A transient signal reconstruction method and system based on a physical information neural network

Abstract

The application discloses a kind of transient signal reconstruction method and system based on physical information neural network, specifically includes: constructing frequency generation subnetwork FGSN, to work condition parameter as input dynamic output frequency matrix, and realize the adaptive distribution of high-low frequency weight in combination with learnable soft mask vector;Physical parameter prediction network PPN is constructed, so that fixed physical parameter is expanded into parameterized physical field varying with propagation position and work condition;Design double-level adaptive weight controller AWC, dynamically adjust loss term weight based on gradient balance at global level, and adaptively adjust regional weight based on the structure attention of prediction error at local level;And build front explicit modeling branch ATPB based on arrival time, inhibit front rising delay through the hard constraint of step function and exponential transition.The application realizes the high-precision, high-generalization full waveform reconstruction of complex transient signal under the premise of guaranteeing physical consistency.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of signal processing and deep learning, and in particular to a transient signal reconstruction method and system based on a physical information neural network. Background Technology

[0002] Transient signals are widely present in engineering scenarios such as explosion mechanics, structural shock response, and complex fluid dynamics. Their dynamic evolution process carries key information such as system state abrupt changes, energy propagation, and structural response. High-precision full waveform reconstruction of transient signals is an important foundation for revealing relevant physical mechanisms, conducting state assessments, and achieving rapid predictions. Transient signals have typical characteristics such as rapid rising edges, local peak concentrations, significant tail decay, and the coexistence of multi-scale time variations. Taking explosion shock wave signals as an example, they simultaneously contain multi-scale structures such as strong nonlinearity, rapid rising edges, significant peaks, and tail decay, making transient signal reconstruction essentially a typical multi-scale, non-stationary function approximation problem, which places higher demands on the model's expressive power, local detail preservation ability, and physical consistency.

[0003] Existing transient signal reconstruction methods are mainly divided into three categories: numerical simulation methods based on governing equations, data-driven methods, and physical information neural networks (PINNs). Numerical simulation methods rely on partial differential equations and finite element or difference solutions. Although they have physical consistency, they require fine meshes and complex boundaries, and recalculation is required for changes in operating conditions, making rapid prediction difficult. Data-driven methods rely solely on sample fitting and lack physical constraints, making them prone to oversmoothing and peak distortion in abrupt transitions and high gradient regions. In recent years, PINNs have attempted to compensate for these shortcomings by introducing physical constraints. However, existing Fourier PINNs and their variants employ fixed or single-scale frequency mapping strategies. The frequency matrix is ​​randomly initialized and remains unchanged, and the frequency band division is artificially preset. This makes them unable to adapt to the non-uniform spectral structure of transient signals where low-frequency trends and high-frequency abrupt changes coexist. Even when some works introduce learnable frequency parameters, they are limited to single-scale offsets and fail to achieve collaborative adaptive allocation of multi-scale frequency components, making it difficult to simultaneously characterize high-frequency transitions and model low-frequency attenuation. Summary of the Invention

[0004] The technical solution of this invention to solve the above-mentioned technical problems is to provide a transient signal reconstruction method based on a physical information neural network, comprising the following steps:

[0005] Obtain the operating condition parameter vector for transient signal reconstruction Where t is time, x is propagation distance, θ is azimuth angle, and v is loading speed;

[0006] Construct a frequency generation subnetwork FGSN, taking the operating condition parameter vector X as input, and outputting a dynamic frequency matrix. Introducing learnable soft mask vectors The Softmax function is used for normalization, and the weight ratios of low-frequency and high-frequency Fourier features are dynamically allocated. A multi-scale Fourier feature map is then constructed according to the following formula:

[0007] ;

[0008] The Physical Parameter Prediction Network (PPN) takes the operating condition parameters Xphys = {x, θ, v} after removing the time variable t as input. It includes three hidden fully connected layers and one physical parameter output fully connected layer connected in sequence. The three hidden fully connected layers are used to extract implicit physical features related to the propagation location and operating condition. The physical parameter output fully connected layer is used to generate the local equivalent propagation velocity c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) based on the implicit physical features.

