A Method for Inverting Submarine Acoustic Parameters Based on Model-Independent Meta-Learning Algorithm

Abstract

This paper presents a method for inverting seabed acoustic parameters based on a model-independent meta-learning algorithm (MAML), relating to the field of seabed acoustic parameter inversion. To overcome the limitations of machine learning-based seabed acoustic parameter inversion methods, such as poor adaptability to unknown environments and weak generalization ability, this method utilizes a multilayer perceptron neural network as the base learner and performs base learning on preprocessed data. The MAML algorithm is then used to perform meta-optimization based on the results of the base learning phase. Through iterative optimization, the algorithm continuously approaches the optimal initialization parameters. The seabed acoustic parameter inversion model incorporating the MAML algorithm can dynamically adjust the model's initialization parameters, achieving better adaptability to different environments. The constructed model exhibits good inversion performance and demonstrates higher inversion accuracy and faster training speed compared to traditional inversion models when the marine environment changes.

Description

Technical Field

[0001] This invention relates to the field of seabed acoustic parameter inversion, and in particular to a method for seabed acoustic parameter inversion based on a model-independent meta-learning algorithm. Background Technology

[0002] Underwater acoustics, as an important means of underwater reconnaissance and communication, plays a crucial role in underwater target detection, location, and identification. When it comes to the development and application of underwater acoustics, a thorough understanding of the marine environment, especially the physical properties of the seabed, is paramount. This information can be effectively applied to fields requiring the calculation of the marine sound field, such as sonar performance evaluation, research on the impact of marine noise on marine life, and investigation of acoustic dispersion in marine sediments. Therefore, exploring methods for estimating the acoustic parameters of seabed acoustic models is an important research direction in the field of underwater acoustics.

[0003] Geosonic models are physical models used to describe the real conditions of the ocean floor. They are typically composed of a layered structure, parameterized by the sound velocity, attenuation, and density of each layer. Generally, they can be divided into two layers: a sediment layer and a basement layer. The sediment layer can be further subdivided into one or more layers of varying depths depending on the needs. The parameters such as sound velocity, attenuation, and density of each layer can be set using either fixed or variable values. As an equivalent and simplified representation of the real seabed structure, geosonic models facilitate seabed geosonic inversion and the calculation and analysis of the ocean sound field.

[0004] Traditional methods for measuring seabed acoustic parameters include laboratory measurements, drilling measurements, and in-situ seabed measurements. However, these traditional methods are only effective at the measurement location, and large-area physical sampling and analysis of acoustic properties is both expensive and time-consuming. Researchers have attempted to use remote sensing acoustic data to invert various acoustic parameters of the seabed, enabling the acquisition of large-area information on the structure and physical properties of the ocean floor. Under low-frequency conditions, remote sensing acoustic field data inversion is the most effective means of obtaining information on seabed acoustic characteristics (Wang Jingqiang. In-situ Measurement Technology and Acoustic Characteristics of Seabed Sediment Acoustics [D]. Graduate School of Chinese Academy of Sciences (Institute of Oceanology), 2015).

[0005] Currently, various methods have been developed for the inversion of seabed acoustic parameters, including two main directions: optimization-based (matched field processing) geoacoustic inversion and machine learning-based geoacoustic inversion. In recent years, machine learning has also received more attention in the field of seabed acoustic parameter inversion and has gradually become the mainstream method. Jacob Piccolo et al. proposed a geoacoustic inversion method based on a generalized additive model, which uses features extracted from broadband acoustic time series to perform nonlinear regression in a machine learning framework to predict sediment sound velocity and attenuation. Yining Shen et al. proposed a matched field acoustic inversion method based on radial basis function neural networks, which estimates geoacoustic parameters by combining the objective function of matched field inversion with a multi-layer neural network. It uses big data and ensemble objective functions for training and parameter estimation, achieving inversion performance comparable to traditional methods. Mingda Liu et al. proposed a multi-range vertical array data processing method based on convolutional neural networks for geoacoustic parameter inversion in shallow water. Through multi-task learning, it simultaneously estimates geoacoustic parameters at different scales. This method is more robust in handling source location uncertainty and shallow water environments, improving the positioning performance of geoacoustic parameter inversion. These methods can automatically learn features and patterns from large amounts of data and, in some cases, achieve higher prediction accuracy. However, machine learning-based methods for inverting seabed acoustic parameters also face challenges and limitations. For example, the quality and quantity of data significantly impact model performance, while the complexity and time-varying nature of the marine environment also affect the inversion results. Furthermore, machine learning methods still have limitations in their adaptability and generalization capabilities to unknown environments. Therefore, machine learning-based methods for inverting seabed acoustic parameters require further improvement and validation.

