Ocean sound speed distribution prediction method based on pruned mixed basis function KAN

Abstract

This invention discloses a method for predicting ocean sound speed distribution based on pruned hybrid basis function KAN, belonging to the field of ocean observation technology. The invention constructs a hybrid basis function KAN network model, which includes an input layer, a hybrid basis function KAN layer, a fully connected layer, and an output layer. The hybrid basis function KAN layer contains n basis functions, and a pruning strategy is used to adaptively select the optimal basis function during model training. This method can adapt to various time series data without requiring specific optimization for a particular data type, achieving high prediction accuracy and providing important guidance for marine scientific research.

Description

Technical Field

[0001] The present invention relates to the field of ocean observation technology, and in particular to a method for predicting ocean sound speed distribution based on a pruned mixed basis function KAN. Background Art

[0002] The underwater sound speed distribution affects the propagation of underwater acoustic signals and is one of the important parameters for underwater positioning and navigation. To efficiently obtain accurate underwater sound speed distribution, researchers have proposed a variety of methods, including methods for constructing spatial sound speed distribution using remote sensing data, historical sound speed data, and latitude and longitude coordinates, and forecasting methods using historical sound speed time series data. Dr. Wu Pengfei and others from the Ocean University of China proposed a multi-source data fusion method that primarily uses a model to learn the impact of remotely sensed sea surface temperature on the characteristics of underwater sound speed distribution. However, the ability of remotely sensed sea surface temperature to influence the sound speed of the entire ocean is limited and cannot reflect changes in sound speed in deep-sea areas. To estimate the sound speed distribution of the entire ocean depth, Lu Jiajun and others proposed a hierarchical long short-term memory neural network (LSTM) for rapid sound speed profile prediction. However, this model can only process data for a single task and requires readjustment of the model structure when switching tasks, resulting in insufficient generalization capabilities.

[0003] The existing model can only handle a single type of task. For time series forecasting tasks, such as predicting sound speed, temperature, salinity, etc., it is necessary to optimize the model structure according to different data distributions. The model is not widely applicable. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting ocean sound speed distribution based on a pruned mixed basis function Kolmogorov–Arnold network (KAN) to overcome the shortcomings of the existing technology.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for predicting ocean sound speed distribution based on pruned mixed basis function KAN is proposed. The specific steps are as follows:

[0007] S1: Extracting spatial historical ocean data sets: Determine the spatial coordinates as longitude M° and latitude N° based on the data forecast location, and extract the ocean data of the location at different historical moments to form a historical data set;

[0008] S2: Determine the data forecast time resolution, forecast start and end time, and maximum time length: Indicates the time resolution required for the forecast task, Indicates the forecast start time, Indicates the maximum forecast time length;

[0009] S3: Secondary screening of spatial historical ocean datasets: based on temporal resolution , filter the data shape reference dataset from the historical dataset in S1;

[0010] S4: performing preprocessing on the reference data set;

[0011] S5: Construct a hybrid basis function KAN network model, which includes an input layer, a hybrid basis function KAN layer, a fully connected layer, and an output layer. There are n basis functions in the hybrid basis function KAN layer. During the model training process, the best basis function can be adaptively selected through a pruning strategy. The number of neurons in the basis function is N, and the number of neurons in the fully connected layer is N; according to the different depth layers, the ocean data distribution forecast is performed in layers, and a hybrid basis function KAN network is constructed for each depth layer. For the hybrid basis function KAN network constructed for each depth layer, the prediction result is a length of The output time series of

[0012] S6: training the hybrid basis function KAN network model;

[0013] S7: Model prediction: According to the task-specified forecast time resolution, forecast start time, and forecast maximum time length, determine the number of forecast iterations and the historical distribution reference data corresponding to the forecast start time. Use 2 or more whole-cycle data before the forecast start time as the training set of the model to obtain the forecast result, then perform denormalization on the forecast result and output the forecasted future distribution data.

[0014] Furthermore, in said S3: the time range covered by the training data at least includes the forecast start time The data of the first two complete change cycles, if the forecast time resolution unit is "hour", the sample coverage should be no less than The first two full-day periods, i.e. not less than the screening forecast time Sample data for the previous two days; when the forecast time resolution is "month", the sample coverage should be no less than The first two full-year cycles, i.e. not less than the time before the screening forecast Sample data from the previous two years;

[0015] Let the secondary screening historical data set be expressed as:

[0016] ;

[0017] in Represents the i-th data profile, a total of I, and the i-th data profile is further expressed as:

[0018] ;

[0019] in is the data value, subscript Expressed as depth layers, represents the transpose of the vector; in formula (1), the S data set is arranged in time order, and the time interval and time resolution are consistent; = 0,1,…,J, where is the depth layer index label, and the maximum depth layer of data distribution is dJ;

[0020] Formula (1) is expanded to obtain the data set matrix:

[0021] .