[0009] A time-of-arrival (ATPB) branch is constructed, taking the operating parameters Xphys = {x, θ, v} after removing the time variable t as input, and outputting the predicted arrival time tarrival(x, θ, v) of the shock wave front corresponding to the propagation distance x, azimuth angle θ, and charge velocity v; based on the predicted arrival time, a generalized exponential transition hard constraint is constructed for the front region.

[0010] ;

[0011] Where H(·) is the Heaviside step function, A is the peak prediction for the current operating condition, and k is the leading edge rate of ascent parameter;

[0012] A two-level adaptive weight controller (AWC) is constructed, which dynamically updates the global weights of each loss term at the global level based on the gradient norm of each loss term. The system then performs normalization processing and dynamically updates the spatial weights of each region at the local level based on the historical prediction errors of each region. ;

[0013] Based on the multi-scale Fourier feature map, the dynamic physical parameters, the frontier explicit hard constraints, and the two-level adaptive weights, the physical information neural network is trained to output the transient signal prediction value u(X) under the corresponding working condition.

[0014] Furthermore, the frequency generation subnetwork FGSN is a multilayer perceptron containing three fully connected layers; during training, the network automatically updates the parameters of FGSN and the soft mask α through backpropagation, enabling the model to adaptively adjust the frequency domain attention according to the current input conditions.

[0015] Furthermore, the Physical Parameter Prediction Network (PPN) is a 4-layer fully connected network, and its output is the local equivalent propagation speed. and attenuation coefficient Substituted into the following physical constraint loss function;

[0016] Consistency Constraints in Propagation:

[0017] ;

[0018] Attenuation consistency constraint:

[0019] .

[0020] Furthermore, the arrival time prediction branch ATPB is a 3-layer fully connected subnetwork; the generalized exponential transition hard constraint in the frontier region makes the network... The output strictly approximates zero when t≥ It rises sharply according to an exponential pattern.

[0021] Furthermore, in the adaptive global loss term, the data consistency loss is calculated in the k-th iteration. Loss of consistency in propagation Structural constraint loss Gradient norm of network parameter θ Global weights of each loss term Update dynamically as follows:

[0022] ;

[0023] Then on Normalization is performed to ensure that the magnitudes of the loss gradients are consistent.

[0024] Furthermore, in the local region adaptation, a soft attention mechanism based on historical prediction errors is introduced for the leading-edge region, peak region, and decay region; let the cumulative error of region r in the previous iteration be... Then the spatial weight of this region in the current round Updated to:

[0025] ;

[0026] Where μ is the temperature coefficient.

[0027] A transient signal reconstruction system based on a physical information neural network includes:

[0028] The input module is used to obtain the operating condition parameter vector for transient signal reconstruction. ;

[0029] The frequency generation subnetwork FGSN takes the operating condition parameter vector X as input and outputs a dynamic frequency matrix. The FGSN contains learnable soft mask vectors. The weight ratio of low-frequency and high-frequency Fourier features is dynamically allocated after normalization by the Softmax function.

[0030] The Physical Parameter Prediction Network (PPN) takes the operating condition parameters Xphys = {x, θ, v} after removing the time variable t as input. It includes three hidden fully connected layers and one physical parameter output fully connected layer connected in sequence. The three hidden fully connected layers are used to extract implicit physical features related to the propagation location and operating condition. The physical parameter output fully connected layer is used to generate the local equivalent propagation velocity c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) based on the implicit physical features.

[0031] Arrival Time Prediction Branch (ATPB) uses the aforementioned operating parameters. Input: The precise time it takes for the leading edge of the shock wave to reach the measuring point. And based on this precise time, construct the generalized exponential transition hard constraints of the frontier region;

[0032] The two-level adaptive weight controller (AWC) is used to dynamically update global weights based on the gradient norm of each loss term at the global level, and to dynamically update spatial weights based on the historical prediction error of each region at the local level.

[0033] The training and output module is used to train the physical information neural network based on the above modules and output the transient signal prediction value u(X) under the corresponding working condition.