[0006] To overcome these limitations in machine learning methods, this invention attempts to introduce the concept of meta-learning into the inversion of seabed acoustic parameters, proposing a seabed acoustic parameter inversion method based on a model-agnostic meta-learning algorithm to improve the adaptability and generalization ability of machine learning models. Model-agnostic meta-learning (MAML) is a meta-learning algorithm proposed by Chelsea Finn et al. for rapidly adapting deep networks, and is widely used in supervised learning and reinforcement learning. The basic idea of ​​the MAML algorithm is to learn an initial parameter θ by training on multiple related tasks, so that on new tasks, with a small number of training samples, the model parameters can be quickly adjusted within a finite number of update steps, thereby adapting to the characteristics of the new task. Currently, the MAML method is widely used in image recognition, speech processing, and robot control. Summary of the Invention

[0007] The purpose of this invention is to overcome the limitations of machine learning-based seabed acoustic parameter inversion methods, such as poor adaptability to unknown environments and weak generalization ability, and to improve the generalization performance and training speed of seabed acoustic parameter inversion models. This invention provides a seabed acoustic parameter inversion method based on a model-agnostic meta-learning (MAML) algorithm. This invention attempts to introduce the model-agnostic meta-learning algorithm into the field of seabed acoustic parameter inversion, aiming to improve the accuracy and stability of seabed acoustic parameter inversion under conditions of frequent changes in the marine environment by combining machine learning and meta-learning methods. Compared with traditional inversion models, it exhibits higher inversion accuracy and faster training speed.

[0008] This invention includes the following steps:

[0009] 1) Input Data Preprocessing: In shallow water environments, sound waves emitted by a sound source undergo multiple reflections between the seabed and the surface. The sound wave data received by the receiver carries a wealth of information about seabed characteristics. This processed sound wave data can be used as input for seabed acoustic parameter inversion algorithms. Assuming there is one receiver in the ocean receiving the sound signal emitted by the sound source, performing a Fast Fourier Transform (FFT) on the time-domain data received by the receiver yields the complex sound pressure data at different frequencies. Among them, f n This indicates the selected nth frequency. This represents the complex sound pressure level at that frequency; when acquiring data in a real marine environment, the source terms at different frequencies... The source terms may differ, and they cannot be guaranteed to be exactly the same in multiple experiments; therefore, processing is required before inversion:

[0010]

[0011] Among them, the complex number H(f) n This indicates that the receiver is at frequency f. n The Green's function value is taken modulo the given value to obtain the inverted data.

[0012]

[0013] Where H represents the inversion dataset, This indicates that the receiver is at frequency f. n The modulus of the Green's function value; this invention ranges from frequency f1 to f n One data point is taken at fixed frequency intervals, and one inversion data H consists of n data points;

[0014] 2) Data Normalization: To facilitate subsequent model training, the inversion data obtained in step 1) is normalized using the following formula:

[0015]

[0016] in, The normalized inversion data is represented by min(h) and max(h), which represent the minimum and maximum values ​​of the inversion data, respectively. At the same time, the data labels used for training will also undergo the same normalization process before entering the neural network.

[0017] 3) Initialize hyperparameters: number of meta-training sets, number of meta-test sets, and number of support sets N. S Number of query sets N Q Perform initialization; determine the model's base learning rate α, meta-learning rate β, and number of base learning iterations k. α The number of learning iterations k β ;

[0018] 4) Establishing the Neural Network Structure: A simple multilayer perceptron neural network is used as the base learner. Its network structure consists of an input layer, an output layer, and four hidden layers. In the input layer of the multilayer perceptron, the input length is set to n, the same as the size of the inversion data. In the hidden layers, each layer consists of a fully connected (FC) layer and a ReLU activation function layer, with the number of neurons in each FC layer being α1, α2, α3, and α4, respectively. Simultaneously, a dropout layer is added in the middle part of the multilayer perceptron to prevent overfitting. Since the multilayer perceptron is used as a regression model, an FC layer without an activation function is set in the output part of the multilayer perceptron, with an output length of 1.

