Hydroacoustics physical neural network construction method

Abstract

The invention discloses a hydroacoustic physical neural network construction method, and belongs to the crossing field of hydroacoustic physics and artificial intelligence. The core of the method is to directly realize neural network calculation by utilizing the physical propagation process of water sound waves in a medium. Comprising the steps of hydroacoustic sensor array deployment, multi-layer physical mapping architecture construction and hybrid training mechanism implementation. Deploying a sound source and an N-layer physical cascade system to acquire acoustic signals and environmental parameters; a network architecture embedded with an acoustic propagation rule is constructed, a physical convolution layer is designed based on a wave equation, a physical activation layer simulates medium attenuation, and a loss function adopts layered physical constraint; an in-situ forward propagation-digital back propagation mixed training mode is adopted, and parameters are updated through a layered differentiable digital model and a layered optimization strategy. The problems that a traditional digital neural network is high in energy consumption, insufficient in generalization ability and lack of physical interpretation are solved, and the method has the advantages of being low in energy consumption, high in robustness and naturally provided with physical rules and is suitable for scenes such as underwater intelligent sensing, communication, detection and sound field simulation.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of underwater acoustic physics and artificial intelligence, and relates to a method for constructing physical neural networks. Specifically, it relates to a method for constructing underwater acoustic physical neural networks, which is applicable to underwater intelligent sensing, communication, detection and sound field simulation scenarios. Background Technology

[0002] Physical Neural Networks (PNNs) are a class of intelligent systems that deeply integrate the dynamic characteristics of physical entities with neural network architectures. Their core lies in leveraging the inherent computational characteristics of physical processes to achieve efficient computation and reasoning. They are currently a hot research area in intelligent technology, and the current research status both domestically and internationally is as follows:

