Methods and apparatus for analyzing the mechanism of tropical cyclone intensity variation based on KAN

Abstract

This application relates to a method and apparatus for analyzing the mechanism of tropical cyclone intensity change based on KAN, belonging to the field of TC intensity change forecasting technology. The method includes: using a factor recursive pruning algorithm based on KAN2.0 attribution scores to screen and obtain a set of high-impact forecasting factors for TC intensity change forecasting; performing factor contribution analysis based on symbolic regression using KAN2.0 trained on the high-impact forecasting factor set to obtain a complete linear equation from the high-impact forecasting factors to TC intensity change; and quantitatively analyzing the direction and degree of contribution of each high-impact forecasting factor to TC intensity change based on the sign and absolute value of the linear coefficients in the equation. This method can effectively improve the stability, accuracy, generalization ability, and interpretability of TC intensity forecasting.

Description

Technical Field

[0001] This application relates to the field of TC (tropical cyclone) intensity change forecasting technology, and in particular to a method and apparatus for analyzing the mechanism of tropical cyclone intensity change based on KAN. Background Technology

[0002] A TC is a strong cyclonic vortex that forms over tropical or subtropical oceans. Its intensity variation is controlled by multiple scale physical processes. The interaction mechanism between its internal dynamics and the external environment is still not fully understood, so accurately predicting the intensity of a TC remains a formidable challenge.

[0003] Deep learning (DL) models have demonstrated great potential in the field of TC intensity forecasting due to their ability to automatically extract features and mine complex nonlinear relationships. For example, some studies have proposed the TC-Rolling model based on convolutional neural networks, which establishes the correlation between TC convection structure and its intensity and adopts a rolling strategy to effectively reduce the forecast bias of TC intensity across multiple time steps and improve the accuracy of short-term TC forecasts. Other studies have proposed a deep learning-driven TC intensity prediction framework, Deep-TCP, which integrates a data constraint module, a spatiotemporal attention module, and a feature enhancement module. This framework can effectively fuse multi-source data and significantly improve the accuracy and robustness of forecasts.

[0004] However, due to the "black box" nature of intelligent models, their internal decision-making processes are difficult to analyze, significantly limiting their interpretability. To analyze the contribution of forecast factors to TC intensity changes, some studies have used Garson variable importance scores to rank the importance of 121 SHIPS (Statistical Scheme for Hurricane Intensity) forecast factors. This method quantifies the relative importance of different features in the model forecast by inversely calculating the contribution ratio of each input variable to the output result. However, due to the large scale of forecast factors, this method is computationally expensive, and it can only assess the overall contribution of each forecast factor, making it difficult to explain the direction of contribution of each factor to the forecast result, resulting in poor interpretability of TC intensity forecasts. Summary of the Invention

[0005] Therefore, it is necessary to provide a method and device for analyzing the mechanism of tropical cyclone intensity change based on KAN to address the technical problem of weak interpretability in current smart TC intensity forecasts. This method and device can effectively screen out high-impact forecasting factors and quantitatively analyze the contribution of each factor to TC intensity change, thereby achieving high-accuracy and highly interpretable TC intensity forecasts.

[0006] A method for analyzing the intensity variation mechanism of tropical cyclones based on KAN, the method comprising:

[0007] A factor recursive pruning algorithm based on KAN2.0 attribution scores was used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts;

[0008] KAN2.0 was trained using a set of high-impact forecasting factors, and factor contribution analysis was performed based on symbolic regression from KAN2.0. The analysis process included:

[0009] First, the symbolic function library of the network is limited to linear functions. Linear function fitting is performed on the activation function of each edge in the network to obtain the optimal linear function, which replaces the original activation function of each edge, thus achieving symbolic regression of the network structure. Second, layer-by-layer expression calculation is performed in the symbolic regression network, including summing the input functions of each child node, linear transformation of child nodes, linear transformation of nodes, and summing the output functions of nodes at each layer. This layer-by-layer expression calculation is propagated to the last layer of the network to obtain the overall linear symbolic output of the network. Finally, based on the overall linear symbolic output of the network, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained. Based on the sign and absolute value of the linear coefficients in the linear equation, the contribution direction and degree of each high-impact forecasting factor to TC intensity changes are quantitatively analyzed.

[0010] In one embodiment, a factor recursive pruning algorithm based on KAN2.0 attribution scores is used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts, including:

[0011] Initialize the full forecast factor set for TC intensity change forecast and divide it into training set, validation set and independent test set;

[0012] The training and validation sets are input into KAN2.0 for iterative training to obtain the attribution score and root mean square error of the validation set output by KAN2.0. The attribution score is used to quantify the global contribution of each forecast factor to the change in TC intensity. The global contribution includes linear and nonlinear contributions.

[0013] The bottom 10% of forecast factors ranked by attribution score are pruned and removed to form a new set of forecast factors. This new set of forecast factors is then re-entered into KAN2.0 to perform the forecast factor pruning and removal operation until the number of forecast factors is less than a set value. Based on the ranking of the root mean square error of the validation set output by KAN2.0 in each round, the set of forecast factors with the lowest root mean square error of the validation set is selected as the high-impact forecast factor set.

[0014] In one embodiment, initializing the full forecast factor set for TC intensity change forecasts includes:

[0015] The initial forecast factor set and the time-series forecast factor set reflecting the temporal characteristics of TC intensity changes were obtained from SHIPS data. These were combined to form a full forecast factor set for TC intensity change forecasts. The full forecast factor set was preprocessed, including filling in default values ​​and standardization. The time-series forecast factor set was supplemented with eight time-series forecast factors, namely the sea level pressure changes over the past 6h, 12h, 18h, and 24h, the TC intensity changes over the past 6h, 12h, and 18h, and the TC life history label. The TC life history label was used to sequentially number each moment in the TC life history.

[0016] In one embodiment, KAN2.0 is trained using a set of high-impact forecast factors, including:

[0017] KAN2.0 was trained using a set of high-impact forecasting factors. The TPE Bayesian optimization algorithm was used to optimize the network hyperparameters during the training process. The optimized KAN2.0 was then tested annually for TC intensity change forecasts, and the root mean square error and mean absolute error were used to evaluate the forecast stability.