[0019] 5) Dataset partitioning: The generated inversion task is partitioned into a meta-training set D. train Heyuan test set D test ;

[0020] 6) Initialize the model parameters of the base learners using the Kaiming normal distribution;

[0021] 7) From the meta-training set D train Randomly select a task T from the given list, and then randomly select N from it. s 1 sample is used as the support set ST for this task, and the remaining N samples are... Q N samples, used as the query set QT for this task, should satisfy N s >N Q ;

[0022] 8) Using the meta-training set D train The support set S in TThe base learner is used for iterative training of base learning, which specifically includes the following steps:

[0023] 8.1) Forward Propagation Calculation: A single training sample is input into the multilayer perceptron neural network, and the value of each neuron in each layer is calculated step by step from front to back. Finally, the prediction result of the training sample is output by the output layer.

[0024] 8.2) Calculate the loss: Calculate the loss value using the prediction results. The loss function chosen is the mean squared error, i.e.:

[0025]

[0026] in, It is the output of the neural network (estimated parameters for underwater acoustic inversion), y tr N represents the actual values ​​of the inversion parameters, and N0 represents the number of inversion data.

[0027] 8.3) Backpropagation calculates and updates the weights; backpropagation calculates the base learner model parameters layer by layer with respect to the loss function. The derivative of the network parameter is used to iteratively update the network parameters using the batch gradient descent (BGD) optimizer;

[0028] 8.4) Repeat steps 8.1) to 8.3) until the number of iterations reaches k. α ;

[0029] 9) Using the meta-training set D train The query set Q T The trained neural network is tested and meta-optimized using the calculated loss value; the meta-optimizer uses the Adam optimizer, and the loss function still uses the mean squared error.

[0030] 10) Repeat steps 6) to 9) until the number of iterations reaches k. β However, in each iteration, the base learner is no longer initialized using the Kaiming normal distribution. Instead, the initial model parameters obtained from the meta-learner in the previous iteration are used to initialize the base learner model parameters. After iterating to the maximum number of iterations, the model will obtain approximately optimal initialization parameters.

[0031] 11) Test the model's effectiveness: using test set D testThe task in the test set is to test the trained model; the base learning rate and the number of base learning iterations are set to be the same as in the training phase; for each task in the test set, fine-tuning is performed using the support set, and testing is performed using the query set, and the test results are averaged as the final test result; the fine-tuning process is the same as steps 7) to 9), except that the loss value calculated in step 9) is no longer subject to meta-optimization; this testing process can be performed multiple times during the meta-learning iteration process in order to observe the effect of the MAML model at different iteration stages.

[0032] This invention introduces the emerging learning paradigm of meta-learning into the field of seabed acoustic parameter inversion. It uses a multilayer perceptron neural network as the base learner and performs base learning on preprocessed data. A model-independent meta-learning algorithm is employed, utilizing the results of the base learning stage for meta-optimization. Through iterative optimization, the model can continuously approach the optimal initialization parameters. The base learner is initialized using these optimal parameters, allowing it to iterate further on a solid foundation, thus improving the adaptability and training speed of the seabed acoustic parameter inversion model in the face of unknown environments.

[0033] Compared with the prior art, the present invention has the following outstanding advantages:

[0034] 1) This invention introduces the emerging learning paradigm of meta-learning into the field of seabed acoustic parameter inversion, and improves the traditional acoustic parameter inversion technology. The seabed acoustic parameter inversion method based on the model-independent meta-learning algorithm has great potential in improving efficiency and model generalization performance.

[0035] 2) Compared with traditional methods, the meta-learning method of this invention can utilize knowledge learned from other tasks to make more accurate estimates of seabed acoustic parameters when facing new marine environments, and greatly improve the convergence speed. Attached Figure Description

[0036] Figure 1 This is a flowchart of the inversion model according to an embodiment of the present invention.

[0037] Figure 2 This is a diagram of the ground acoustic inversion neural network structure according to an embodiment of the present invention.

[0038] Figure 3 This is a schematic diagram of the seabed acoustic model according to an embodiment of the present invention.

[0039] Figure 4 This is a marine environment model diagram according to an embodiment of the present invention.