[0022] Furthermore, the S4 includes:

[0023] S4-1: Divide the training set and validation set

[0024] Take the first IC column of the historical data set S as the training data set T, as shown in formula (4); the last C columns of S are used as the verification data set E, as shown in formula (5), where IC ≥ C; C is the natural change period of the data;

[0025] ;

[0026] ;

[0027] S4-2: Normalize the training data set T to , the normalization formula is shown in formula (6), where is the normalized data, is the data before normalization, is the mean of the sequence data, is the standard deviation of the sequence data; From formula (7), we can get Indicates the summation of the j-th row data of matrix T from the first column to the last column; It is obtained from formula (8); then the normalized training data set is Specifically divided into training input sets and training label set The training input set X is shown in formula (10), and the training label set Y is shown in formula (11);

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] S4-3: Re-split the training input set and training label set according to the depth layer

[0035] The training input set and training label set are divided into , ; , They are expressed by formulas (12) and (13) respectively;

[0036] ;

[0037] ;

[0038] Indicates that for the data of the j-th row of matrix X, that is, the data of the j-th depth layer, each sliding window takes data of size C, and the sliding window step size is 1; It means that for the j-th row data of matrix Y, that is, the data of the j-th depth layer, each sliding window takes data of size 1, and the sliding window step size is 1.

[0039] Furthermore, the S6 includes:

[0040] S6-1: Before model training, determine the learning rate of each depth layer. And the number of iterations is , j represents the corresponding depth layer, j=1, 2,…, J;

[0041] S6-2: During model training, the hybrid basis function KAN network model of each depth layer is trained separately, using the hybrid basis function KAN Represents the mixed basis function KAN network of the j-th depth layer. The input and output of the model are expressed as:

[0042] ;

[0043] in Represents the output matrix of the model, expressed as:

[0044] ;

[0045] Then calculate the mean square error (MSE) between the model's output value and the training label set:

[0046] ;

[0047] Then use the MSE value to update the model parameters; the same is true for other depth layer training methods;

[0048] S6-3: Implement pruning strategy;

[0049] S6-4: Model verification. Model verification is also performed separately for each depth layer; using the training input set The next period data of the last time period data is used as the input of the model to predict the data of a future time resolution, that is, the sequence data of length 1, and then the sliding window (sliding window step size is 1) takes the new value as the input for predicting the next time resolution until the prediction completes a time period. The remaining depth layers are similar.

[0050] Furthermore, the S6-3 includes:

[0051] S6-31: Pre-train the model first. At the beginning of model training, freeze the weight coefficients so that they cannot be trained. Only the parameters in the basis function are trained. All weight coefficients are initialized to , pre-train the model for a certain number of times. At this time, the output of the mixed basis function KAN layer is:

[0052] ;

[0053] S6-32: Prune the model. First, freeze the trainable parameters in all basis functions, then unfreeze the weight coefficients to make them trainable. After a certain number of training iterations, observe the weight coefficients of each basis function and find the largest coefficient. The basis function corresponding to this coefficient is the optimal basis function. Unfreeze its trainable parameters, set its weight coefficient to 1, and all other weight coefficients to 0. Continue training until the number of iterations is complete.

[0054] Furthermore, the S6-4 includes:

[0055] The prediction result of the first depth layer is a time series of length C, as shown in formula (17):

[0056] ;

[0057] The same is true for the other depth layers, so the final predicted data set is , as shown in formula (18):

[0058] ;

[0059] Since the training data set is normalized before model training, the predicted data should be denormalized (the inverse operation of the original normalization operation), that is, the predicted data should be restored to the scale range of the original data to facilitate comparative analysis with the verification data.

[0060] The denormalization formula is:

[0061] ;

[0062] Prediction results after denormalization :

[0063] ;

[0064] in, Represents the value predicted at the i-th temporal resolution of the j-th depth layer.