[0018] In one embodiment, by performing linear function fitting on the activation function of each edge in the network, an optimal linear function is obtained to replace the original activation function of each edge, thereby achieving symbolic regression of the network structure, including:

[0019] For each edge in the KAN2.0 network, the pre-activation value of the activation function for each edge is obtained based on the data samples. and post-activation value And search for the optimal linear parameters within the preset parameter range to adjust the pre-activation value. Activation value The mapping relationship is fitted to the optimal value, and the optimal linear function is finally obtained to replace the original activation function of each edge, so as to realize the symbolic regression of the network structure; among them, the optimal linear parameters include the optimal linear coefficient and the optimal intercept.

[0020] In one embodiment, layer-by-layer expression computation is performed in the network structure symbolic regression network, including the summation of the input functions of each child node, the linear transformation of the child nodes, the linear transformation of the nodes, and the summation of the output functions of the nodes at each layer. This layer-by-layer expression computation is then propagated to the last layer of the network to obtain the overall linear symbolic output of the network, including:

[0021] In each layer of the KAN2.0 network with symbolic regression, all input functions passed to the same child node of the current layer are summed to obtain the preliminary output function of each child node in the current layer. Scaling and bias adjustments at the child node level are applied to the preliminary output functions of each child node in the current layer to complete the linear transformation of the child nodes, resulting in the preliminary output function of each node in the current layer. Node-level scaling and bias adjustments are applied to the preliminary output functions of each node in the current layer to complete the linear transformation of the nodes, resulting in the final output function of each node in the current layer. The final output functions of each node in the current layer are summed to obtain the input function of the next layer. This layer-by-layer expression is calculated and propagated to the last layer of the KAN2.0 network to obtain the overall linear symbolic output of the KAN2.0 network. Here, the input function, preliminary output function, and final output function are all linear functions.

[0022] In one embodiment, based on the overall linear symbolic output of the network, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained. Then, based on the sign and absolute value of the linear coefficients in the linear equation, the contribution direction and degree of each high-impact forecasting factor to TC intensity changes are quantitatively analyzed, including:

[0023] Based on the overall linear symbolic output of the KAN2.0 network, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained, expressed as follows: ;in, This represents the change in TC intensity. Indicates the first One high-impact forecasting factor, Indicates the first The linear coefficients corresponding to the high-impact forecasting factors The intercept is... , The number of high-impact forecasting factors;

[0024] Based on the sign and absolute value of each linear coefficient, the contribution direction and degree of each high-impact forecasting factor to the change in TC intensity are quantitatively analyzed. The sign of the linear coefficient indicates the direction of contribution of the high-impact forecasting factor to the change in TC intensity. When the linear coefficient is positive and the corresponding high-impact forecasting factor is positive / negative, it indicates that the corresponding high-impact forecasting factor has a positive / negative contribution to the change in TC intensity, which is conducive to the enhancement / weakening of TC intensity. When the linear coefficient is negative and the corresponding high-impact forecasting factor is positive / negative, it indicates that the corresponding high-impact forecasting factor has a negative / positive contribution to the change in TC intensity, which is conducive to the weakening / enhancing of TC intensity. The absolute value of the linear coefficient indicates the degree of contribution of the high-impact forecasting factor to the change in TC intensity; the larger the absolute value of the linear coefficient, the greater the contribution of the corresponding high-impact forecasting factor to the change in TC intensity.

[0025] In one embodiment, high-impact forecasting factors are classified into climate and persistence factors, kinetic factors, and thermodynamic factors; wherein, climate and persistence factors are used to reflect the historical evolution characteristics, climate background, and persistence status of TC; kinetic factors are used to reflect the kinetic characteristics of the large-scale environmental field in which TC is located; and thermodynamic factors are used to reflect the energy supply conditions for TC development.

[0026] In one embodiment, after quantitatively analyzing the direction and degree of contribution of each high-impact forecasting factor to the change in TC intensity, the method further includes:

[0027] A set of high-impact forecasting factors that can reflect the direction and degree of contribution to TC intensity changes will be transferred to the training of the existing TC intensity change forecasting model until convergence is achieved to obtain a well-trained TC intensity change forecasting model for TC intensity change forecasting tasks; the existing TC intensity change forecasting model is an MLP model.

[0028] A device for analyzing the mechanism of tropical cyclone intensity change based on KAN, the device comprising:

[0029] The factor recursive pruning module is used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts using a factor recursive pruning algorithm based on KAN2.0 attribution scores.

[0030] The factor contribution analysis module is used to train KAN2.0 using a set of high-impact forecast factors and perform factor contribution analysis based on symbolic regression of KAN2.0. The analysis process includes: First, limiting the symbolic function library of the network to linear functions, and obtaining the optimal linear function by performing linear function fitting on the activation function of each edge in the network to replace the original activation function of each edge, thus realizing symbolic regression of the network structure; Second, performing layer-by-layer expression calculation in the network of symbolic regression of the network structure, including summing the input functions of each child node in each layer of the network, linear transformation of child nodes, linear transformation of nodes, and summing the output functions of nodes. Through layer-by-layer expression calculation and propagation to the last layer of the network, the overall linear symbolic output of the network is obtained; Finally, based on the overall linear symbolic output of the network, the linear equation representing the relationship between high-impact forecast factors and TC intensity changes is obtained, and the contribution direction and degree of each high-impact forecast factor to TC intensity changes are quantitatively analyzed according to the sign and absolute value of the linear coefficients in the linear equation.

[0031] The above-mentioned method and apparatus for analyzing the intensity change mechanism of tropical cyclones based on KAN have the following advantages compared with existing technologies:

[0032] 1. The factor recursive pruning algorithm based on KAN2.0 attribution scores is used to screen forecast factors. It can effectively screen out important forecast factors related to TC intensity changes, improve the stability and accuracy of TC intensity change forecasts, and can be generalized to traditional TC intensity change forecast models.

[0033] 2. By using KAN2.0 trained with a set of high-impact forecasting factors to perform factor contribution analysis based on symbolic regression, a complete linear equation from high-impact forecasting factors to TC intensity changes is obtained. Based on the sign and absolute value of each linear coefficient in the equation, the direction and degree of contribution of each high-impact forecasting factor to TC intensity changes are quantitatively analyzed. Thus, the data-driven KAN2.0 model can be used to accurately understand the physical mechanism of TC intensity changes, making the high-impact forecasting factors highly interpretable and reusable, and ultimately achieving high-accuracy and highly interpretable TC intensity forecasts. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating a method for analyzing the intensity variation mechanism of tropical cyclones based on KAN in one embodiment.