[0034] Compared with existing technologies, this invention has the following advantages: First, by constructing a Frequency Generation Subnetwork (FGSN) and introducing a learnable soft mask vector, it breaks through the limitations of traditional fixed frequency matrices and fixed high-low frequency ratios, enabling the model to adaptively adjust frequency domain focus according to input conditions. This automatically enhances high-frequency weights in transient high-frequency signal regions and automatically emphasizes low-frequency features in smooth low-frequency regions, significantly improving the high-frequency detail recovery capability and spectrum adaptation accuracy of complex transient signals. Second, by constructing a Physical Parameter Prediction Network (PPN), it upgrades the equivalent wave velocity and attenuation coefficient into a parameterized physical field that dynamically evolves with space and operating conditions, replacing the rigid constraints of traditional global constants. This allows physical consistency constraints to adaptively adjust with changes in the propagation environment, greatly enhancing the model's performance. The invention significantly improves the generalization performance and physical reliability of the model under unseen operating conditions. Third, it designs a two-level adaptive weight controller (AWC). At the global level, it dynamically adjusts the weights of each loss term based on gradient balancing to eliminate optimization competition and ill-conditioned gradients. At the local level, it automatically focuses on high-error regions such as leading-edge distortion based on a structural attention mechanism of prediction error. This improves training stability and convergence efficiency while avoiding tedious manual weight tuning, thus reducing application costs. Fourth, it pioneers an explicit leading-edge modeling branch (ATPB) based on arrival time. Utilizing step functions and exponential transitions to construct hard constraints, it strictly binds the arrival time of the leading edge to the waveform, fundamentally eliminating the leading-edge rise delay and smoothing distortion caused by traditional indirect modeling, ensuring the steepness and timing accuracy of the shock wave leading edge. In summary, this invention significantly improves the accuracy, robustness, and generalization ability of transient signal full waveform reconstruction while ensuring physical consistency, and reduces the cost of manual parameter tuning. It can be widely applied in practical engineering fields such as explosion shock wave monitoring, seismic signal processing, and ultrasonic non-destructive testing. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0036] Figure 1 This is a flowchart illustrating the overall scheme of the transient signal reconstruction method based on physical information neural network described in this invention.

[0037] Figure 2 This is a network structure diagram of the transient signal reconstruction method based on physical information neural network described in this invention;

[0038] Figure 3 This is a graph showing the shock wave curves at different observation points with different velocities when the angle is 0°, according to the present invention.

[0039] Figure 4 This is a comparison chart of the prediction performance of the method of this invention with other methods (MLP, CNN, PINN, Fourier PINN);

[0040] Figure 5 This is a schematic diagram of the actual experimental layout of the present invention;

[0041] Figure 6 This is a schematic diagram showing the setup of the Autodyn calculation model of the present invention;

[0042] Figure 7 This is a graph showing the iterative convergence curve of the loss function in this invention. Detailed Implementation

[0043] This invention proposes a transient signal reconstruction method and system based on physical information neural networks. The aim is to design a transient signal reconstruction method based on physical information neural networks, which significantly improves the accuracy, robustness and generalization ability of transient signal full waveform reconstruction while ensuring physical consistency, and at the same time reduces the cost of manual parameter tuning.

[0044] The transient signal reconstruction method based on physical information neural networks proposed in this invention will be described below in specific embodiments:

[0045] In the technical solution of this embodiment, such as Figure 1 , Figure 2 As shown, a transient signal reconstruction method based on a physical information neural network includes the following steps:

[0046] Obtain the operating condition parameter vector for transient signal reconstruction Where t is time, x is propagation distance, θ is azimuth angle, and v is loading speed;

[0047] Construct a frequency generation subnetwork FGSN, taking the operating condition parameter vector X as input, and outputting a dynamic frequency matrix. Introducing learnable soft mask vectors The Softmax function is used for normalization, and the weight ratios of low-frequency and high-frequency Fourier features are dynamically allocated. A multi-scale Fourier feature map is then constructed according to the following formula:

[0048] ;

[0049] The Physical Parameter Prediction Network (PPN) takes the operating condition parameters Xphys = {x, θ, v} after removing the time variable t as input. It includes three hidden fully connected layers and one physical parameter output fully connected layer connected in sequence. The three hidden fully connected layers are used to extract implicit physical features related to the propagation location and operating condition. The physical parameter output fully connected layer is used to generate the local equivalent propagation velocity c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) based on the implicit physical features.