[0040] Figure 5 This is a cross-sectional view of seawater sound velocity according to an embodiment of the present invention.

[0041] Figure 6 The sound velocity c of the deposition layer in an embodiment of the present inventions Scatter plot of inversion results.

[0042] Figure 7 The deposition layer attenuation coefficient α in this embodiment of the invention s Scatter plot of inversion results.

[0043] Figure 8 The deposition layer sound velocity c under different meta-learning iterations in embodiments of the present invention. s The changes in the MSE loss value.

[0044] Figure 9 The deposition layer attenuation coefficient α under different meta-learning iterations in embodiments of the present invention. s The changes in the MSE loss value. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the following embodiments will be used to further illustrate this invention in conjunction with the accompanying drawings.

[0046] This invention, based on a machine learning-based seabed acoustic parameter inversion model and combined with a model-independent meta-learning algorithm, improves the generalization performance and training speed of the seabed acoustic parameter inversion method when facing different marine environments. The flowchart of its inversion model is shown below. Figure 1 As shown, it includes the following steps:

[0047] 1) Input Data Preprocessing. In shallow water environments, sound waves emitted by a sound source undergo multiple reflections between the seabed and the surface, and the sound wave data received by the receiver carries a wealth of information about seabed characteristics. This processed sound wave data can be used as input for seabed acoustic parameter inversion algorithms. Assume there is one receiver in the ocean receiving the sound signal emitted by the sound source. After performing a Fast Fourier Transform (FFT) on the time-domain data received by the receiver, the complex sound pressure levels at different frequencies can be obtained. Among them, f n This indicates the selected nth frequency. This represents the complex sound pressure level at that frequency. When acquiring data in a real marine environment, the source terms at different frequencies... The source terms may differ, and even in multiple experiments, they cannot be guaranteed to be exactly the same. Therefore, processing is required before performing the inversion:

[0048]

[0049] Among them, the complex number H(f) n This indicates that the receiver is at frequency f. n The Green's function value is taken modulo the given value to obtain the inverted data.

[0050]

[0051] Where H represents the inversion dataset, This indicates that the receiver is at frequency f. n The modulus of the Green's function value under the given conditions. This invention ranges from frequency f1 to f... n A data point is taken at fixed frequency intervals, and a set of inversion data H consists of n data points.

[0052] 2) Data Normalization. To facilitate subsequent model training, the inversion data obtained in step 1) is normalized using the following formula:

[0053]

[0054] in, The normalized inversion data is represented by min(h) and max(h), which represent the minimum and maximum values ​​of the inversion data, respectively. The data labels used for training also undergo the same normalization process before entering the neural network.

[0055] 3) Initialize hyperparameters. This includes setting the number of meta-training sets, the number of meta-test sets, and the number of support sets N. s Number of query sets N Q Perform initialization. Determine the model's base learning rate α, meta-learning rate β, and number of base learning iterations k. α The number of learning iterations k β .

[0056] 4) Establish the neural network structure. A simple multilayer perceptron neural network is used as the base learner in this invention, and its network structure is as follows: Figure 2 As shown, it consists of an input layer, an output layer, and four hidden layers. In the input layer of the multilayer perceptron, the input length is set to n, the same as the size of the inversion data. In the hidden layers, each layer consists of a fully connected (FC) layer and a ReLU activation function layer, with the number of neurons in each FC layer being α1, α2, α3, and α4, respectively. Simultaneously, a dropout layer is added in the middle part of the multilayer perceptron to prevent overfitting. Since the multilayer perceptron is used as a regression model, an FC layer without an activation function is set in the output part of the multilayer perceptron, and the output length of this layer is 1.

[0057] 5) Dataset partitioning. The generated inversion task is partitioned into a meta-training set D. train Heyuan test set D test .

[0058] 6) Initialize the model parameters of the base learners using the Kaiming normal distribution.

[0059] 7) From the meta-training set Dtrain Randomly select a task T from the given list, and then randomly select N from it. s 1 sample is used as the support set ST for this task, and the remaining N samples are... Q N samples, used as the query set QT for this task, should satisfy N s >N Q .

[0060] 8) Using the meta-training set D train The support set S in T The base learner is used for iterative training of base learning, which specifically includes the following steps:

[0061] 8.1) Forward Propagation Calculation. A single training sample is input into the multilayer perceptron neural network, and the value of each neuron in each layer is calculated progressively from front to back. Finally, the output layer outputs the prediction result of the training sample.