[0065] After the denormalization operation is completed, the root mean square error (RMSE) between the actual value and the predicted value is calculated:

[0066] ;

[0067] in Represents the RMSE of the predicted time resolution at the i-th time resolution. If the RMSE value is not less than the desired threshold, return to S6, increase the number of iterations of the training model, and continue training the model until the model converges, that is, the RMSE is less than the desired threshold or does not change significantly.

[0068] Compared with the prior art, the present invention has at least the following beneficial effects:

[0069] This paper proposes a method for predicting ocean sound speed distribution based on a pruned mixed basis function Kolmogorov-Arnold neural network, which is widely applicable to fitting data of different distribution types. For a given task, the model uses historical ocean data from the spatial region where the task is located as a reference to accurately predict the future ocean sound speed distribution in the target area. To accelerate model training efficiency, a pruning strategy is also proposed to reduce model training time. This method can adapt to a variety of time series data without the need for specific optimization for a specific data type. It achieves high prediction accuracy and provides important guidance for marine scientific research. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is the overall flow chart of the present invention.

[0071] Figure 2 It is a schematic diagram of the basic structure of the mixed basis function KAN neural network model.

[0072] Figure 3This is a comparison chart of the predicted sound speed distribution and the actual sound speed.

[0073] Figure 4 This is a comparison chart of the predicted temperature distribution and the actual distribution. DETAILED DESCRIPTION

[0074] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to specific embodiments and the accompanying drawings. It is apparent that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments disclosed herein without inventive effort are also within the scope of protection of the present invention.

[0075] Example 1:

[0076] A method for forecasting ocean time series distribution based on pruned mixed basis function Kolmogorov-Arnold neural network is specifically implemented as follows: Figure 1 As shown:

[0077] 1. Predicting the speed of sound

[0078] Step 1: Extract spatial historical ocean datasets based on data forecast locations

[0079] According to the data forecast location, the spatial coordinates are determined to be 168.5°E longitude and 16.5°N latitude. The sound velocity profile data measured for 60 months in this spatial area from 2016 to 2020 are selected from the global Argo dataset to form a spatial historical sound velocity dataset as the reference dataset of the model.

[0080] Step 2: Determine the data forecast time resolution, forecast start and end time, and maximum time length

[0081] use Indicates the time resolution required for the forecast task, For 1 month; Indicates the forecast start time, For January 2020; Indicates the maximum forecast time length, For 1 year.

[0082] Step 3: Secondary screening of spatial historical data

[0083] According to the time resolution , filter data from the historical data set in step 1 to form a training reference data set, and the training data coverage time range includes at least the forecast start time The data of the first two complete change cycles, if the forecast time resolution unit is "hour", the sample coverage should be no less than The first two full-day periods, i.e. not less than the screening forecast time Sample data for the previous two days; when the forecast time resolution is "month", the sample coverage should be no less than The first two full-year cycles, i.e. not less than the time before the screening forecast Sample data for the previous two years.

[0084] In this example, the sound speed profile data measured in this spatial region from 2016 to 2020 is used as the spatial historical sound speed dataset. The forecast start time is January 2020. Before that, there are four full-year cycles of training reference data, which meets the training requirements.

[0085] The historical sound speed distribution dataset is represented as:

[0086] ;

[0087] Where i = 1~60 means 5 years and 60 months from January 2016 to December 2020 are arranged in chronological order. It represents the sound speed distribution data corresponding to the time.

[0088] The i-th sound velocity profile can be further expressed as:

[0089] = 1, 2, …, 58

[0090] in is the speed of sound, unit: m / s, subscript Expressed as depth layers, The maximum value is 58, that is, the maximum depth layer of the sound velocity distribution is 58 layers. ” stands for the transpose of a vector.

[0091] Expand and write the collected historical sound speed distribution data set S into a sound speed value data matrix with 58 rows and 60 columns:

[0092] ;

[0093] After the historical sound speed distribution data set is collected, proceed to step 4.

[0094] Step 4:

[0095] (1) The data change time period is C = 12. The first 48 sound speed distribution data of the historical sound speed distribution data set S are used as the training data set, and the remaining 12 sound speed distribution data are used as the validation data set.

[0096] (2) Specific processing of training set

[0097] The first 48 columns of the historical sound speed dataset S are divided into the training dataset T, and the last 12 columns of S are used as the validation dataset E.

[0098] Training dataset: ;

[0099] Validation dataset: ;

[0100] Normalize the training data set T to .