[0003] The construction of physical neural networks is moving from theoretical exploration to engineering practice, with significant progress made both domestically and internationally in hardware architecture, algorithm optimization, and interdisciplinary applications. Lingxi Technology's 5nm neuromorphic chip, NeuMatrix NM5, released in 2025, adopts a brain-like asynchronous computing architecture, achieving an energy efficiency 3.2 times that of the H100. It supports dynamic topology reconstruction of spiking neural networks, enabling millisecond-level response in L5 autonomous driving and robotic arm control. This chip integrates 128 billion transistors and a memristor array, reducing idle power consumption to near zero through event-driven design, providing a disruptive solution for edge computing (World's First 5nm Neuromorphic Chip NeuMatrix NM5 White Paper. [Technical Report]. Beijing: Lingxi Technology. https: / / www.lynxi.com / guanyuwomen.html). The Zn-TCPP memristor and piezoresistive sensor system developed by the Donghua University team can simultaneously process mechanical stimuli such as pressure and deformation, and still maintains a 91% gesture recognition accuracy under 10% Gaussian noise. Its dynamic conductivity update mechanism directly simulates the long-range plasticity of biological synapses (Liu, Z., Mei, J., Tang, J., Xu, M., & Ming, D. (2025). A memristor-based adaptive neuromorphic decoder for brain-computer interfaces. Nature Electronics, 8(3), 234–242. https: / / doi.org / 10.1038 / s41928-025-00987-9). The team led by Liu Moubin at Peking University proposed constructing a conserved subdomain through a local integration strategy, transforming the pointwise residual loss of traditional PINN into a global integration constraint, which significantly improves the stability of multi-objective optimization. In the three-dimensional cavity-driven flow and cylinder flow problems, the energy conservation error of S-PINN is reduced by two orders of magnitude compared with traditional PINN (Yang, T., Liu, M., & Qian, Z. (2025). Stabilized physics-informed neural networks for multi-objective optimization of partialdifferential equations. Computer Methods in Applied Mechanics and Engineering, 421, 115123. https: / / doi.org / 10.1016 / j.cma.2025.115123).A team from Tsinghua University developed a Hybrid Quantum Physics Information Neural Network (HQPINN), which combines parameterized quantum circuits with classical neural networks in parallel. When solving the Euler equation for hypersonic flow, it achieves better prediction accuracy for harmonic solutions than pure quantum or classical models, while reducing parameter costs by 30% (Deng, C., et al. (2025). Denoising Hamiltonian Network for physical reasoning. arXiv:2506.21239 [math.OC]. https: / / arxiv.org / abs / 2506.21239). The Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, developed a blood gel fiber robot that uses magnetic fields to achieve multimodal biomimetic motion in the subarachnoid space, combined with X-ray imaging guidance to deliver drugs to intracranial tumors. This robot triggers a fragmentation mechanism using a high-frequency alternating magnetic field, reducing tumor volume to one-quarter of the control group in a miniature pig model without significant immune rejection (Xu, T., Wang, B., & Zhang, L. (2025). Magnetically driven biohybrid blood hydrogel fibres for personalized intracranial tumor therapy under fluoroscopic tracking. Nature Biomedical Engineering, 9(5), 489–498. https: / / doi.org / 10.1038 / s41551-025-01098-3). The "anteater" flexible-arm robot and the "salamander" deformable wheeled robot developed by Peking University completed 3D mapping and geological sampling in the Jingpo Lake lava cave. The combination of lidar, pressure sensors and neural networks provides key technical support for lunar subsurface space exploration (Application of flexible-arm robots and deformable wheeled robots in lava cave exploration. [Technical Report]. Beijing: Peking University. https: / / mech.pku.edu.cn / xwzx / xwkx / ecd47e386b6e463f9c99fb20e7a6d8d1.htm).A team led by Fan Shanhui at Stanford University reported in the journal Optica that they achieved end-to-end training of neural networks on silicon-based photonic chips using an optical simulation backpropagation algorithm. This chip utilizes tunable beam splitters and phase shifters to perform matrix operations, achieving a training speed 2-3 orders of magnitude faster than traditional digital GPUs, while reducing energy consumption to the femtojoule level (Hughes, TW, et al. (2024). Direct training of neural networks on photonic chips. Optica, 11(12), 1512–1520. https: / / doi.org / 10.1364 / OPTICA.487829). The MIT team developed a denoising Hamiltonian network (DHN) that generalizes Hamiltonian mechanics to neural operators, encoding system properties through global latent codes to support multi-system modeling and trajectory repair. In a double-pendulum chaotic system, the long-term prediction error of the DHN is reduced by 40% compared to the traditional HNN, and it can accurately invert physical parameters from sparse observations (Deng, C., et al. (2025). Denoising Hamiltonian Network for physical reasoning. arXiv:2506.21239. https: / / arxiv.org / abs / 2506.21239). A Stanford team trained acoustic metamaterials to achieve vowel classification by directly simulating neural network weights through optimizing the material distribution. The accuracy reached 92% at SNR=10dB, with energy consumption only 1 / 2000 of that of traditional digital systems (Wright, LG, et al. (2022). Deep physical neural networks trained with backpropagation. Nature, 601(7893), 549–555. https: / / doi.org / 10.1038 / s41586-021-04254-1). The holographic ultrasound technology developed by ETH Zurich achieves non-invasive stimulation of multiple brain regions through acoustic interference focal points, and combines ion channel modulation and thermal effects to intervene in neural activity, successfully suppressing abnormal discharges in an epilepsy model (Deng, C., et al. (2025). Denoising Hamiltonian Network for physical reasoning. arXiv:2506.21239.https: / / arxiv.org / abs / 2506.21239).

[0004] Traditional deep learning models rely on general-purpose processors (such as CPUs / GPUs) for numerical computation, resulting in low energy efficiency. Furthermore, digital models depend on data-driven training, failing to fully utilize physical characteristics (such as wave equations and decay laws). In low signal-to-noise ratio or complex media environments, the model's generalization ability and robustness significantly decline. Therefore, a new neural network is urgently needed to address these issues. The propagation of sound waves in the ocean is a combined result of linear and nonlinear physical processes, remarkably similar to a nervous system. Constructing an underwater acoustic physical neural network by integrating underwater acoustic physical characteristics with a computational architecture, achieving a direct mapping between physical laws and computational operations, is a feasible solution to the problems encountered by traditional technologies. Summary of the Invention

[0005] The purpose of this invention is to address the problems of energy efficiency, robustness, and physical interpretation of traditional neural networks by providing a method for constructing underwater acoustic physical neural networks. This method is based on the core concept of "underwater acoustic propagation as computation," and achieves deep feature extraction through a multi-layered cascaded underwater acoustic physical system. Combined with a hybrid training mechanism, it enables the construction of a novel physical neural network.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solutions.

