Adaptive prediction of IMQ-RBF interpolation variable shape parameters using an SSA-MLP-RF hybrid model

Junbo Yang; Ling Wang; Dianxuan Gong; Junbo Yang; Ling Wang; Dianxuan Gong

doi:10.3934/era.2025316

Electronic Research Archive

2025, Volume 33, Issue 11: 7146-7171. doi: 10.3934/era.2025316

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Research article

Adaptive prediction of IMQ-RBF interpolation variable shape parameters using an SSA-MLP-RF hybrid model

College of Sciences, North China University of Science and Technology, Tangshan 063210, China

Received: 11 October 2025 Revised: 08 November 2025 Accepted: 14 November 2025 Published: 24 November 2025

The shape parameter is crucial for radial basis functions (RBF) interpolation accuracy. Fixed global parameters often fail with complex data, whereas variable shape parameters improve flexibility by adjusting each basis function dynamically. To address the issue that variable shape parameter selection in the inverse multiple quadratic radial basis function (IMQ-RBF) interpolation is influenced by multiple factors, we proposed a hybrid prediction model based on the sparrow search algorithm (SSA) combining a multilayer perceptron and random forest (SSA-MLP-RF), which maps local geometric features of data points to the corresponding shape parameters. First, a dataset was constructed from scattered points, including the shape parameter values and 17 local features, to accumulate influencing factors. Subsequently, outlier removal, variance inflation factor analysis, XGBoost feature average gain, and mutual information methods were applied to perform feature selection, identifying seven key features. Finally, SSA was employed to optimize the hyperparameters of the MLP and RF, and a weighted combination model was constructed to achieve adaptive selection of shape parameters. Based on the test set results, the ablation experiments verified that the proposed SSA-MLP-RF hybrid model achieved significant performance improvement. Compared with several classical metaheuristic algorithms (particle swarm optimizatio, genetic algorithm, whale optimization algorithm, and blood-sucking leech optimizer), the SSA-MLP-RF model demonstrated the best predictive accuracy for the deformation shape parameter, achieving an R² of 0.9203, with MAE, RMSE, MAPE, and NMSE values of 0.0391, 0.0499, 3.8201%, and 0.0797, respectively, and a Rényi entropy of 0.1200. The findings validated the effectiveness and rationality of the proposed model, providing a reliable approach for the adaptive selection of shape parameters in RBF interpolation.
- inverse multiple quadratic radial basis function,
- shape parameters,
- sparrow search algorithm,
- multilayer perceptron,
- random forest,
- hybrid prediction model
Citation: Junbo Yang, Ling Wang, Dianxuan Gong. Adaptive prediction of IMQ-RBF interpolation variable shape parameters using an SSA-MLP-RF hybrid model[J]. Electronic Research Archive, 2025, 33(11): 7146-7171. doi: 10.3934/era.2025316

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Abstract

The shape parameter is crucial for radial basis functions (RBF) interpolation accuracy. Fixed global parameters often fail with complex data, whereas variable shape parameters improve flexibility by adjusting each basis function dynamically. To address the issue that variable shape parameter selection in the inverse multiple quadratic radial basis function (IMQ-RBF) interpolation is influenced by multiple factors, we proposed a hybrid prediction model based on the sparrow search algorithm (SSA) combining a multilayer perceptron and random forest (SSA-MLP-RF), which maps local geometric features of data points to the corresponding shape parameters. First, a dataset was constructed from scattered points, including the shape parameter values and 17 local features, to accumulate influencing factors. Subsequently, outlier removal, variance inflation factor analysis, XGBoost feature average gain, and mutual information methods were applied to perform feature selection, identifying seven key features. Finally, SSA was employed to optimize the hyperparameters of the MLP and RF, and a weighted combination model was constructed to achieve adaptive selection of shape parameters. Based on the test set results, the ablation experiments verified that the proposed SSA-MLP-RF hybrid model achieved significant performance improvement. Compared with several classical metaheuristic algorithms (particle swarm optimizatio, genetic algorithm, whale optimization algorithm, and blood-sucking leech optimizer), the SSA-MLP-RF model demonstrated the best predictive accuracy for the deformation shape parameter, achieving an R² of 0.9203, with MAE, RMSE, MAPE, and NMSE values of 0.0391, 0.0499, 3.8201%, and 0.0797, respectively, and a Rényi entropy of 0.1200. The findings validated the effectiveness and rationality of the proposed model, providing a reliable approach for the adaptive selection of shape parameters in RBF interpolation.

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