[0101] Normalized training set: ;

[0102] The normalized training data set Specifically divided into training input sets and training label set , a training method with an interval of one cycle is adopted, that is, 12 columns of data are used to predict the 13th column of data (that is, when the data from January to December 2016 is used as the training input, the data from January 2017 is used as the training output; when the data from February 2016 to January 2017 is used as the training input, the data from February 2017 is used as the training output), and so on.

[0103] Training input set: ;

[0104] Training label set: ;

[0105] Then X and Y are further divided into , .

[0106] After the sound velocity distribution sample data is preprocessed, go to step 5.

[0107] Step 5: Construct a hybrid basis function KAN network model. The model structure is as follows Figure 2 shown.

[0108] According to the different depth layers, the ocean data distribution forecast is performed in layers, and a hybrid basis function KAN network is constructed for each depth layer. For the hybrid basis function KAN network constructed for each depth layer, the prediction result is an output time series with a length of 12.

[0109] The number of basis functions, the number of basis function neurons, and the number of neurons in the fully connected layer are 4, 256, and 256 respectively.

[0110] The basis functions are B-spline, Jacobi, Taylor, and Wavelet.

[0111] Step 6: Model training

[0112] Before model training, determine the learning rate of each depth layer = 0.0001 and the number of iterations is , represents the corresponding depth layer, j = 1, 2, ..., 58;

[0113] (1) Model training

[0114] Training the first depth layer When building a network, the input to the model is: = , the corresponding model output is = ; Then calculate the MSE value to update the model parameters. The training method of the remaining layers is similar.

[0115] (2) Implementation of pruning strategy

[0116] The first step is to pre-train the model a certain number of times

[0117] In the model, the weight coefficients of the hybrid basis function KAN layer and the parameters in the basis function are all trainable. At the beginning of model training, the weight coefficients are frozen so that they cannot be trained, and only the parameters in the basis function are trained. All weight coefficients are initialized to . First, pre-train the model ten times.

[0118] At this time, the output of the mixed basis function KAN layer is

[0119] ;

[0120] The second step is to prune the model

[0121] After pre-training is complete, all trainable parameters in the basis functions are frozen, and the weight coefficients are unfrozen to allow training. After ten more training runs, the weight coefficients of each basis function are observed, and the largest coefficient is found. The basis function corresponding to this coefficient is the optimal basis function. Its trainable parameters are unfrozen, and its weight coefficient is set to 1, while the other weight coefficients are set to 0.

[0122] Then continue training until the number of iterations is completed.

[0123] (3) Model validation

[0124] For the training input set The last time period data sliding window gets new data in one step, that is The model uses this as input to predict data for one future time resolution, that is, a sequence of length 1. The window is then slid one step to obtain the new value, which serves as the input for predicting the next time resolution, until the prediction completes a time period. The remaining depth layers are similar.

[0125] The prediction result of the first depth layer is a time series of sound speed values ​​with a length of 12:

[0126] ;

[0127] The same is true for the other depth layers, so the final predicted sound speed data set is :

[0128] ;

[0129] The predicted sound speed data set is denormalized using the inverse operation of the original normalization operation, that is, the predicted data is restored to the scale range of the original data to facilitate comparative analysis with the verification data.

[0130] Prediction results after denormalization As shown below:

[0131] ;

[0132] After the denormalization operation is completed, the root mean square error is calculated. If the RMSE value is not less than the desired threshold, return to step 6, increase the number of iterations of the training model, and continue training the model until the model converges, that is, the RMSE is less than the desired threshold or does not change significantly.

[0133] In order to verify the prediction accuracy of the model, the prediction results of the hybrid basis function KAN are compared with the LSTM prediction results and the actual sound speed distribution. The intuitive comparison diagram is as follows: Figure 3 To demonstrate the improved model training efficiency achieved by the pruning strategy, Table 1 shows the RMSE of the prediction errors and the training time costs for both the pruned and unpruned models. The average RMSE of the prediction errors for the hybrid basis function KAN is 0.71, and the average RMSE of the prediction errors for the LSTM is 0.95. Table 1 shows that the pruning strategy can reduce model training time costs without compromising prediction accuracy.