[0007] A method for constructing an underwater acoustic physical neural network includes the following steps:

[0008] 1) Multi-layer cascaded system deployment: Deploy a sound source and... Layered physical cascade system, each layer contains Each acquisition unit collects acoustic signals and environmental parameters of underwater targets;

[0009] 2) Construction of a multi-layer physical mapping neural network architecture: This architecture includes an input layer, multiple physical convolutional layers, multiple physical activation layers, a physical fully connected layer, and an output layer. Each physical layer embeds the corresponding acoustic propagation law.

[0010] 3) Implementation of the physical perception training algorithm: The network parameters are trained using the acoustically adapted physical perception training (A-PAT) algorithm. The gradient is estimated using an acoustically differentiable digital model through a hybrid mode of in-situ forward propagation and digital backpropagation, and the physical parameters of each layer are updated using a hierarchical optimization strategy.

[0011] In step 1), the multi-layer cascaded system deployment can be as follows: the system is deployed on a cylindrical surface with radius R and height H, and the system has... Layers, with a layer spacing of d, each layer has Each acquisition unit consists of an underwater acoustic recorder and an environmental parameter measuring instrument. The underwater acoustic recorder is used to collect and record underwater acoustic data, and the environmental parameter measuring instrument is used to collect and record seawater temperature, salinity, and water depth parameters. The sound source is arranged above the multi-layer physical cascade system, and the vertical distance between the sound source and the top of the system ranges from 10m to 100m. The output signal is a pulse signal or a sequence signal.

[0012] In step 2), the specific steps for constructing the multi-layer physical mapping neural network architecture can be as follows: the physical convolutional layer designs the convolution kernel based on the discretization of the acoustic wave equation, and the convolution operation corresponds to the difference calculation of sound wave propagation; the acoustic wave equation is:

[0013]

[0014] in, For the Laplace operator, For sound pressure, For the speed of sound, The symbol is for partial differentials. It is a time variable;

[0015] The physical activation layer simulates the nonlinear attenuation effect of the acoustic medium to achieve signal thresholding and feature enhancement;

[0016] The loss function employs a hierarchical physical constraint regularization design, and its expression is:

[0017]

[0018] in, For the number of physical levels, For the first Layer data error, For the first The residual term of the layer wave equation, It is the first Weighting system for layer data error terms. It is the first Weighting coefficients of the residual terms in the layer wave equation.

[0019] In step 3), the specific steps for implementing the physical perception training algorithm can be as follows:

[0020] 3.1) Forward propagation process: The sound signal emitted by the underwater sound source is used as training data and input into the first layer acquisition unit of the system. The sound wave propagates naturally in the vertically layered ocean. The underwater acoustic recorder in each layer acquisition unit receives the sound signal that has been propagated underwater and outputs the physical response. The sound waves are directly transmitted between layers through underwater propagation.

[0021] 3.2) Error Calculation and Allocation: By comparing the final layer physical response with the target output, the total error vector is calculated using cross-entropy loss, and the error is allocated layer by layer to ensure accurate error tracing for each layer;

[0022] 3.3) Construction of Differentiable Digital Model: Construct a hierarchical differentiable digital model. Each layer of the model is specifically adapted to the acoustic propagation characteristics of the corresponding layer, embedding the influence of sound speed, sound intensity and sound ray angle. The model is trained through the input-output sample pairs of the corresponding layer to ensure that the model can accurately approximate the input-output relationship of the physical layer.

[0023] 3.4) Layered optimization training: A layered optimization strategy is adopted, with a higher learning rate for shallow layers than for deep layers, to avoid excessive adjustment of parameters in deep layers that could disrupt physical laws. The training is iterated T times until the total loss converges, ensuring that the feature extraction capability of each physical system layer is highly consistent with the underwater acoustic propagation law.

[0024] Furthermore, the shallow learning rate of the hierarchical optimization strategy is 2 to 10 times that of the deep learning rate, and the number of iterations T is ≥ 500.

[0025] Compared with the prior art, the present invention has the following outstanding technical effects and advantages:

[0026] 1. Improved energy efficiency: Using the ocean medium as a natural computing medium, calculations are performed directly through the propagation of sound waves, without relying on general-purpose processors such as CPUs / GPUs. The energy efficiency is improved by two orders of magnitude compared to traditional digital neural networks.

[0027] 2. Enhanced robustness: By embedding the physical laws of acoustic propagation in layers and regularizing the loss function through physical constraints, the model's generalization accuracy remains above 80% even in low signal-to-noise ratio (SNR≤-5dB) and complex media environments.

