By performing an inverse Fourier transform on the frequency response, the predicted impulse response of the transceiver pair can be obtained, which is used to compare with the measured impulse response.

[0046] Specifically, the predicted impulse response is compared with the measured impulse response based on a constraint cost function, which is a joint cost function including data fitting terms, physical constraint terms, and boundary constraints. The specific definitions of each loss term are as follows:

[0047] The data fitting loss is used to constrain the degree of matching between the predicted results and the measured data. It is constructed using the mean square error between the measured impulse response and the predicted impulse response. The data fitting loss includes: ,in, Let i be the measured impulse response of the i-th transmit / receive pair. To predict the impulse response, M represents the total number of transmit and receive pairs, and T represents the number of time sampling points.

[0048] Physical equation constraint loss is used to ensure that the wave field and flow field satisfy physical laws. It is the core regularization term of PINN and includes two types of constraints:

[0049] Constraints on the wave equation of a moving medium in the frequency domain: ,in, Angular frequency, The equation, which represents the unit direction vector of the transducer pair, describes the frequency domain propagation of sound waves in a moving medium. It requires no initial conditions, only spatial constraints.

[0050] Network prediction Substituting into the equation, the residual constraint loss of the equation includes: ,in, These are the predicted frequency response, sound velocity field, and flow velocity field, respectively. These are the spatial coordinates within the river cross-section.

[0051] Fluid continuity equation constraints: To ensure the physical rationality of the flow field, the velocity field is constrained to satisfy the continuity equation for incompressible fluids. The corresponding loss term is: The physical constraints are the sum of the constraints from the wave equation of the moving medium in the frequency domain and the fluid continuity equation. .

[0052] Boundary constraint loss is based on the 3D topographic model of the riverbed obtained from surveying, with solid wall boundary conditions applied:

[0053] The normal flow velocity at the riverbed boundary is 0, satisfying the impermeable boundary condition. ,in, Let be the unit normal vector at the riverbed boundary. The sound pressure at the riverbed boundary satisfies the reflection boundary condition at the solid-liquid interface: This indicates that the rate of change of the frequency response along the normal direction is zero.

[0054] The corresponding loss term is used to constrain the network output to meet the actual terrain boundaries, avoiding non-physical solutions. The loss term is defined as follows: ,in, This indicates the boundary area of ​​the riverbed.

[0055] The specific operation and parameter update instructions for the inversion iteration in this embodiment are as follows: The inversion process of this invention is an end-to-end network training process. The updates of the sound velocity field and the flow velocity field are automatically completed by the gradient optimization of the network. The specific iteration process is as follows:

[0056] Initialization: Initialize the network parameters of the frequency domain PINN using the Xavier initialization method to ensure training stability.

[0057] Iterative training: Perform the following operations in each iteration:

[0058] A. Sampling: Randomly sample spatial points (x, y, z) within the cross-section, randomly sample frequency points f within the working frequency band, traverse all sound source indices S, and construct training batches.

[0059] B. Forward prediction: Input the sampled input into the network to obtain the predicted sound velocity field c(x,y,z), vector flow velocity field vx,y,z, and frequency domain sound pressure p(x,y,z,f,S).

[0060] C. Loss Calculation:

[0061] For each sound source S, extract the predicted frequency response of the receiving point, perform an inverse Fourier transform to obtain the predicted impulse response, and calculate the data fitting loss.

[0062] The residual between the frequency domain wave equation and the fluid continuity equation is automatically differentiated to obtain the physical constraint loss;

[0063] For the sampling points at the riverbed boundary, calculate the boundary constraint loss;

[0064] The total cost function is obtained by summarizing the results.

[0065] D. Parameter Update: The gradient of the total cost function with respect to all network parameters is calculated using the backpropagation algorithm, and the network parameters are updated using the Adam optimizer.

[0066] Convergence criterion: Training stops when the change in total loss is less than a threshold or the number of iterations reaches a preset value.

[0067] Output results: After training, the three-dimensional sound velocity field and vector flow velocity field of the entire cross section can be obtained through network output, thus completing the inversion.

[0068] In this embodiment, the final constraint cost function has a data loss weight of 1.0, the wave equation loss weight is 0.1, the fluid equation loss weight is 0.01, and the boundary loss weight is 0.1. The Adam optimizer is used for training with an initial learning rate of 1e-4. After 15,000 iterations, the loss converges. Figure 2 As shown, this embodiment is a cross-sectional view of the river channel. Figure 3 As shown, measurement points are set on the river channel profile. RTX1 and RTX2 are transmit / receive full-duplex transducer units, and REF1 and REF2 are reference hydrophones. In actual operation, RTX1 and RTX2 are excited sequentially to obtain the system's impulse response function. When RTX1 is excited, REF1 acquires the reference signal, and RTX2 acquires the desired signal for NLMS system identification. Figure 4The image shows the expected sound velocity profile obtained through inversion. The sound velocity field during inversion consists of the average sound velocity and the sound velocity perturbation field. The number and density of spatial sampling points during inversion need to be selected based on the actual situation, determined by the number of effective points of the impulse response function or the effective frequency range of the system. Figure 5 The figure shows the expected inverted profile vector flow field. During inversion, the velocity field consists of the average velocity vector and the velocity vector perturbation field. The number and density of spatial sampling points during inversion need to be selected based on the actual situation, determined by the number of effective points of the impulse response function or the effective frequency range of the system.