[0134] Table 1 Prediction error and time cost

[0135] Pruning No pruning RMSE (m / s) 0.71 0.71 Time cost (seconds) 45 65

[0136] 2. Forecast Temperature

[0137] Step 1: Extract spatial historical ocean datasets based on data forecast locations

[0138] According to the data forecast location, the spatial coordinates are determined to be longitude 168.5°E and latitude 16.5°N. The temperature profile data measured for 60 months in this spatial area from 2016 to 2020 are selected from the global Argo dataset to form a spatial historical temperature dataset as the reference dataset of the model.

[0139] Step 2: Determine the data forecast time resolution, forecast start and end time, and maximum time length

[0140] use Indicates the time resolution required for the forecast task, For 1 month; Indicates the forecast start time, For January 2020; Indicates the maximum forecast time length, For 1 year.

[0141] Step 3: Secondary screening of spatial historical data

[0142] According to the time resolution , filter data from the historical data set in step 1 to form a training reference data set, and the training data coverage time range includes at least the forecast start time The data of the first two complete change cycles, if the forecast time resolution unit is "hour", the sample coverage should be no less than The first two full-day periods, i.e. not less than the screening forecast time Sample data for the previous two days; when the forecast time resolution is "month", the sample coverage should be no less than The first two full-year cycles, i.e. not less than the time before the screening forecast Sample data for the previous two years.

[0143] In this example, the temperature profile data measured in this spatial region from 2016 to 2020 is used as the spatial historical temperature dataset. The forecast start time is January 2020. Before that, there are four full-year cycles of training reference data, which meets the training requirements.

[0144] The historical temperature distribution dataset is represented as:

[0145] ;

[0146] Where i = 1~60 means 5 years and 60 months from January 2016 to December 2020 are arranged in chronological order. It represents the temperature distribution data corresponding to the time.

[0147] The i-th temperature profile can be further expressed as:

[0148] = 1, 2, …, 58

[0149] in is the temperature value, unit is m / s, subscript Expressed as depth layers, The maximum value is 58, that is, the maximum depth layer of the temperature distribution is 58 layers. ” stands for the transpose of a vector.

[0150] Expand and write the collected historical temperature distribution data set S into a temperature value data matrix with 58 rows and 60 columns:

[0151] ;

[0152] After the historical temperature distribution data set is collected, go to step 4.

[0153] Step 4:

[0154] (1) The data change time period is C = 12. The first 48 temperature distribution data of the historical temperature distribution data set S are used as the training data set, and the remaining 12 temperature distribution data are used as the validation data set.

[0155] (2) Specific processing of training set

[0156] The first 48 columns of the historical temperature dataset S are divided into the training dataset T, and the last 12 columns of S are used as the validation dataset E.

[0157] Training dataset: ;

[0158] Validation dataset: ;

[0159] Normalize the training data set T to .

[0160] Normalized training set: ;

[0161] The normalized training data set Specifically divided into training input sets and training label set , a training method with an interval of one cycle is adopted, that is, 12 columns of data are used to predict the 13th column of data (that is, when the data from January to December 2016 is used as the training input, the data from January 2017 is used as the training output; when the data from February 2016 to January 2017 is used as the training input, the data from February 2017 is used as the training output), and so on.

[0162] Training input set: ;

[0163] Training label set: ;

[0164] Then X and Y are further divided into , .

[0165] After the temperature distribution sample data preprocessing is completed, go to step 5.

[0166] Step 5: Construct a hybrid basis function KAN network model

[0167] According to the different depth layers, the ocean data distribution forecast is performed in layers, and a hybrid basis function KAN network is constructed for each depth layer. For the hybrid basis function KAN network constructed for each depth layer, the prediction result is an output time series with a length of 12.

[0168] The number of basis functions, the number of basis function neurons, and the number of neurons in the fully connected layer are 4, 256, and 256 respectively.

[0169] The basis functions are B-spline, Jacobi, Taylor, and Wavelet.

[0170] Step 6: Model Training

[0171] Before model training, determine the learning rate of each depth layer = 0.0001 and the number of iterations is , represents the corresponding depth layer, j = 1, 2, ..., 58;

[0172] (1) Model training

[0173] Training the first depth layer When building a network, the input to the model is: = , the corresponding model output is = ; Then calculate the MSE value to update the model parameters. The training method of the remaining layers is similar.

[0174] (2) Implementation of pruning strategy

[0175] The first step is to pre-train the model a certain number of times

[0176] In the model, the weight coefficients of the hybrid basis function KAN layer and the parameters in the basis function are all trainable. At the beginning of model training, the weight coefficients are frozen so that they cannot be trained, and only the parameters in the basis function are trained. All weight coefficients are initialized to . First, pre-train the model ten times.