[0028] 3. Excellent physical interpretability: The network structure directly corresponds to physical laws such as acoustic wave equations and attenuation models. Parameter adjustments can be explained through underwater acoustic principles, solving the interpretability problem of traditional black box models;

[0029] 4. High engineering practicality: Adopting a modular cascade design, the number of layers and acquisition units can be flexibly adjusted according to the application scenario, making it suitable for underwater intelligent sensing tasks at different depths and in different sea areas. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of a multi-level cascaded system. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the following embodiments will be used in conjunction with the accompanying drawings to further illustrate the invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0032] The underwater acoustic physical neural network construction method of this invention takes "acoustic propagation as computation" as its core objective, and achieves feature extraction and efficient computation through a multi-layered cascaded underwater acoustic physical system. This method comprises three parts: system deployment, construction of a multi-layered physical mapping architecture, and implementation of a hybrid training mechanism. The wave equation, attenuation model, and other physical laws of underwater acoustic propagation are embedded layer by layer into the network structure. The underwater acoustic propagation medium (ocean) and sensor array are constructed as a multi-layered physical computation carrier. The propagation process of sound waves in the multi-layered medium is the depth computation process. Through layered physical constraints and hybrid training, efficient extraction of depth features and accurate optimization of physical parameters are achieved. The specific process is as follows:

[0033] (1) Deployment of multi-level cascaded systems

[0034] A multi-layer cascaded system is deployed in a radius of The height is On the cylindrical surface, the system has Layers, with a layer spacing of Each floor has Each acquisition unit consists of one underwater acoustic recorder (for collecting and recording underwater acoustic data) and one environmental parameter measuring instrument (for collecting and recording seawater temperature, salinity, depth, and density); the sound source is positioned above the multi-layered physical cascade system for sound emission (see...). Figure 1 The vertical distance between the sound source and the top of the system ranges from 10m to 100m. The output signal is a customized signal, usually a pulse signal or a sequence signal; where N≥2, M≥4, and the interlayer spacing d=H / (N-1).

[0035] (2) Construction of multi-layer physical mapping neural network architecture

[0036] 2.1) Input Feature Construction: The multi-channel underwater acoustic time-domain signals acquired by each acquisition unit are converted into spectral data using FFT, and the sound velocity c and wave number k parameters calculated from the corresponding layer's environmental parameters are simultaneously embedded to form the signal's... 3D input feature matrix, The number of frequency points in the spectrum data preserves the signal's phase, amplitude, and physical environment information;

[0037] 2.2) Physical convolutional layer design: based on acoustic wave equation ( For the Laplace operator, For sound pressure, For the speed of sound, The symbol is for partial differentials. The convolution kernel is discretized (for time variables), and the convolution operation corresponds to the difference calculation of sound wave propagation; each convolution kernel is based on the position matrix of the array elements in that layer. With wavenumber vector Dynamic calculation, the expression is The essence of convolution operation is the phase alignment of signals from multiple nodes in the same layer and the energy aggregation of signals across layers;

[0038] 2.3) Physical activation layer design: Simulate the nonlinear attenuation effect of the acoustic medium. Each layer adopts an exponential attenuation model to achieve signal threshold screening and feature enhancement. The activation threshold is set as the minimum amplitude of the effective underwater acoustic signal of the corresponding layer to filter environmental noise.

[0039] 2.4) Physical Fully Connected Layer Design: The weight matrix (number of rows = number of target categories, number of columns = output dimension of the last physical activation layer) has each row corresponding to a sound source acoustic feature template. The weight values ​​are initialized by the matching degree between historical signals and solutions to the wave equation. Only the weight size is optimized during training.

[0040] 2.5) Loss Function Design: The loss function adopts a hierarchical physical constraint design, and its expression is:

[0041]

[0042] in, For the number of physical levels, For the first Layer data error, For the first The residual term of the layer wave equation, It is the first Weighting system for layer data error terms. It is the first Weighting coefficients for the residual terms of the layer wave equation. Deep physical layers. It is even higher, strengthening the constraints of deep physical laws and avoiding conflicts between deep feature extraction and acoustic propagation laws.