[0050] Construct the arrival time prediction branch ATPB, using the aforementioned operating parameters. Input: The precise time it takes for the leading edge of the shock wave to reach the measuring point. Based on the precise time Constructing hard constraints for generalized exponential transitions in the frontier region:

[0051] ;

[0052] Where H(·) is the Heaviside step function, A is the peak prediction for the current operating condition, and k is the leading edge rate of ascent parameter;

[0053] A two-level adaptive weight controller (AWC) is constructed, which dynamically updates the global weights of each loss term at the global level based on the gradient norm of each loss term. The system then performs normalization processing and dynamically updates the spatial weights of each region at the local level based on the historical prediction errors of each region. ;

[0054] Based on the multi-scale Fourier feature map, the dynamic physical parameters, the frontier explicit hard constraints, and the two-level adaptive weights, the physical information neural network is trained to output the transient signal prediction value u(X) under the corresponding working condition.

[0055] Furthermore, the frequency generation subnetwork FGSN is a multilayer perceptron containing three fully connected layers; during training, the network automatically updates the parameters of FGSN and the soft mask α through backpropagation, enabling the model to adaptively adjust the frequency domain attention according to the current input conditions.

[0056] Specifically, the operating condition parameter vector for transient signal reconstruction is defined as follows: ,in For time, For transmission distance, It is the azimuth angle. The loading speed is [value]. The output is the predicted value of the transient signal under the corresponding operating condition. Traditional methods use a fixed frequency matrix. Using hard-coded ratios (e.g., 1:3) to divide high and low frequencies is difficult to adapt to spectrum variations under different operating conditions. This invention constructs a Frequency Generation Subnetwork (FGSN), specifically a multilayer perceptron containing three fully connected layers, based on operating condition parameters. As input, output dynamic frequency matrix Simultaneously, a learnable soft mask vector is introduced. To ensure the sum equals 1, normalization is performed using the Softmax function, dynamically allocating the weights of low-frequency and high-frequency Fourier features. The improved multi-scale Fourier feature mapping formula is as follows:

[0057] ;

[0058] During training, the network automatically updates the parameters and soft mask of the FGSN through backpropagation. This allows the model to adaptively adjust its frequency domain focus based on the current input conditions. For operating conditions with concentrated high-frequency abrupt changes, Automatically increases; for operating conditions where low frequency trends are predominant, It automatically increases, thus completely overcoming the fixed spectrum mismatch problem.

[0059] Furthermore, the Physical Parameter Prediction Network (PPN) is a 4-layer fully connected network, and its output is the local equivalent propagation speed. and attenuation coefficient Substituted into the following physical constraint loss function;

[0060] Consistency Constraints in Propagation:

[0061] ;

[0062] Attenuation consistency constraint:

[0063] .

[0064] The local equivalent propagation velocity c(x, θ, v) and local equivalent attenuation coefficient αdec(x, θ, v) do not need to be manually pre-set for each predicted operating condition. During model training, the operating condition parameters Xphys corresponding to the training samples are input into the PPN. The PPN forward propagation obtains c(x, θ, v) and αdec(x, θ, v) for the current training sample, and these are substituted into the propagation consistency constraint and attenuation consistency constraint to calculate the physical constraint loss. The physical constraint loss, along with the data consistency loss and structural constraint loss, participates in network training. Backpropagation updates the weights and biases of each fully connected layer of the PPN, allowing the PPN to gradually learn the nonlinear mapping relationship between the operating condition parameters and the local equivalent propagation velocity and local equivalent attenuation coefficient. After training is complete, for new propagation distance x, azimuth angle θ, and charge velocity v, the corresponding Xphys is input into the PPN, and c(x, θ, v) and αdec(x, θ, v) for the corresponding operating condition can be obtained through a single forward propagation.

[0065] Through the above parameter generation and joint optimization mechanism, the local equivalent propagation speed c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) can be dynamically adjusted with the propagation position and operating parameters. This expands the original global physical constraints with fixed propagation speed or fixed attenuation parameters into a parameterized physical field related to the operating conditions, thereby improving the adaptability of physical constraints to complex propagation environments and different operating conditions, and enhancing the physical consistency and generalization ability of the model when reconstructing transient signals in operating conditions not involved in training.