[0177] At this time, the output of the mixed basis function KAN layer is

[0178] ;

[0179] The second step is to prune the model

[0180] After pre-training is complete, all trainable parameters in the basis functions are frozen, and the weight coefficients are unfrozen to allow training. After ten more training runs, the weight coefficients of each basis function are observed, and the largest coefficient is found. The basis function corresponding to this coefficient is the optimal basis function. Its trainable parameters are unfrozen, and its weight coefficient is set to 1, while the other weight coefficients are set to 0.

[0181] Then continue training until the number of iterations is completed.

[0182] (3) Model validation

[0183] For the training input set The last time period data sliding window gets new data in one step, that is The model uses this as input to predict data for one future time resolution, that is, a sequence of length 1. The window is then slid one step to obtain the new value, which serves as the input for predicting the next time resolution, until the prediction completes a time period. The remaining depth layers are similar.

[0184] The prediction result of the first depth layer is a temperature value time series with a length of 12:

[0185] ;

[0186] The same is true for the other depth layers, so the final predicted temperature data set is :

[0187] ;

[0188] The predicted temperature data set is denormalized using the inverse operation of the original normalization operation, that is, the predicted data is restored to the scale range of the original data to facilitate comparative analysis with the verification data.

[0189] Prediction results after denormalization As shown below:

[0190] ;

[0191] After the denormalization operation is completed, the root mean square error is calculated. If the RMSE value is not less than the desired threshold, return to step 6, increase the number of iterations of the training model, and continue training the model until the model converges, that is, the RMSE is less than the desired threshold or does not change significantly.

[0192] In order to verify the prediction accuracy of the model, the prediction results of the hybrid basis function KAN are compared with the LSTM prediction results and the actual temperature distribution. The intuitive comparison diagram is as follows: Figure 4 To demonstrate the improved model training efficiency achieved by the pruning strategy, Table 2 shows the RMSE of the prediction errors and the training time costs for both pruning and non-pruning models. The average RMSE of the prediction errors for the hybrid basis function KAN is 0.27, and the average RMSE of the prediction errors for the LSTM is 0.32. Table 2 shows that the pruning strategy can reduce model training time costs without compromising prediction accuracy.

[0193] Table 2 Prediction error and time cost

[0194] Pruning No pruning RMSE (m / s) 0.27 0.27 Time cost (seconds) 45 65

[0195] The specific embodiments described above further illustrate the purpose, technical solutions and beneficial effects disclosed in the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting ocean sound speed distribution based on pruned mixed basis function KAN, characterized in that: The method comprises the following specific steps: S1: Extracting spatial historical ocean data sets: Determine the spatial coordinates as longitude M° and latitude N° based on the data forecast location, and extract the ocean data of the location at different historical moments to form a historical data set; S2: Determine the data forecast time resolution, forecast start and end time, and maximum time length: Indicates the time resolution required for the forecast task, Indicates the forecast start time, Indicates the maximum forecast time length; S3: Secondary screening of spatial historical ocean datasets: based on temporal resolution , filter the data shape reference dataset from the historical dataset in S1; S4: performing preprocessing on the reference data set; S5: Construct a hybrid basis function KAN network model, which includes an input layer, a hybrid basis function KAN layer, a fully connected layer, and an output layer. There are n basis functions in the hybrid basis function KAN layer. During the model training process, the best basis function can be adaptively selected through a pruning strategy. The number of neurons in the basis function is N, and the number of neurons in the fully connected layer is N. According to the different depth layers, the ocean data distribution forecast is performed in layers, and a hybrid basis function KAN network is constructed for each depth layer. For the hybrid basis function KAN network constructed for each depth layer, the prediction result is a length of The output time series of S6: training the hybrid basis function KAN network model; S7: Model prediction: According to the task-specified forecast time resolution, forecast start time, and forecast maximum time length, determine the number of forecast iterations and the historical distribution reference data corresponding to the forecast start time. Use 2 or more whole-cycle data before the forecast start time as the training set of the model to obtain the forecast result, then perform denormalization on the forecast result and output the forecasted future distribution data.