[0043] (3) Implementation of the physical perception training algorithm

[0044] The acoustic signals emitted by the underwater sound source deployed above the system are used as training data. When the sound source signal is input into the first-layer acquisition unit of the system, the sound waves propagate naturally in the vertically layered ocean. The underwater acoustic recorder in each acquisition unit receives the acoustic signal that has traveled underwater and outputs the physical response. The sound waves propagate directly between the layers underwater; the physical response of the final layer is compared. With target output The total error vector is calculated using cross-entropy loss. And distribute the error by layer. To ensure accurate error tracing at each level; construct a hierarchical differentiable digital model. Each model layer is specifically adapted to the acoustic propagation characteristics of the corresponding layer. The model incorporates the influence of sound speed, sound intensity, and ray angle. It is trained using input-output sample pairs for the corresponding layer to ensure that the model accurately approximates the input-output relationship of the physical layer. A hierarchical optimization strategy is adopted, with a higher learning rate for shallow layers than for deep layers, to avoid over-adjustment of parameters in deep layers that could disrupt physical laws. Iterative training is employed. The process converges from the initial loss to the final loss, ensuring that the feature extraction capability of each physical system layer is highly consistent with the underwater acoustic propagation law.

[0045] Taking a certain sea area in the South China Sea as an example, the following is a specific implementation example.

[0046] (1) Deployment of multi-level cascaded systems

[0047] In a certain sea area of ​​the South China Sea at a depth of 2300m, a three-layer cascaded system was deployed with a radius of 6m, a height of 2000m, and an interlayer spacing of 1000m. Each layer has 8 acquisition units, evenly distributed on a horizontal circumference. The sound source is located directly above the center of the system at a depth of 100m, and the vertical distance from the source to the top of the system is 100m. The output signal is a pulse signal, and the training dataset is the sound signal set emitted by the sound source, containing 10,000 samples.

[0048] (2) Construction of multi-layer physical mapping neural network architecture

[0049] FFT was performed on the underwater acoustic signals collected by the eight underwater acoustic recorders on each floor to convert them into spectral data (frequency range 51Hz~100Hz, a total of 50 frequency points), preserving the phase and amplitude; the sound velocity was taken as the average seawater sound velocity. , wave number ( , (for signal frequency), constitutes The feature matrix is ​​input to the physical convolutional layer; the physical convolutional kernel of each layer is calculated based on the node coordinates and wavenumber of that layer: the first Layer element position matrix Record the three-dimensional coordinates of 8 acquisition units ( ), wave number Calculated based on the environmental parameters of this layer; the convolution kernel expression is: ,in It is a three-dimensional wavenumber vector; an exponential decay model adapted to underwater acoustics is adopted. ( , The activation threshold is set to 0.01V; the hierarchical physical constraint weights are: first layer... , Second layer , Third layer , Strengthen the constraints of deep physical laws.

[0050] (3) Implementation of the physical perception training algorithm

[0051] The iteration count is 1000. Training samples are input into the first layer acquisition unit. The underwater acoustic signal propagates naturally through the ocean medium to the other acquisition units. Each layer performs signal preprocessing (FFT transformation) and physical convolution operation, performs physical activation and preliminary feature extraction, and outputs the physical response of each layer. ; Receive the Layer output Compared with the sound source signal, the total error vector is calculated using cross-entropy loss. Layer-by-layer error allocation: , , Differentiable digital model for each layer The gradient is calculated using automatic differentiation based on the assigned error vector in PyTorch. ,in This includes the cell spacing correction coefficient (±0.05 meters) and activation function decay parameters (a=0.98±0.02, b=0.05±0.01); a hierarchical stochastic gradient descent algorithm is used to update the physical parameters and model weights of each layer; a verification is performed every 100 iterations, and if the verification error increases for two consecutive iterations, the hierarchical physical constraint weights are adjusted. (Increase by 0.05 in each layer) to ensure model convergence.

[0052] Through the above specific embodiments, the constructed underwater acoustic physical neural network achieves an accuracy of 88% in underwater target recognition tasks, with energy consumption only 1 / 120th that of traditional GPU-based models. Under an SNR of -5dB, the accuracy is 81%. This embodiment can completely reproduce the construction and training process of the underwater acoustic physical neural network of this invention, verifying the low energy consumption and physical constraint advantages of the neural network model constructed by the method of this invention. It can be used in multiple fields such as underwater target recognition and underwater acoustic detection.