[0035] Figure 2 This is a line graph showing the RMSE (Root Mean Square Error) and MAE (Mean Absolute Error) of the KAN2.0 validation set based on factor recursive pruning in one embodiment; where, Figure 2 (a) is a line graph of RMSE. Figure 2 (b) is a line graph of MAE;

[0036] Figure 3 This is a flowchart illustrating the factor contribution analysis steps in one embodiment;

[0037] Figure 4 This is a schematic diagram illustrating the annual test results of KAN2.0 for 24-hour TC intensity forecasts from 1982 to 2020 under both the full forecast factor set and the high-impact forecast factor set in one embodiment; wherein, Figure 4 (a) RMSE of the test results year by year. Figure 4 (b) MAE for annual test results;

[0038] Figure 5 This is a schematic diagram of the attribution scores and linear coefficients of symbolic regression for high-impact forecasting factors with attribution scores greater than 0.1 in one embodiment. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0040] Before providing a further detailed description of the embodiments of this application, the nouns and terms involved in the embodiments of this application will be explained, and the nouns and terms involved in the embodiments of this application shall be interpreted as follows.

[0041] 1. Attribution Score: The attribution score is a quantitative metric used to measure the importance of nodes and edges in KAN 2.0. Its core principle is to iteratively propagate downstream contributions from the output layer, quantifying edge contributions layer by layer and summing them into node contributions, thereby measuring the global importance of input features. For an L-layer KAN, the number of nodes in each layer is... , define the first Layer Nodes The attribution score is ,node The corresponding number Strip edge The attribution score is but:

[0042] ;

[0043] ;

[0044] in, , For the edge The standard deviation of the activation values, For nodes The standard deviation of activation values. Attribution scores, through the logic of iteratively passing from the output layer to the input layer, use the contribution of downstream nodes / edges as the core weight for the importance of upstream nodes / edges. Compared to the traditional L1 norm, attribution scores can overcome the limitations of local information, exclude locally active but globally ineffective nodes / edges, and effectively measure the global importance of input features.

[0045] 2. MAE and RMSE: MAE represents the average absolute error between the predicted and actual values, and RMSE is the square root of MAE. They are expressed as follows:

[0046] ;

[0047] ;

[0048] in, For the observed values, Here, is the predicted value, and N is the total number of samples. The smaller the RMSE and MAE, the closer the predicted value is to the observed value, and the better the prediction effect.

[0049] In one embodiment, such as Figure 1 As shown, a method for analyzing the intensity variation mechanism of tropical cyclones based on KAN is provided, including the following steps:

[0050] Step 1, Factor recursive pruning: The factor recursive pruning algorithm based on KAN2.0 attribution scores is used to screen and obtain the set of high-impact forecast factors for TC intensity change forecast.

[0051] Step 2, Factor Contribution Analysis: KAN2.0 is trained using a set of high-impact forecasting factors, and factor contribution analysis is performed based on symbolic regression of KAN2.0. The analysis process includes: First, the symbolic function library of the network is limited to linear functions, and the optimal linear function is obtained by fitting the activation function of each edge in the network to replace the original activation function of each edge, thus realizing symbolic regression of the network structure; Second, layer-by-layer expression calculation is performed in the network of symbolic regression of the network structure, including the summation of the input functions of each child node in each layer of the network, linear transformation of child nodes, linear transformation of nodes, and summation of the output functions of nodes. Through layer-by-layer expression calculation and propagation to the last layer of the network, the linear symbolic output of the network as a whole is obtained; Finally, based on the linear symbolic output of the network as a whole, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained, and the contribution direction and degree of each high-impact forecasting factor to TC intensity changes are quantitatively analyzed according to the sign and absolute value of the linear coefficients in the linear equation.

[0052] The KAN-based method for analyzing the mechanisms of tropical cyclone intensity changes has two advantages: first, the set of high-impact forecasting factors is selected based on model training performance, ensuring good forecasting results; second, by utilizing attribution scores and symbolic regression in KAN2.0, the impact of different high-impact forecasting factors on forecast results can be quantitatively analyzed, enabling a data-driven model to understand the physical mechanisms. This method can effectively improve the stability, accuracy, generalization ability, and interpretability of TC intensity forecasts.

[0053] A factor recursive pruning algorithm based on KAN2.0 attribution scores was used to screen and obtain a set of high-impact forecasting factors for TC intensity change forecasts, including:

[0054] Initialize the full forecast factor set for TC intensity change forecast and divide it into training set, validation set and independent test set;

[0055] The training and validation sets are input into KAN2.0 for iterative training to obtain the attribution score and root mean square error of the validation set output by KAN2.0. The attribution score is used to quantify the global contribution of each forecast factor to the change in TC intensity. The global contribution includes linear and nonlinear contributions.

[0056] The bottom 10% of forecast factors ranked by attribution score are pruned and removed to form a new set of forecast factors. This new set of forecast factors is then re-entered into KAN2.0 to perform the forecast factor pruning and removal operation until the number of forecast factors is less than a set value. Based on the ranking of the root mean square error of the validation set output by KAN2.0 in each round, the set of forecast factors with the lowest root mean square error of the validation set is selected as the high-impact forecast factor set.

[0057] In one embodiment, a factor recursive pruning algorithm based on KAN2.0 attribution scores is used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts, including:

[0058] Initialize the full forecast factor set for TC intensity change forecast and divide it into training set, validation set and independent test set;

[0059] The training and validation sets are input into KAN2.0 for iterative training to obtain the attribution score and root mean square error of the validation set output by KAN2.0. The attribution score is used to quantify the global contribution of each forecast factor to the change in TC intensity. The global contribution includes linear and nonlinear contributions.