[0062] 8.2) Calculate the loss. Calculate the loss value using the prediction results. The loss function chosen is the mean squared error, i.e.:

[0063]

[0064] in, It is the output of the neural network (estimated parameters for underwater acoustic inversion), y tr N represents the actual value of the inversion parameters, and N0 represents the number of inversion parameters.

[0065] 8.3) Backpropagation calculates and updates the weights. Backpropagation calculates the base learner model parameters layer by layer with respect to the loss function. The derivative of the network parameter is used to iteratively update the network parameters using the batch gradient descent (BGD) optimizer.

[0066] 8.4) Repeat steps 8.1) to 8.3) until the number of iterations reaches k. α .

[0067] 9) Using the meta-training set D train The query set Q T The trained neural network is tested and meta-optimized using the calculated loss value. The meta-optimizer uses the Adam optimizer, and the loss function still uses mean squared error.

[0068] 10) Repeat steps 6) to 9) until the number of iterations reaches k. β However, in each iteration, the base learner is no longer initialized using the Kaiming normal distribution. Instead, the initial model parameters obtained from the meta-learner in the previous iteration are used to initialize the base learner model parameters. After iterating to the maximum number of iterations, the model will obtain approximately optimal initial parameters.

[0069] 11) Test the model's effectiveness. Use the test set D. test The trained model is then tested using the tasks described in the training phase. The base learning rate and number of base learning iterations are set to be the same as in the training phase. For each task in the test set, fine-tuning is performed using the support set, and testing is conducted using the query set. The test results are then averaged to obtain the final test result. The fine-tuning process is the same as steps 7) to 9), except that the loss value calculated in step 9) is not further optimized using meta-optimization. This testing process can be performed multiple times during the meta-learning iterations to observe the performance of the MAML model at different iteration stages.

[0070] To address the shortcomings of traditional methods in the field of seabed acoustic parameter inversion, particularly their poor adaptability and weak generalization performance in the face of drastic changes in the marine environment, this invention proposes a seabed acoustic parameter inversion method based on a model-independent meta-learning algorithm. The specific method is as follows: Complex sound pressure levels at different frequencies received by a receiver are used as the inversion object. After data processing and dataset segmentation, a multilayer perceptron neural network is used as the base learner for base learning training. Then, a model-independent meta-learning algorithm is employed to perform meta-optimization using the results of the base learning stage. Through iterative optimization, the model can continuously approach the optimal initialization parameters. Using the optimal initialization parameters allows the seabed acoustic parameter inversion model to further iterate and learn on a better foundation when facing new marine environments, thereby improving the inversion accuracy and training speed.

[0071] The feasibility of the method described in this invention will be verified by computer simulation.

[0072] Typical underwater acoustic models, such as Figure 3 As shown. In the simulation, the ocean is modeled as a distance-independent shallow-water waveguide, with the seabed consisting of a sedimentary layer and a basement layer, as... Figure 4 As shown. The sound speed of seawater adopts the typical sound speed distribution near the Yellow River and Bohai Sea in autumn in my country. The specific sound speed profile is shown in the figure. Figure 5 As shown. The sound source and receiver are at a depth of 50m and are 800m apart. The source frequency ranges from f1 = 3000Hz to f... 25 =3960Hz, one point is taken every 40Hz, so that one inversion data H consists of n=25 data points. Water depth h w =100m, seawater density ρ w =1.69g / cm 3 Deposition layer density ρ s =1.69g / cm 3 basal layer density ρ b =2.2g / cm 3 The attenuation coefficient of the basal layer is α b= 0.05dB / λ. The inverted parameters include the sedimentary sound velocity c. s and deposition layer attenuation coefficient α s Each parameter is used to train a separate neural network for inversion. Simultaneously, the basal layer sound velocity c is changed. b and sediment depth h s To simulate different marine environments, i.e., to form different tasks requiring meta-learning. The values ​​of these parameters are shown in Table 1.