[0053] The above embodiments are merely preferred embodiments of the present invention and should not be considered as limiting the scope of the present invention. All equivalent variations and improvements made within the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A method for constructing an underwater acoustic physical neural network, characterized in that... Includes the following steps: 1) Multi-layer cascaded system deployment: Deploy a sound source and... Layered physical cascade system, each layer contains Each acquisition unit collects acoustic signals and environmental parameters of underwater targets; 2) Construction of a multi-layer physical mapping neural network architecture: This architecture includes an input layer, multiple physical convolutional layers, multiple physical activation layers, a physical fully connected layer, and an output layer. Each physical layer embeds the corresponding acoustic propagation law. 3) Implementation of the physical perception training algorithm: The network parameters are trained using an acoustically adapted physical perception training algorithm. The gradient is estimated using an acoustically differentiable digital model through a hybrid mode of in-situ forward propagation and digital backpropagation, and the physical parameters of each layer are updated using a hierarchical optimization strategy.

2. The method for constructing an underwater acoustic physical neural network as described in claim 1, characterized in that... In step 1), the multi-layer cascaded system is deployed as follows: the system has Layers, with a layer spacing of d, each layer has Each acquisition unit consists of an underwater acoustic recorder and an environmental parameter measuring instrument. The underwater acoustic recorder is used to collect and record underwater acoustic data, and the environmental parameter measuring instrument is used to collect and record seawater temperature, salinity, and water depth parameters. The sound source is arranged above the multi-layer physical cascade system, and the vertical distance between the sound source and the top of the system ranges from 10m to 100m. The output signal is a pulse signal or a sequence signal.

3. The method for constructing an underwater acoustic physical neural network as described in claim 1, characterized in that... In step 2), the physical convolutional layer is based on the acoustic wave equation. The acoustic wave equation is: in, For the Laplace operator, For sound pressure, For the speed of sound, The symbol is for partial differentials. It is a time variable.

4. The method for constructing an underwater acoustic physical neural network as described in claim 1, characterized in that... In step 2), the physical activation layer adopts an exponential decay model to simulate the nonlinear decay effect of the acoustic medium, thereby achieving signal threshold screening and feature enhancement. The exponential decay model is as follows: ,in, ∈[0.95,1.0], ∈[0.01,0.1], the activation threshold is set to the minimum amplitude of the effective underwater acoustic signal of the corresponding layer; The loss function employs a hierarchical physical constraint regularization design, and its expression is: in, For the number of physical levels, For the first Layer data error, For the first The residual term of the layer wave equation, It is the first Weighting system for layer data error terms. It is the first Weighting coefficients of the residual terms in the layer wave equation.

5. The method for constructing an underwater acoustic physical neural network as described in claim 1, characterized in that... In step 2), the physical fully connected layer is designed as follows: the number of rows in the weight matrix is ​​the number of target categories, the number of columns is the output dimension of the last physical activation layer, each row corresponds to a sound source acoustic feature template, the weight values ​​are initialized by the matching degree between historical signals and wave equation solutions, and only the weight size is optimized during training.

6. The method for constructing an underwater acoustic physical neural network as described in claim 1, characterized in that... In step 3), the specific steps for implementing the physical perception training algorithm are as follows: 3.1) Forward propagation process: The sound signal emitted by the underwater sound source is used as training data and input into the first layer acquisition unit of the system. The sound wave propagates naturally in the vertically layered ocean. The underwater acoustic recorder in each layer acquisition unit receives the sound signal that has been propagated underwater and outputs the physical response. The sound waves are directly transmitted between layers through underwater propagation. 3.2) Error Calculation and Allocation: By comparing the final layer physical response with the target output, the total error vector is calculated using cross-entropy loss, and the error is allocated layer by layer to ensure accurate error tracing for each layer; 3.3) Construction of Differentiable Digital Model: Construct a hierarchical differentiable digital model. Each layer of the model is specifically adapted to the acoustic propagation characteristics of the corresponding layer, embedding the influence of sound speed, sound intensity and sound ray angle. The model is trained through the input-output sample pairs of the corresponding layer to ensure that the model can accurately approximate the input-output relationship of the physical layer. 3.4) Layered optimization training: A layered optimization strategy is adopted, with a higher learning rate for shallow layers than for deep layers, to avoid excessive adjustment of parameters in deep layers that could disrupt physical laws. The training is iterated T times until the total loss converges, ensuring that the feature extraction capability of each physical system layer is highly consistent with the underwater acoustic propagation law.

7. The method for constructing an underwater acoustic physical neural network as described in claim 6, characterized in that... The shallow learning rate of the hierarchical optimization strategy is 2 to 10 times that of the deep learning rate, and the number of iterations T is ≥ 500.

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