[0066] Furthermore, the arrival time prediction branch ATPB is a 3-layer fully connected subnetwork; the generalized exponential transition hard constraint in the frontier region makes the network... The output strictly approximates zero when t≥ It rises sharply according to an exponential pattern.

[0067] Specifically, to improve the prediction accuracy of the arrival time of the transient signal leading edge, an independent arrival time prediction branch (ATPB) is introduced. ATPB employs a three-layer fully connected sub-network, taking the operating condition parameters Xphys = {x, θ, v} (after removing the time variable t) as input. By learning the nonlinear relationship between propagation distance, azimuth angle, and charge velocity with the shock wave propagation time sequence, it outputs the predicted arrival time tarrival(x, θ, v) of the shock wave leading edge at the measuring point under the corresponding operating condition. This predicted arrival time further participates in the construction of the generalized exponential transition hard constraint in the leading edge region, ensuring that the leading edge position of the waveform predicted by the main network is consistent with the arrival time output by ATPB.

[0068] Based on explicit arrival times, a generalized exponential transition hard constraint is constructed for the frontier region. For the predicted signal within the frontier region... The following physical evolution equations should be satisfied:

[0069] ;

[0070] in, For Heaviside step function, For the peak prediction of the current operating conditions, This is the rise rate parameter of the physical front. This constraint strongly binds the arrival time of the physical front to the predicted signal waveform, enabling the network to... The output is strictly close to zero. The time rises sharply according to an exponential pattern, completely eliminating the "smoothing" phenomenon at the forefront.

[0071] Furthermore, in the global loss term adaptation (gradient balancing), the data consistency loss is calculated in the k-th iteration. Loss of consistency in propagation Structural constraint loss Gradient norm of network parameter θ Global weights of each loss term Update dynamically as follows:

[0072] ;

[0073] Then on Normalization is performed to ensure that the magnitudes of the loss gradients are consistent.

[0074] In the local region adaptation, a soft attention mechanism based on historical prediction errors is introduced for the leading-edge region, peak region, and decay region; let the cumulative error of region r in the previous iteration be... Then the spatial weight of this region in the current round Updated to:

[0075] ;

[0076] Where μ is the temperature coefficient. The region with the larger error (such as the leading-edge distortion region under complex working conditions) will have its weight automatically amplified in the next round, achieving focused optimization of the "difficult sample region".

[0077] Detection and experimental verification:

[0078] 1. Simulation data experimental verification:

[0079] The transient signal dataset of the shock wave was generated using Autodyn finite element software. A schematic diagram of the Autodyn computational model setup is shown below. Figure 6As shown, a center-initiated detonation condition was adopted, with a charge mass W = 0.17 kg, a charge density ρ = 1.63 g / cm³, an air domain size of 2400 mm × 1200 mm, and a grid size of 2 mm × 2 mm. A two-dimensional axisymmetric model and a multi-material Euler algorithm were used. Monitoring points were arranged at 100 mm intervals within a range of 200 mm to 1100 mm from the detonation center, and azimuth angles were set at 30° intervals within a range of 0° to 180°, forming a total of 70 monitoring points. Six charge movement speed conditions were set (0, 272, 340, 680, 1020, 1360 m / s), and a total of 420 sets of simulated transient signal samples were obtained. These samples were divided into training, validation, and test sets in a 7:2:1 ratio. The shock wave curves at different observation point positions at different speeds when the angle is 0 are shown in the figure. Figure 3 As shown, the experimental layout diagram is as follows: Figure 5 As shown.

[0080] SPF-PINN was compared with four benchmark models: MLP, CNN, PINN, and Fourier PINN, using a unified data partitioning, training strategy, and evaluation metrics (RMSE, PPE, RTE). The results are as follows: Figure 4 As shown, the experimental results show that the RMSE of SPF-PINN is reduced to 22.47538, which is 65.95%, 31.06%, 74.99%, and 58.68% lower than that of MLP, CNN, PINN, and Fourier PINN, respectively; the peak error PPE is 23.78 kPa; and the rise time error RTE is only 2 data points.