[0060] The bottom 10% of forecast factors ranked by attribution score are pruned and removed to form a new set of forecast factors. This new set of forecast factors is then re-entered into KAN2.0 to perform the forecast factor pruning and removal operation until the number of forecast factors is less than the set value (10). Based on the ranking of the root mean square error of the validation set output by KAN2.0 in each round, the set of forecast factors with the lowest root mean square error of the validation set is selected as the high-impact forecast factor set.

[0061] In one embodiment, initializing the full forecast factor set for TC intensity change forecasts includes:

[0062] By acquiring the initial forecast factor set (including 121 forecast factors) and the time-series forecast factor set reflecting the temporal characteristics of TC intensity changes from SHIPS data, a full forecast factor set for TC intensity change forecasts is formed. The full forecast factor set is then preprocessed, including filling in default values ​​and standardization. Compared with the initial forecast factor set, the time-series forecast factor set is supplemented with 8 additional time-series forecast factors, namely the sea level pressure changes over the past 6h, 12h, 18h, and 24h (DPRE-6, DPRE-12, DPRE-18, DPRE-24), the TC intensity changes over the past 6h, 12h, and 18h ​​(DELV-6, DELV-12, DELV-18), and the TC life history label (Life). The TC life history label is used to sequentially number each moment in the TC life history. For example, the TC inception moment is recorded as 1, the next moment (6h later) is recorded as 2, and so on, with the extinction moment recorded as n.

[0063] Specifically, for the default value, the characteristic average value of the intensity level of the TC in the sample is used to fill it; the maximum wind speed of TC for 1 minute and 10m is used to characterize the intensity of TC, and the forecast quantity is the change in TC intensity in the next 24 hours (dvs24), that is, the difference between the intensity of TC in the next 24 hours and the intensity at the current moment; the full forecast factor set from 1982 to 2018 is used as the training set, the full forecast factor set from 2019 to 2020 is used as the validation set, and the full forecast factor set from 2021 to 2022 is used as the independent test set.

[0064] Figure 2 Line plots of RMSE and MAE for the KAN2.0 validation set after recursive pruning of 129 full forecast factor sets are presented. Figure 2It can be seen that KAN2.0 has the best forecast performance for dvs24 when the number of forecast factors is 87, with a validation set RMSE of 10.79kt and MAE of 7.86kt. Therefore, these 87 factors are the high-impact forecast factor set for dvs24, including: vs0, TWXC_t24, DTL_t24, VMPI_t24, SHGC_t24, TLAT_t24, DELV-6, V500_t24, TWAC_t24, MTPW_v2, IR00_v16, MTPW_v10, CD26_t24, DELV-12, T250_t24, Z850_t24, IR00_v6, CD20_t24, V000_t24, and DELV-24. life, V20C_t24, MTPW_v4, SHDC_t24, PSLV_v6, RHHI_t24, PSLV_v5, IR00_v20, IR00_v13, TLON_t24, HE07_t24, G250_t 24. MTPW_v3, PENV_t24, U200_t24, VVAC_t24, V300_t24, E000_t24, IR00_v11, PSLV_v10, RHMD_t24, ENEG_t24, RHLO_t 24. SHTD_t24, HE05_t24, IR00_v2, EPOS_t24, T150_t24, V850_t24, PSLV_v4, D200_t24, T200_t24, G200_t24, COHC_t2 4. PSLV_v17, TADV_t24, IR00_v7, MTPW_v5, RSST_t24, SHTS_t24, PSLV_v18, PSLV_v3, SHRS_t24, DELV-18, VVAV_t24, I R00_v14, SHRD_t24, U20C_t24, CFLX_t24, G150_t24, IR00_v18, PSLV_v12, PSLV_v19, IR00_v5, O500_t24, PSLV_v14, R EFC_t24, MTPW_v19, PSLV_v16, O700_t24, CSST_t24, TGRD_t24, PSLV_v11, PSLV_v15, EPSS_t24, MTPW_v11, IR00_v17.

[0065] In one embodiment, KAN2.0 is trained using a set of high-impact forecast factors, including:

[0066] KAN2.0 was trained using a set of high-impact forecasting factors. The TPE Bayesian optimization algorithm was employed during training to optimize the network hyperparameters. The optimized KAN2.0 was then used for year-by-year testing of TC intensity change forecasts, and the root mean square error (RMSE) and mean absolute error (MAE) were used to evaluate forecast stability. TPE is a tree-based Bayesian optimization algorithm used to solve the global optimization problem of black-box functions.

[0067] Specifically, the optimized KAN2.0 in this application has 1 hidden layer, 10 nodes, an optimizer named "Adam", a learning rate of 0.05, a regularization coefficient of 0.2, an L1 regularization coefficient of 1, an entropy regularization coefficient of 10, 1500 training steps, and no early stopping.

[0068] In one embodiment, such as Figure 3 As shown, to analyze the impact of various high-impact forecasting factors on TC intensity changes, this application designed a factor contribution analysis step based on KAN2.0 symbolic regression. The core of this step is to transform the KAN2.0 network structure, which possesses high fitting performance, into an explicit mathematical symbolic expression, thereby quantitatively analyzing the degree and direction of contribution of each high-impact forecasting factor to dvs24. Specifically, this includes the following steps:

[0069] After training KAN2.0 using a set of high-impact forecasting factors (referred to as the high-impact factor set), firstly, to facilitate the analysis of the contributions of the forecasting factors, the symbolic function library (lib) of KAN2.0 is limited to linear functions. For each edge in the KAN2.0 network, the pre-activation value of the activation function for each edge is obtained based on data samples. and post-activation value And search for the optimal linear parameters within the preset parameter range to adjust the pre-activation value. Activation value The mapping relationship is best fitted, and finally the optimal linear function is obtained. To replace the original activation function of each edge, symbolic regression of the network structure is achieved; where the optimal linear parameters include the optimal linear coefficients ( ) and optimal intercept ( ).

[0070] Secondly, in each layer of the KAN2.0 network with symbolic regression, all input functions passed to the same child node of the current layer are summed to obtain the preliminary output function of each child node in the current layer. Scaling and bias adjustments at the child node level are applied to the preliminary output functions of each child node in the current layer to complete the linear transformation of the child nodes, resulting in the preliminary output function of each node in the current layer. Node-level scaling and bias adjustments are applied to the preliminary output functions of each node in the current layer to complete the linear transformation of the nodes, resulting in the final output function of each node in the current layer. The final output functions of each node in the current layer are summed to obtain the input function of the next layer. This layer-by-layer expression is calculated and propagated to the last layer of the KAN2.0 network to obtain the overall linear symbolic output of the KAN2.0 network. Here, the input function, preliminary output function, and final output function are all linear functions. .