2. The method for predicting ocean sound speed distribution according to claim 1, wherein: In S3: the training data coverage time range at least includes the forecast start time For the data of the first two complete change cycles, when the forecast time resolution unit is "hour", the sample coverage should be no less than The first two full-day periods, i.e. not less than the screening forecast time Sample data for the previous two days; when the forecast time resolution is "month", the sample coverage should be no less than The first two full-year cycles, i.e. not less than the time before the screening forecast Sample data from the previous two years; Let the secondary screening historical data set be expressed as: ； in Represents the i-th data profile, a total of I, and the i-th data profile is further expressed as: ； in is the data value, subscript Expressed as depth layers, represents the transpose of the vector; in formula (1), the S data set is arranged in time order, and the time interval and time resolution are consistent; = 0,1,…,J, where is the depth layer index label, and the maximum depth layer of data distribution is dJ; Formula (1) is expanded to obtain the data set matrix: 。 3. The method for predicting ocean sound speed distribution according to claim 1, wherein: The S4 includes: S4-1: Divide the training set and validation set Take the first IC column of the historical data set S as the training data set T, as shown in formula (4); the last C columns of S are used as the verification data set E, as shown in formula (5), where IC ≥ C; C is the natural change period of the data; ; ； S4-2: Normalize the training data set T to , the normalization formula is shown in formula (6), where is the normalized data, is the data before normalization, is the mean of the sequence data, is the standard deviation of the sequence data; From formula (7), we can get: Indicates the summation of the j-th row data of matrix T from the first column to the last column; It is obtained from formula (8); then the normalized training data set is Specifically divided into training input sets and training label set The training input set X is shown in formula (10), and the training label set Y is shown in formula (11); ; ; ; ; ; ； S4-3: Re-split the training input set and training label set according to the depth layer The training input set and training label set are divided into , ; , They are expressed by formulas (12) and (13) respectively; ; ; Indicates that for the data of the j-th row of matrix X, that is, the data of the j-th depth layer, each sliding window takes data of size C, and the sliding window step size is 1; It means that for the j-th row data of matrix Y, that is, the data of the j-th depth layer, each sliding window takes data of size 1, and the sliding window step size is 1.

4. The method for predicting ocean sound speed distribution according to claim 1, wherein: The S6 includes: S6-1: Before model training, determine the learning rate of each depth layer. And the number of iterations is , j represents the corresponding depth layer, j=1, 2,…, J; S6-2: During model training, the hybrid basis function KAN network model of each depth layer is trained separately, using the hybrid basis function KAN Represents the mixed basis function KAN network of the j-th depth layer. The input and output of the model are expressed as: ; in Represents the output matrix of the model, expressed as: ; Then calculate the mean square error (MSE) between the model's output value and the training label set: ; Then use the MSE value to update the model parameters; S6-3: Implement pruning strategy; S6-4: Model Validation: Using the Training Input Set The next period data of the last time period data is used as the input of the model to predict the data of the next time resolution, that is, the sequence data of length 1, and then the sliding window is taken to obtain the new value as the input for predicting the next time resolution until the prediction completes one time period.

5. The method for predicting ocean sound speed distribution according to claim 4, wherein: The S6-3 includes: S6-31: Pre-train the model first. At the beginning of model training, freeze the weight coefficients so that they cannot be trained. Only the parameters in the basis function are trained. All weight coefficients are initialized to , pre-train the model. At this time, the output of the mixed basis function KAN layer is: ； S6-32: Prune the model. First, freeze the trainable parameters in all basis functions, then unfreeze the weight coefficients to enable them to be trained. After training, observe the weight coefficients of each basis function and find the largest coefficient. At this time, the basis function corresponding to this coefficient is the best basis function. Unfreeze its trainable parameters, set its weight coefficient to 1, and set other weight coefficients to 0. Then continue training until the number of iterations is completed.

6. The method for predicting ocean sound speed distribution according to claim 4, wherein: The S6-4 includes: The prediction result of the first depth layer is a time series of length C, as shown in formula (17): ; The final predicted data set is , as shown in formula (18): ; The predicted data is denormalized. The denormalization formula is: ; Prediction results after denormalization : ; in, represents the value predicted at the i-th temporal resolution of the j-th depth layer; After the denormalization operation is completed, the root mean square error between the actual value and the predicted value is calculated: ; in represents the RMSE of the predicted i-th time resolution; if the RMSE value is not less than the expected threshold, return to S6, increase the number of iterations of the training model, and continue training the model until the model converges, that is, the RMSE is less than the expected threshold or there is no obvious change.

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