[0081] Table 1 Comparison of evaluation indicators for different methods:

[0082]

[0083] To verify the contributions of the two core modules, multi-scale Fourier feature mapping and structure-aware physical constraint loss function, two variant models were constructed: (1) removing multi-scale Fourier feature mapping; and (2) removing structure-aware physical constraint loss function. Experiments showed that after removing Fourier feature mapping, RMSE increased to 80.24 and PPE increased to 183.92 kPa; after removing structure-aware loss function, RMSE increased to 55.21 and PPE increased to 94.23 kPa, verifying the independent effect and synergistic gain of the two modules.

[0084] Table 2 Comparison of ablation test indicators:

[0085]

[0086] like Figure 7 The iterative convergence curve of the loss function was recorded, verifying the stability of model training and the synergistic optimization effect of multiple constraints.

[0087] 2. Verification using actual collected data:

[0088] The verification was conducted using shock wave data collected from the surface of a dummy's body in the impact zone of a certain type of artillery. The sensor was an Endevco_Model 8515C-50 piezoresistive pressure sensor with a measurement range of 0~340 kPa and a sampling frequency of 2 MSa / s. Shock wave signals collected from the same dummy's body surface under six different operating conditions were used, and 102,400 data points near the differential pressure peak were used for full waveform reconstruction. The average RMSE was 10.52099, the average PPE was 0.497875 kPa, and the average RTE was 54.5 sampling points under the six operating conditions.

[0089] Table 3 Evaluation Indicators for Reconfiguration Results under Different Working Conditions:

[0090]

[0091] This application can be applied to simulate explosion accidents in hazardous locations such as chemical plants and gas stations, rapidly reconstructing the shock wave evolution process under complex working conditions to guide safety distance calculations and emergency response plan development. In the field of structural health monitoring, the model can be deployed on edge computing devices to reconstruct the transient vibration response of structures in real time based on sparse sensor data, achieving rapid damage assessment. In education and training, it can serve as the core algorithm module of an explosion injury simulation system, providing highly realistic training scenarios for emergency rescue personnel. Furthermore, the frequency domain enhancement and physical parameterization framework of this invention can be extended to the reconstruction and prediction of other complex transient signals such as sound wave propagation and electromagnetic pulses.

[0092] A transient signal reconstruction system based on a physical information neural network includes:

[0093] The input module is used to obtain the operating condition parameter vector for transient signal reconstruction. ;

[0094] The frequency generation subnetwork FGSN takes the operating condition parameter vector X as input and outputs a dynamic frequency matrix. The FGSN contains learnable soft mask vectors. The weight ratio of low-frequency and high-frequency Fourier features is dynamically allocated after normalization by the Softmax function.

[0095] The Physical Parameter Prediction Network (PPN) takes the operating condition parameters Xphys = {x, θ, v} after removing the time variable t as input. It includes three hidden fully connected layers and one physical parameter output fully connected layer connected in sequence. The three hidden fully connected layers are used to extract implicit physical features related to the propagation location and operating condition. The physical parameter output fully connected layer is used to generate the local equivalent propagation velocity c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) based on the implicit physical features.

[0096] Arrival Time Prediction Branch (ATPB) uses the aforementioned operating parameters. Input: The precise time it takes for the leading edge of the shock wave to reach the measuring point. And based on this precise time, construct the generalized exponential transition hard constraints of the frontier region;

[0097] The two-level adaptive weight controller (AWC) is used to dynamically update global weights based on the gradient norm of each loss term at the global level, and to dynamically update spatial weights based on the historical prediction error of each region at the local level.

[0098] The training and output module is used to train the physical information neural network based on the above modules and output the transient signal prediction value u(X) under the corresponding working condition.