[0071] Then, based on the overall linear symbolic output of the KAN2.0 network, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained, expressed as follows: ;in, This represents the change in TC intensity. Indicates the first One high-impact forecasting factor, Indicates the first The linear coefficients corresponding to the high-impact forecasting factors The intercept is... , This represents the number of high-impact forecasting factors.

[0072] Finally, based on the sign and absolute value of each linear coefficient, the contribution direction and degree of each high-impact forecasting factor to the change in TC intensity are quantitatively analyzed. The sign of the linear coefficient indicates the direction of contribution of the high-impact forecasting factor to the change in TC intensity. When the linear coefficient is positive and the corresponding high-impact forecasting factor is positive / negative, it indicates that the corresponding high-impact forecasting factor has a positive / negative contribution to the change in TC intensity, which is conducive to the enhancement / weakening of TC intensity. When the linear coefficient is negative and the corresponding high-impact forecasting factor is positive / negative, it indicates that the corresponding high-impact forecasting factor has a negative / positive contribution to the change in TC intensity, which is conducive to the weakening / enhancing of TC intensity. The absolute value of the linear coefficient indicates the degree of contribution of the high-impact forecasting factor to the change in TC intensity; the larger the absolute value of the linear coefficient, the greater the contribution of the corresponding high-impact forecasting factor to the change in TC intensity. Furthermore, if it is assumed that only a single high-impact forecasting factor affects the change in TC intensity, the threshold at which this high-impact forecasting factor will cause the TC to strengthen or weaken in the future can be estimated by combining the linear intercept.

[0073] In one embodiment, the types of high-impact forecasting factors include climate and persistence factors, kinetic factors, and thermodynamic factors. Climate and persistence factors reflect the historical evolution characteristics, climate background, and persistence status of the TC, primarily including the current TC intensity (vs0), the distance of the TC from land (DTL_t24), the latitude of the 850 hPa vortex center (TLAT_t24), TC intensity variations (DELV-6, DELV-12, DELV-24), the TC lifespan marker (Life), and the zonal movement speed of the TC (PSLV_v6). Kinetic factors reflect the dynamic characteristics of the large-scale environmental field in which the TC is located, primarily including the environmental tangential wind (V50). The thermodynamic factors used to reflect the energy supply conditions for TC development mainly include the maximum potential intensity of TC (VMPI_t24), total precipitable water (MTPW_v2, MTPW_v10, MTPW_v4), brightness temperature (IR00_v16, IR00_v6), ocean heat content (CD26_t24, CD20_t24), and 250 hPa air temperature (T250_t24).

[0074] In one embodiment, after quantitatively analyzing the direction and degree of contribution of each high-impact forecasting factor to the change in TC intensity, the above method further includes:

[0075] A set of high-impact forecasting factors that reflect the direction and degree of contribution to TC intensity changes will be transferred to the training of the existing TC intensity change forecasting model until convergence is achieved, allowing the model to perform TC intensity change forecasting tasks. The existing TC intensity change forecasting model is an MLP (Multilayer Perceptron) model. During training, the hyperparameters of the MLP model are set as follows: 5 hidden layers with 128, 256, 128, 256, and 256 nodes per layer, respectively; the optimizer is "Adam"; adaptive learning rate; activation function is "ReLU"; L2 regularization coefficient is 0.0005; maximum number of iterations is 200; and there is no early stopping.

[0076] To verify the beneficial effects of the method proposed in this application, the following experiments were also conducted, as detailed below:

[0077] The forecast stability of KAN2.0 from 1982 to 2020 was analyzed using the Leave-One-Year-Out (LOYO) method. Figure 4The annual test results of KAN2.0 for 24-hour TC intensity forecasts from 1982 to 2020 are presented under the full forecast factor set (129) and the high-impact forecast factor set (87). Figure 4 The red line represents KAN-129, the blue line represents KAN-87, and the unmarked years indicate that the model's forecasts did not converge. Analysis Figure 4 It can be seen that KAN-129 exhibits poor forecast stability, with convergence occurring in six years (1988, 1990, 1993, 1994, 1995, and 2007). The average RMSE for years with convergence is 11.56kt, and the average MAE is 8.56kt. KAN-87, on the other hand, shows significantly improved forecast stability, with no years exhibiting convergence. It demonstrates good forecasting ability and accuracy in year-by-year testing, with an average RMSE of 11.45kt and an MAE of 8.42kt. Therefore, using a recursive pruning method to select the high-impact forecasting factor set can effectively improve the model's forecast stability and accuracy.

[0078] To evaluate the generalization ability of the models, the independent test results of KAN-129 and KAN-87 for dvs24 were compared. Table 1 shows the forecast errors of KAN-129, KAN-87, MLP-129, MLP-87, and the official operational forecasts and various deep learning models for the 24-hour TC intensity change forecast. As shown in Table 1, KAN-129 has an RMSE of 11.20kt and a MAE of 8.11kt, while KAN-87 has an RMSE of 10.90kt and a MAE of 7.87kt. Compared with the best official operational forecast (JTWC) and the best single deep learning model (MLP-87), KAN-87's MAE is reduced by approximately 4.6% and 5.7%, respectively. This demonstrates that KAN2.0 has strong generalization ability, and the high-impact factor set after recursive pruning effectively improves the forecast accuracy of KAN2.0 for dvs24. However, its forecasting performance is slightly lower than that of the current best hybrid models TC-Pred (ConvGRU) and Deep-TCP (ConvGPU).

[0079] Table 1. Comparison of errors between official forecasts and deep learning models for 24-hour TC intensity forecasts (Unit: kt; Model suffix "-87" represents the high-impact forecast factor set, and "-129" represents the full forecast factor set.)