[0069] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0070] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-parameter inversion method for underwater flow fields based on physical information neural networks, characterized in that, include: S1. Data Acquisition and Preprocessing: Based on the preset base stations of the river acoustic tomography, acquire the measured impulse response data, which includes the impulse response time of any pair of transceiver base stations. S2. Constructing a Neural Network: Construct a physical information neural network model. The input of the model includes the spatial coordinates, frequency, and sound source location encoding of any point within the river cross-section. The output includes the sound velocity field and flow velocity field of the flow field. S3. Frequency Response Prediction: The frequency response is calculated using the sound velocity field and flow velocity field obtained in step S2, and the frequency response is transformed to obtain the predicted impulse response. S4. Response Comparison: After comparing the predicted impulse response with the measured impulse response, the sound velocity field and flow velocity field are adjusted based on the comparison results, and the final sound velocity field and flow velocity field are output. Among them, the predicted impulse response is compared with the measured impulse response based on the constraint cost function, which is a joint cost function that includes data fitting terms, physical constraint terms and boundary constraints. The gradient of any parameter of the neural network is calculated using the constraint cost function to update the network parameters until the function converges, and the final sound velocity field and flow velocity field are output to complete the inversion.

2. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 1, characterized in that: The degree of matching between the data fitting term constrains the predicted results and the measured data, and is constructed using the mean square error between the measured impulse response and the predicted impulse response.

3. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 1 or 2, characterized in that: The physical constraints include constraints from the wave equation of the moving medium in the frequency domain and constraints from the fluid continuity equation. The frequency domain motion medium wave equation constraint is based on the acoustic Helmholtz equation of the moving fluid in the frequency domain. The sound velocity field, flow velocity field and predicted impulse response output by the neural network are substituted into the Helmholtz equation to calculate the residual constraint loss of the equation. The fluid continuity equation constraint is to constrain the velocity field to satisfy the continuity equation for incompressible fluids.

4. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 1 or 2, characterized in that: Boundary constraints are based on the three-dimensional topographic model of the riverbed obtained by surveying and mapping. Solid wall boundary conditions are applied, including the normal flow velocity at the riverbed boundary satisfying the non-permeable boundary condition and the sound pressure at the riverbed boundary satisfying the reflection boundary condition of the solid-liquid interface.

5. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 2, characterized in that: Data fitting constraints include: ,in, Let i be the measured impulse response of the i-th transmit / receive pair. To predict the impulse response, M is the total number of transmit and receive pairs, and T is the number of time sampling points.

6. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 3, characterized in that: The Helmholtz equations include: ,in, Angular frequency, For the unit direction vector formed by the transducer pair, the wave equation constraint of the frequency domain moving medium does not require initial conditions, only spatial constraints; Substituting the sound velocity field, flow velocity field, and predicted impulse response output by the neural network into the Helmholtz equation, the residual constraint loss of the equation is calculated, including: ,in, These are the predicted frequency response, sound velocity field, and flow velocity field, respectively. These are the spatial coordinates within the river cross-section.

7. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 6, characterized in that: The continuity equations include: The corresponding loss term is: The physical constraint term is the sum of the constraints of the frequency domain moving medium wave equation and the fluid continuity equation.

8. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 4, characterized in that: The normal flow velocity at the riverbed boundary satisfies the impermeable boundary condition as follows: ,in, The unit vector normal to the riverbed boundary. For the velocity field; The sound pressure at the riverbed boundary satisfies the reflection boundary condition of the solid-liquid interface as follows: This indicates that the rate of change of the frequency response along the normal direction is zero; The loss term is defined as: ,in, This indicates the boundary area of ​​the riverbed.

9. The underwater flow field multi-parameter inversion method based on physical information neural network according to claim 1, characterized in that: Inversion and network parameter updates include: Initialization: Initialize the neural network parameters; Sampling: Randomly sample spatial points (x,y,z) within the cross-section, randomly sample frequency points f within the working frequency band, traverse all sound source indices S, and construct training batches; Forward prediction: Input the sampled signal into the network to obtain the predicted sound velocity field c(x,y,z), the flow velocity field v(x,y,z), and the predicted frequency response p(x,y,z,f,S); Loss calculation: For each sound source S, extract the predicted frequency response of the receiving point, perform inverse Fourier transform to obtain the predicted impulse response, and calculate the data fitting loss; automatically differentiate to calculate the residual between the frequency domain wave equation and the fluid continuity equation to obtain the physical constraint loss; calculate the boundary constraint loss for the sampling points of the riverbed boundary; and summarize to obtain the total cost function. Parameter update: The gradient of the total cost function with respect to all network parameters is calculated using the backpropagation algorithm, and the network parameters are updated. Training stops when the change in total loss is less than a threshold or the number of iterations reaches a preset value. Output results: Once training is complete, the three-dimensional sound velocity field and vector flow velocity field of the entire cross section are obtained through network output, thus completing the inversion.

10. A system applying the underwater flow field multi-parameter inversion method based on physical information neural networks as described in any one of claims 1-9, characterized in that: include: Data acquisition and preprocessing module: used to acquire measured impulse response data based on preset base stations in river acoustic tomography; Neural network module: used to predict the sound velocity field and flow velocity field. The input of the model includes the spatial coordinates, frequency and sound source location code of any point in the river cross section. The output includes the sound velocity field and flow velocity field of the flow field. Frequency response prediction module: The frequency response is calculated using the sound velocity field and flow velocity field obtained by the neural network module, and the frequency response is transformed to obtain the predicted impulse response; Response Comparison Module: After comparing the predicted impulse response with the measured impulse response, the sound velocity field and flow velocity field are adjusted based on the comparison results, and the final sound velocity field and flow velocity field are output. Among them, the predicted impulse response is compared with the measured impulse response based on the constraint cost function, which is a joint cost function that includes data fitting terms, physical constraint terms and boundary constraints. The gradient of any parameter of the neural network is calculated using the constraint cost function to update the network parameters until the function converges, and the final sound velocity field and flow velocity field are output to complete the inversion.

Images