[0099] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A transient signal reconstruction method based on a physical information neural network, characterized in that, Includes the following steps: Obtain the operating condition parameter vector for transient signal reconstruction Where t is time, x is propagation distance, θ is azimuth angle, and v is loading speed; Construct a frequency generation subnetwork FGSN, taking the operating condition parameter vector X as input, and outputting a dynamic frequency matrix. Introducing learnable soft mask vectors The Softmax function is used for normalization, and the weight ratios of low-frequency and high-frequency Fourier features are dynamically allocated. A multi-scale Fourier feature map is then constructed according to the following formula: ； The Physical Parameter Prediction Network (PPN) takes the operating condition parameters Xphys = {x, θ, v} after removing the time variable t as input. It includes three hidden fully connected layers and one physical parameter output fully connected layer connected in sequence. The three hidden fully connected layers are used to extract implicit physical features related to the propagation location and operating condition. The physical parameter output fully connected layer is used to generate the local equivalent propagation velocity c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) respectively based on the implicit physical features. A time-of-arrival (ATPB) prediction branch is constructed, taking the operating parameters Xphys = {x, θ, v} after removing the time variable t as input, and outputting the predicted arrival time tarrival(x, θ, v) of the shock wave front corresponding to the propagation distance x, azimuth angle θ, and charge velocity v; based on the predicted arrival time, a generalized exponential transition hard constraint is constructed for the front region. ； Where H(·) is the Heaviside step function, A is the peak prediction for the current operating condition, and k is the leading edge rate of ascent parameter; A two-level adaptive weight controller (AWC) is constructed, which dynamically updates the global weights of each loss term at the global level based on the gradient norm of each loss term. The system then performs normalization processing and dynamically updates the spatial weights of each region at the local level based on the historical prediction errors of that region. ; Based on multi-scale Fourier feature mapping, dynamic physical parameters, frontier explicit hard constraints, and two-level adaptive weights, a physical information neural network is trained to output the transient signal prediction value u(X) under the corresponding working condition.

2. The method according to claim 1, characterized in that, The frequency generation subnetwork FGSN is a multilayer perceptron containing three fully connected layers. During training, the network automatically updates the parameters of FGSN and the soft mask α through backpropagation, enabling the model to adaptively adjust the frequency domain attention according to the current input conditions.

3. The method according to claim 1, characterized in that, The physical parameter prediction network outputs the local equivalent propagation speed. and attenuation coefficient Substituted into the following physical constraint loss function; Consistency constraint in propagation: ； Attenuation consistency constraint: 。 4. The method according to claim 1, characterized in that, The arrival time prediction branch is a 3-layer fully connected subnetwork; the generalized exponential transition hard constraint in the front region makes the network... The output strictly approximates zero when t≥ It rises sharply according to an exponential pattern.

5. The method according to claim 1, characterized in that, The dual-level adaptive weight controller includes global loss term adaptation and local region adaptation. In the global loss term adaptation, data consistency loss is calculated in the k-th iteration. Loss of consistency in propagation Structural constraint loss Gradient norm of network parameter θ Global weights of each loss term Update dynamically as follows: ； Then on Normalization is performed to ensure that the magnitudes of the loss gradients are consistent.

6. The method according to claim 5, characterized in that, In the local region adaptation, a soft attention mechanism based on historical prediction errors is introduced; let the cumulative error of region r in the previous iteration be... Then the spatial weight of this region in the current round Updated to: ； Where μ is the temperature coefficient.

7. A transient signal reconstruction system based on a physical information neural network, used to execute the transient signal reconstruction method based on a physical information neural network as described in any one of claims 1 to 6, characterized in that, include: The input module is used to obtain the operating condition parameter vector for transient signal reconstruction. ; The frequency generation subnetwork FGSN takes the operating condition parameter vector X as input and outputs a dynamic frequency matrix. The FGSN contains learnable soft mask vectors. The weight ratio of low-frequency and high-frequency Fourier features is dynamically allocated after normalization by the Softmax function. The Physical Parameter Prediction Network (PPN) takes the operating condition parameters Xphys = {x, θ, v} after removing the time variable t as input. It includes three hidden fully connected layers and one physical parameter output fully connected layer connected in sequence. The three hidden fully connected layers are used to extract implicit physical features related to the propagation location and operating condition. The physical parameter output fully connected layer is used to generate the local equivalent propagation velocity c(x, θ, v) and the local equivalent attenuation coefficient αdec(x, θ, v) respectively based on the implicit physical features. Arrival Time Prediction Branch (ATPB) uses the aforementioned operating parameters. Input: The precise time it takes for the leading edge of the shock wave to reach the measuring point. And based on this precise time, construct the generalized exponential transition hard constraints of the frontier region; The two-level adaptive weight controller (AWC) is used to dynamically update global weights based on the gradient norm of each loss term at the global level, and to dynamically update spatial weights based on the historical prediction error of each region at the local level. The training and output module is used to train the physical information neural network based on the above modules and output the transient signal prediction value u(X) under the corresponding working condition.

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