[0073] By selecting the above parameter values, 400 tasks will be generated, with 390 used as the training set and 10 as the test set. Each task contains 400 data points, with 350 used as the support set and 50 as the query set. All these partitionings were achieved through random sampling. The inversion of the sedimentary layer's sound velocity c... s At that time, the base learning rate of the model was 1×10. -5 The meta-learning rate is 1×10⁻⁶. -3 The base learning iterations were 1000, and the meta-learning iterations were 390. The inverted sedimentary layer attenuation coefficient α was calculated. s At that time, the base learning rate of the model was 1×10. -5 The meta-learning rate is 1×10⁻⁶. -3 The number of iterations for base learning was 500, and the number of iterations for meta-learning was 390. The number of neurons in each FC layer was α1 = 256, α2 = 1024, α3 = 256, and α4 = 25.

[0074] Table 1 Summary of Parameter Values

[0075]

[0076] The following is an analysis of the simulation results of the method described in this invention: In the simulation, the meta-learning MAML algorithm was used for 390 iterations. During the meta-learning iterations, a test was performed every 39 iterations thereafter to evaluate the algorithm's performance. Simultaneously, tests were also conducted without meta-learning for comparison, resulting in 12 test results. The sound velocity c in the sedimentary layer... s and deposition layer attenuation coefficient α s Some simulation results are shown in Tables 2 and 3; the simulation results are expressed as mean square error (MSE) calculated after data normalization.

[0077] Table 2 Sound velocity c in sedimentary layers s Calculation results of mean square error

[0078]

[0079] Table 3. Deposition layer attenuation coefficient α s Calculation results of mean square error

[0080]

[0081] Figure 6 and 7 The sound velocity c of the sediment layer is displayed. s and deposition layer attenuation coefficient α s A scatter plot of the inversion prediction results, where each point represents a predicted value. Combined with the MSE loss values ​​given in Table 3, the sound velocity c in the sedimentary layer... s The inversion results after meta-learning were excellent, with predicted values ​​largely centered on the true values, representing a significant improvement over the results without meta-learning. The sedimentary layer attenuation coefficient α... s The inversion results were poor, with a large MSE loss. This may be due to the deposition layer attenuation coefficient α. s This is due to insufficient data volume or improper neural network structure settings. Specifically, regarding data volume, the simulation used 50 different sedimentary layer sound velocity values ​​c. s and 8 different deposition layer attenuation coefficients α s The relatively small amount of data on the deposition layer attenuation coefficient may lead to unsatisfactory inversion results. On the other hand, an inappropriate neural network structure could also be a major cause, including improper selection of base learner layers, incorrect number of neurons in each layer, or incorrect layer number settings. Adjusting the neural network structure or replacing it with a more advanced and efficient convolutional neural network as the base learner can be attempted. However, it is worth noting that in such cases, meta-learning can still significantly improve the inversion results.

[0082] Figure 8 and 9 The sound velocity c in the sedimentary layer s and deposition layer attenuation coefficient α s The graph shows the change in MSE loss value with the number of base learning iterations during the inversion process. Since the MSE loss value without meta-learning differs significantly in magnitude from the result after multiple meta-learning iterations, the logarithm of the MSE loss value was applied. Figure 8 and Figure 9 It is evident that meta-learning significantly improves the initialization parameters of base learning, allowing iterative learning to proceed from a better foundation (i.e., a lower MSE loss value). This also enables base learning to iterate and produce a better model within a limited number of steps. Without meta-learning, the model fails to converge within 1000 steps, while with multiple meta-learning iterations, it often converges within tens of steps. Ideally, meta-learning yields optimal initialization parameters, requiring only one iteration from the base learner to obtain a well-fitting model.

[0083] The simulation results above demonstrate that the seabed acoustic parameter inversion method based on the model-independent meta-learning algorithm has great potential in improving efficiency and model generalization performance. Compared with traditional methods, the meta-learning-based method can utilize knowledge learned from other tasks to make more accurate estimates of seabed acoustic parameters when facing new marine environments, and greatly improves the convergence speed.