[0080]

[0081] It is worth noting that comparing the independent test results of MLP-129 and MLP-87, the RMSE of MLP-87 was 11.73kt and the MAE was 8.35kt. Compared with MLP-129, the RMSE and MAE decreased by about 8% and 7%, respectively. This shows that the high-impact forecasting factor set screened by KAN2.0 can not only improve the forecasting accuracy of KAN2.0, but also improve the forecasting accuracy of MLP. This indicates that the factor recursive pruning algorithm based on attribution scores can effectively screen out important forecasting factors related to TC intensity changes and can be applied to other intelligent models for TC intensity forecasting.

[0082] Regarding model interpretability, the focus is on analyzing the contribution of 25 high-impact forecasting factors with attribution scores greater than 0.1 to dvs24. Figure 5 This is a schematic diagram showing the attribution scores and linear coefficients of the symbolic regression for 25 high-impact forecasting factors with attribution scores greater than 0.1. The linear intercept is 4.67, and the factors are sorted from highest to lowest attribution score. Figure 5 In the horizontal axis, green represents climate and persistence factors, orange represents thermodynamic factors, and blue represents kinetic factors; Figure 5 Only values ​​with an attribution score greater than 0.1 or an absolute value of a linear coefficient greater than 1 are indicated.

[0083] Depend on Figure 5 It can be seen that for climate and persistence factors, vs0, Life, TLAT_t24, and PSLV_v6 all show negative contributions. Among them, vs0 has the largest negative contribution to dvs24, that is, the larger the vs0, the more favorable it is for TC weakening, which is consistent with the characteristics of TC intensity change. Life has the second largest impact on dvs24, meaning that the later the TC life cycle stage, the less favorable it is for TC enhancement. TLAT_t24 has a negative impact on dvs24, that is, the higher the TC latitude, the less favorable it is for TC intensity enhancement. PSLV_v6 also shows a negative contribution, that is, the greater the zonal movement speed of TC, the less favorable it is for TC intensity enhancement. Relatively speaking, DELV-6, DTL_t24, DELV-12, and DELV-24 show positive contributions. Among them, the impact of the past 6-hour TC intensity change (DELV-6) is the most important. That is, when the past TC intensity is enhanced, it is more favorable for the TC enhancement in the next 24 hours; and when the past TC intensity is weakened, it is more favorable for the TC weakening in the next 24 hours. DTL_t24 has the second largest positive contribution to dvs24, meaning that the farther the TC is from the land, the more beneficial it is to the enhancement of TC strength.

[0084] Regarding the dynamic factors, the maximum symmetrical tangential wind at 850 hPa in the next 24 hours (TWXC_t24) and the tangential wind at an average of 1000 hPa 500 km from the TC center (V000_t24) both contribute positively to dvs24. Among them, TWXC_t24 has the greatest impact on dvs24, showing that the larger TWXC_t24 is, the more favorable it is for TC intensification. The positive contribution of V000_t24 to dvs24 is relatively small. On the other hand, the vertical wind shear at 850–200 hPa in the next 24 hours (SHGC_t24 and SHDC_t24), the tangential wind at an average of 500 hPa 500 km from the TC center (V500_t24), and the symmetrical tangential wind at an average of 850 hPa 0–600 km from the TC center (TWAC_t24) all contribute negatively to dvs24. Among them, SHGC_t24 and SHDC_t24 have the largest negative contributions to dvs24, meaning that the stronger the vertical wind shear, the more favorable it is for TC to weaken. This is consistent with the influence mechanism of environmental wind vertical shear on TC intensity, that is, when the vertical shear of the horizontal wind is large, the resulting "ventilation effect" will lead to heat loss from the upper layers of the TC, thereby inhibiting the development of the TC. The negative contributions of V500_t24 and TWAC_t24 are relatively small. In addition, the influence of the 200hPa meridional wind (V20C_t24) on dvs24 in the next 24 hours should be distinguished between northerly and southerly winds. When the upper-level wind is northerly (V20C_t24<0), it will carry a large amount of dry and cold air into the TC. The stronger the northerly wind, the less favorable it is for the TC to strengthen. When the upper-level wind is southerly (V20C_t24>0), the southerly wind will carry a large amount of warm and humid air into the TC. The stronger the southerly wind, the more favorable it is for the TC to strengthen.

[0085] For thermodynamic factors, VMPI_t24, total precipitable water (MTPW_v10) at a distance of 800–1000 km from the TC center, the depth of the ocean 26°C isotherm (CD26_t24), and the depth of the ocean 20°C isotherm (CD20_t24) all contribute positively to dvs24. VMPI_t24 has the greatest impact on TC intensity variation; a larger VMPI_t24 favors 24-hour TC enhancement. MTPW_v10 has the second largest positive contribution to dvs24. The total precipitable water in this region reflects the humidity conditions of the large-scale environmental field; a wetter large-scale environmental field is more conducive to TC enhancement. Ocean heat content has a significant impact on dvs24. CD26_t24 and CD20_t24 both contribute positively to dvs24; that is, the deeper CD26_t24 and CD20_t24 are, the higher the ocean heat content, which is more conducive to TC enhancement. The factors that negatively contribute to dvs24, in descending order of contribution, are: the standard deviation of brightness temperature at a distance of 100-300 km from the TC center (IR00_v6), the total precipitable water at a distance of 0-200 km from the TC center (MTPW_v2), the minimum brightness temperature at a distance of 20-120 km from the TC center (IR00_v16), the atmospheric temperature at 250 hPa at a distance of 200-800 km from the TC center (T250_t24), and the total precipitable water at a distance of 200-400 km from the TC center (MTPW_v4). Specifically: the larger IR00_v6 is, the greater the asymmetry in the spatial distribution of brightness temperature near the TC eyewall, leading to the outward loss of upper-level potential vorticity and equivalent potential temperature, ultimately resulting in the loss of the TC warm core and a weakening of TC intensity. The higher IR00_v16 and T250_t24 are, the higher the TC outflow layer temperature, which is more unfavorable for TC enhancement. This aligns with the Carnot engine principle, which states that the greater the temperature difference between the ocean surface and the outflow layer, the higher the efficiency of the Carnot engine, leading to a greater increase in total temperature (TC).

[0086] In summary, the KAN-based tropical cyclone intensity change mechanism analysis method proposed in this application can quantitatively analyze the impact of different types of high-impact forecast factors on TC intensity changes. Furthermore, the impact mechanism obtained based on symbolic formula analysis is basically consistent with existing physical understanding. This demonstrates that this method can effectively understand complex physical laws using data-driven models and has strong interpretability.