[0084] 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 inverting seabed acoustic parameters based on a model-independent meta-learning algorithm, characterized in that... Includes the following steps: 1) Input Data Preprocessing: In shallow water environments, sound waves emitted by a sound source undergo multiple reflections between the seabed and the surface. The sound wave data received by the receiver carries a large amount of seabed characteristic information. This sound wave data is processed and used as input for the seabed acoustic parameter inversion algorithm. Assuming there is one receiver in the ocean receiving the sound signal emitted by the sound source, the time-domain data received by the receiver is subjected to a Fast Fourier Transform (FFT) to obtain the complex sound pressure data of the receiver at different frequencies. Among them, f n This indicates the selected nth frequency. This represents the complex sound pressure level at that frequency; when acquiring data in a real marine environment, the source terms at different frequencies... The source terms may differ, and they cannot be guaranteed to be exactly the same in multiple experiments; therefore, processing is required before inversion: Among them, the complex number H(f) n This indicates that the receiver is at frequency f. n The Green's function value is taken modulo the given value to obtain the inverted data. Where H represents the inversion dataset, This indicates that the receiver is at frequency f. n The modulus of the Green's function value; from frequency f1 to f n One data point is taken at fixed frequency intervals, and one inversion data H consists of n data points; 2) Data Normalization: To facilitate subsequent model training, the inversion data obtained in step 1) is normalized using the following formula: in, The normalized inversion data is represented by min(h) and max(h), which represent the minimum and maximum values ​​of the inversion data, respectively. At the same time, the data labels used for training will also undergo the same normalization process before entering the neural network. 3) Initialize hyperparameters: number of meta-training sets, number of meta-test sets, and number of support sets N. S Number of query sets N Q Perform initialization; determine the base learning rate α, meta-learning rate β, and number of base learning iterations k. α The number of learning iterations k β ; 4) Establishing the Neural Network Structure: A simple multilayer perceptron neural network is used as the base learner. Its network structure consists of an input layer, an output layer, and four hidden layers. In the input layer, the input length is set to n, the same as the size of the inverted data. In the hidden layers, each layer consists of a fully connected layer and a ReLU activation function layer, with the number of neurons in each fully connected layer being α1, α2, α3, and α4, respectively. Simultaneously, a random deactivation layer is added to the middle part of the multilayer perceptron to prevent overfitting. Since the multilayer perceptron is used as a regression model, a fully connected layer without an activation function is set in the output part of the multilayer perceptron, with an output length of 1. 5) Dataset partitioning: The generated inversion task is partitioned into a meta-training set D. train Heyuan test set D test ; 6) Initialize the model parameters of the base learners using the Kaiming normal distribution; 7) From the meta-training set D train Randomly select a task T from the given list, and then randomly select N from it. S 1 sample is used as the support set S for this task T The remaining N Q 1 sample is used as the query set Q for this task. T It should satisfy N S >N Q ; 8) Using the meta-training set D train The support set S in T The base learning iterative training is performed using a base learner, specifically including the following steps: 8.1) Forward Propagation Calculation: A single training sample is input into the multilayer perceptron neural network, and the value of each neuron in each layer is calculated step by step from front to back. Finally, the output layer outputs the prediction result of the training sample. 8.2) Calculate the loss: Calculate the loss value using the prediction results. The loss function chosen is the mean squared error, i.e.: in, It is the output of the neural network, i.e., the estimated value of the seabed acoustic inversion parameters, y tr N represents the actual values ​​of the inversion parameters, and N0 represents the number of inversion parameters. 8.3) Backpropagation calculates and updates weights: Backpropagation calculates the base learner model parameters with respect to the loss function layer by layer. The derivative of the parameter is used to iteratively update the network parameters using the batch gradient descent optimizer. 8.4) Repeat steps 8.1) to 8.3) until the number of iterations reaches k. α ; 9) Using the meta-training set D train The query set Q T The trained neural network is tested and meta-optimized using the calculated loss value; the meta-optimizer uses the Adam optimizer, and the loss function still uses the mean squared error. 10) Repeat steps 6) to 9) until the number of iterations reaches k. β However, in each iteration, the base learner is no longer initialized using the Kaiming normal distribution. Instead, the initial model parameters obtained from the meta-learner in the previous iteration are used to initialize the base learner model parameters. After iterating to the maximum number of iterations, the model will obtain approximately optimal initialization parameters. 11) Test the model's effectiveness: using test set D test The task in the test is to test the trained model; Set the base learning rate and the number of base learning iterations to be the same as those in the training phase; For each task in the test set, fine-tune it using the support set, test it using the query set, and average the test results to get the final test result. The fine-tuning process is the same as steps 7) to 9), except that the loss value calculated in step 9) is no longer subject to meta-optimization. This testing process is performed multiple times during the meta-learning iterations in order to observe the effect of the MAML model at different iteration stages.

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