[0087] It is worth noting that the ranking of forecast factors by attribution scores is not entirely consistent with the ranking of the absolute values ​​of their linear coefficients in symbolic regression. Most factors with high attribution scores have large absolute values ​​of their linear coefficients, while some factors with low attribution scores still have large absolute values ​​of their linear coefficients (e.g., Life, SHDC_t24), or factors with high attribution scores have small absolute values ​​of their linear coefficients (e.g., TLAT_t24, V500_t24, TWAC_t24). This is mainly because attribution scores measure the global importance of a factor to the forecast result, including both linear and nonlinear contributions. However, the linear coefficients obtained from the linear symbolic output only reflect the linear contribution of a factor to the forecast result, and therefore are not entirely consistent with the attribution scores.

[0088] In one embodiment, a KAN-based tropical cyclone intensity change mechanism analysis device is provided, comprising:

[0089] The factor recursive pruning module is used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts using a factor recursive pruning algorithm based on KAN2.0 attribution scores.

[0090] The factor contribution analysis module is used to train KAN2.0 using a set of high-impact forecast factors and perform factor contribution analysis based on symbolic regression of KAN2.0. The analysis process includes: First, limiting the symbolic function library of the network to linear functions, and obtaining the optimal linear function by performing linear function fitting on the activation function of each edge in the network to replace the original activation function of each edge, thus realizing symbolic regression of the network structure; Second, performing layer-by-layer expression calculation in the network of symbolic regression of the network structure, including summing the input functions of each child node in each layer of the network, linear transformation of child nodes, linear transformation of nodes, and summing the output functions of nodes. Through layer-by-layer expression calculation and propagation to the last layer of the network, the overall linear symbolic output of the network is obtained; Finally, based on the overall linear symbolic output of the network, the linear equation representing the relationship between high-impact forecast factors and TC intensity changes is obtained, and the contribution direction and degree of each high-impact forecast factor to TC intensity changes are quantitatively analyzed according to the sign and absolute value of the linear coefficients in the linear equation.

[0091] Specific limitations regarding the KAN-based tropical cyclone intensity change mechanism analysis device can be found in the limitations of the KAN-based tropical cyclone intensity change mechanism analysis method above, and will not be repeated here. Each module in the aforementioned KAN-based tropical cyclone intensity change mechanism analysis device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0092] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0093] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application.

Claims

1. A method for analyzing the intensity variation mechanism of tropical cyclones based on KAN, characterized in that, The method includes: A factor recursive pruning algorithm based on KAN2.0 attribution scores was used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts; KAN2.0 was trained using the aforementioned high-impact forecast factor set, and factor contribution analysis was performed based on the symbolic regression of KAN2.

0. The analysis process included: First, the symbolic function library of the network is limited to linear functions. Then, by performing linear function fitting on the activation function of each edge in the network, the optimal linear function is obtained to replace the original activation function of each edge, achieving symbolic regression of the network structure. Second, layer-by-layer expression calculation is performed in the symbolic regression network, including summation of the input functions of each sub-node, linear transformation of the sub-node, linear transformation of the node, and summation of the output functions of the node at each layer. This layer-by-layer expression calculation is propagated to the last layer of the network to obtain a linear equation relating high-impact forecasting factors to TC intensity changes. Based on the sign and absolute value of the linear coefficients in the linear equation, the contribution direction and degree of each high-impact forecasting factor to TC intensity changes are quantitatively analyzed. Among them, a factor recursive pruning algorithm based on KAN2.0 attribution scores was used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts, including: Initialize the full forecast factor set for TC intensity change forecast and divide it into training set, validation set and independent test set; The training set and validation set are input into KAN2.0 for iterative training to obtain the attribution score and root mean square error of the validation set output by KAN2.0; wherein, the attribution score is used to quantify the global contribution of each forecast factor to the change in TC intensity, and the global contribution includes linear contribution and nonlinear contribution. The bottom 10% of forecast factors ranked by attribution score are pruned and removed to form a new set of forecast factors. This new set of forecast factors is then re-entered into KAN2.0 to perform the forecast factor pruning and removal operation until the number of forecast factors is less than a set value. Based on the ranking of the root mean square error of the validation set output by KAN2.0 in each round, the set of forecast factors with the lowest root mean square error of the validation set is selected as the high-impact forecast factor set.

2. The method for analyzing the intensity variation mechanism of tropical cyclones based on KAN according to claim 1, characterized in that, The initialization of the full forecast factor set for TC intensity change forecast includes: The initial forecast factor set and the time-series forecast factor set reflecting the temporal characteristics of TC intensity changes are obtained from SHIPS data. These are combined to form a full forecast factor set for TC intensity change forecasts. The full forecast factor set is then preprocessed, including filling in default values ​​and standardization. The time-series forecast factor set is supplemented with eight time-series forecast factors, namely, sea level pressure changes over the past 6h, 12h, 18h, and 24h, TC intensity changes over the past 6h, 12h, and 18h, and TC life history tags. The TC life history tags are used to sequentially number each moment in the TC life history.

3. The method for analyzing the intensity variation mechanism of tropical cyclones based on KAN according to claim 1, characterized in that, Training KAN2.0 using the aforementioned high-impact forecast factor set includes: KAN2.0 was trained using the high-impact forecast factor set. The TPE Bayesian optimization algorithm was used to optimize the network hyperparameters during the training process. The optimized KAN2.0 was then tested annually for TC intensity change forecasts, and the root mean square error and mean absolute error were used to evaluate the forecast stability.

4. The method for analyzing the intensity variation mechanism of tropical cyclones based on KAN according to claim 1, characterized in that, By performing linear function fitting on the activation function of each edge in the network, the optimal linear function is obtained and replaced with the original activation function of each edge, thus achieving symbolic regression of the network structure, including: For each edge in the KAN2.0 network, the pre-activation value of the activation function for each edge is obtained based on the data samples. and post-activation value And search for the optimal linear parameters within the preset parameter range to adjust the pre-activation value. Activation value The mapping relationship is fitted to the optimal value, and the optimal linear function is finally obtained to replace the original activation function of each edge, so as to realize the symbolic regression of the network structure; wherein, the optimal linear parameters include the optimal linear coefficient and the optimal intercept.

5. The method for analyzing the intensity variation mechanism of tropical cyclones based on KAN according to claim 4, characterized in that, In a network structured symbolic regression, layer-by-layer expression computation is performed, including the summation of input functions of child nodes at each layer, linear transformation of child nodes, linear transformation of nodes, and summation of output functions of nodes. This layer-by-layer expression computation is then propagated to the last layer of the network to obtain the overall linear symbolic output of the network, including: In each layer of the KAN2.0 network with symbolic regression, all input functions passed to the same child node of the current layer are summed to obtain the preliminary output function of each child node in the current layer. Scaling and bias adjustments at the child node level are applied to the preliminary output functions of each child node in the current layer to complete the linear transformation of the child nodes, resulting in the preliminary output function of each node in the current layer. Node-level scaling and bias adjustments are applied to the preliminary output functions of each node in the current layer to complete the linear transformation of the nodes, resulting in the final output function of each node in the current layer. The final output functions of each node in the current layer are summed to obtain the input function of the next layer. The linear symbolic output of the KAN2.0 network is obtained by calculating and propagating the expression layer by layer to the last layer. Here, the input function, preliminary output function, and final output function are all linear functions.

6. The method for analyzing the intensity variation mechanism of tropical cyclones based on KAN according to claim 5, characterized in that, Based on the overall linear symbolic output of the network, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained. Then, based on the sign and absolute value of the linear coefficients in the linear equation, the contribution direction and degree of each high-impact forecasting factor to TC intensity changes are quantitatively analyzed, including: Based on the overall linear symbolic output of the KAN2.0 network, a linear equation representing the relationship between high-impact forecasting factors and TC intensity changes is obtained, expressed as follows: ;in, This represents the change in TC intensity. Indicates the first One high-impact forecasting factor, Indicates the first The linear coefficients corresponding to the high-impact forecasting factors The intercept is... , The number of high-impact forecasting factors; Based on the sign and absolute value of each linear coefficient, the contribution direction and degree of each high-impact forecasting factor to the change in TC intensity are quantitatively analyzed. The sign of the linear coefficient indicates the direction of contribution of the high-impact forecasting factor to the change in TC intensity. When the linear coefficient is positive and the corresponding high-impact forecasting factor is positive / negative, it indicates that the corresponding high-impact forecasting factor has a positive / negative contribution to the change in TC intensity, which is conducive to the enhancement / weakening of TC intensity. When the linear coefficient is negative and the corresponding high-impact forecasting factor is positive / negative, it indicates that the corresponding high-impact forecasting factor has a negative / positive contribution to the change in TC intensity, which is conducive to the weakening / enhancing of TC intensity. The absolute value of the linear coefficient indicates the degree of contribution of the high-impact forecasting factor to the change in TC intensity. The larger the absolute value of the linear coefficient, the greater the contribution of the corresponding high-impact forecasting factor to the change in TC intensity.

7. The method for analyzing the mechanism of tropical cyclone intensity change based on KAN according to claim 1 or 6, characterized in that, The high-impact forecasting factors are classified into climate and persistence factors, kinetic factors, and thermodynamic factors. Among them, the climate and persistence factors are used to reflect the historical evolution characteristics, climate background, and persistence status of the TC; the kinetic factors are used to reflect the kinetic characteristics of the large-scale environmental field in which the TC is located; and the thermodynamic factors are used to reflect the energy supply conditions for the development of the TC.

8. The method for analyzing the mechanism of tropical cyclone intensity change based on KAN according to claim 1 or 6, characterized in that, After quantitatively analyzing the contribution direction and degree of each high-impact forecasting factor to the change in TC intensity, the method further includes: A set of high-impact forecasting factors that can reflect the direction and degree of contribution to TC intensity changes will be transferred to the training of an existing TC intensity change forecasting model until convergence is achieved to obtain a well-trained TC intensity change forecasting model for TC intensity change forecasting tasks; wherein, the existing TC intensity change forecasting model is an MLP model.

9. A device for analyzing the mechanism of tropical cyclone intensity change based on KAN, characterized in that, The device includes: The factor recursive pruning module is used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts using a factor recursive pruning algorithm based on KAN2.0 attribution scores. The factor contribution analysis module is used to train KAN2.0 using the high-impact forecast factor set and perform factor contribution analysis based on the symbolic regression of KAN2.

0. The analysis process includes: first, limiting the symbolic function library of the network to linear functions, and obtaining the optimal linear function by performing linear function fitting on the activation function of each edge in the network to replace the original activation function of each edge, thus realizing the symbolic regression of the network structure; second, performing layer-by-layer expression calculation in the network of symbolic regression of the network structure, including the summation of the input functions of each child node in each layer of the network, linear transformation of child nodes, linear transformation of nodes, and summation of the output functions of nodes. Through layer-by-layer expression calculation and propagation to the last layer of the network, the linear symbolic output of the network as a whole is obtained; finally, based on the linear symbolic output of the network as a whole, the linear equation representing the relationship between high-impact forecast factors and TC intensity changes is obtained, and the contribution direction and degree of each high-impact forecast factor to TC intensity changes are quantitatively analyzed according to the sign and absolute value of the linear coefficients in the linear equation. Among them, a factor recursive pruning algorithm based on KAN2.0 attribution scores was used to screen and obtain a set of high-impact forecast factors for TC intensity change forecasts, including: Initialize the full forecast factor set for TC intensity change forecast and divide it into training set, validation set and independent test set; The training set and validation set are input into KAN2.0 for iterative training to obtain the attribution score and root mean square error of the validation set output by KAN2.0; wherein, the attribution score is used to quantify the global contribution of each forecast factor to the change in TC intensity, and the global contribution includes linear contribution and nonlinear contribution. The bottom 10% of forecast factors ranked by attribution score are pruned and removed to form a new set of forecast factors. This new set of forecast factors is then re-entered into KAN2.0 to perform the forecast factor pruning and removal operation until the number of forecast factors is less than a set value. Based on the ranking of the root mean square error of the validation set output by KAN2.0 in each round, the set of forecast factors with the lowest root mean square error of the validation set is selected as the high-impact forecast factor set.

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