Design and Comparison of Parallel Dynamic Matérn Kernel-Based Regression Models and Machine Learning Approaches: Application to Bias Correction in Numerical Weather Prediction

doi:10.1007/s42967-025-00490-6

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (3): 1115-1156.doi: 10.1007/s42967-025-00490-6

Design and Comparison of Parallel Dynamic Matérn Kernel-Based Regression Models and Machine Learning Approaches: Application to Bias Correction in Numerical Weather Prediction

Violeta Migallón, Héctor Penadés, José Penadés

Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, 03690, Alicante, Spain

收稿日期:2024-09-09 修回日期:2025-02-20 出版日期:2026-06-20 发布日期:2026-05-29
通讯作者: José Penadés, Email: jpenades@ua.es E-mail:jpenades@ua.es
基金资助:
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research was partially funded by MCIN/AEI/10.13039/501100011033, Grant PID2021-123627OB-C55, by “ERDF A way of making Europe”, and by ValgrAI—Valencian Graduate School and Research Network for Artificial Intelligence and Generalitat Valenciana.

Design and Comparison of Parallel Dynamic Matérn Kernel-Based Regression Models and Machine Learning Approaches: Application to Bias Correction in Numerical Weather Prediction

Violeta Migallón, Héctor Penadés, José Penadés

Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, 03690, Alicante, Spain

Received:2024-09-09 Revised:2025-02-20 Online:2026-06-20 Published:2026-05-29
Contact: José Penadés, Email: jpenades@ua.es E-mail:jpenades@ua.es
Supported by:
Qingxin Meng was supported by the Key Projects of the Natural Science Foundation of Zhejiang Province of China (No. Z22A013952) and the National Natural Science Foundation of China (Nos.12271158 and 11871121). Maoning Tang was supported by the Natural Science Foundation of Zhejiang Province of China (No. LY21A010001).

摘要/Abstract

摘要： Mathematical modelling is fundamental to understanding real-world phenomena. Despite the inherent complexity in designing such models, numerical approaches and, more recently, machine learning techniques, have emerged as powerful tools in this area. This work proposes integrating the finite element method (FEM) into forecasting and introduces parallel techniques for regression problems, with a specific focus on the use of Matérn kernels on local mesh support. This approach generalises the modelling based on radial basis function kernels and offers more flexibility to control the smoothness of the modelled functions. An exhaustive study explores the impact of diverse norms and Matérn kernel variations on the performance of models, and aims to improve the computational efficiency of the model fitting and prediction processes. Furthermore, a heuristic framework is introduced to derive optimal complexity parameters for each Matérn-based FEM kernel. The proposed parallel approaches use dynamic strategies, which significantly reduce the computational time of the algorithms compared to other methods and parallel computing techniques presented in recent years. The proposed methodology is assessed in the context of bias corrections for temperature forecasts made by the Local Data Assimilation and Prediction System (LDAPS) model. A comprehensive comparative analysis which includes machine learning algorithms provides significant insights into the training process, norm selection, and kernel choice, and shows that Matérn-based methods emerge as a choice to be considered for regression problems.

关键词: Numerical modelling, Parallel programming, Matérn kernels, Machine learning

Abstract: Mathematical modelling is fundamental to understanding real-world phenomena. Despite the inherent complexity in designing such models, numerical approaches and, more recently, machine learning techniques, have emerged as powerful tools in this area. This work proposes integrating the finite element method (FEM) into forecasting and introduces parallel techniques for regression problems, with a specific focus on the use of Matérn kernels on local mesh support. This approach generalises the modelling based on radial basis function kernels and offers more flexibility to control the smoothness of the modelled functions. An exhaustive study explores the impact of diverse norms and Matérn kernel variations on the performance of models, and aims to improve the computational efficiency of the model fitting and prediction processes. Furthermore, a heuristic framework is introduced to derive optimal complexity parameters for each Matérn-based FEM kernel. The proposed parallel approaches use dynamic strategies, which significantly reduce the computational time of the algorithms compared to other methods and parallel computing techniques presented in recent years. The proposed methodology is assessed in the context of bias corrections for temperature forecasts made by the Local Data Assimilation and Prediction System (LDAPS) model. A comprehensive comparative analysis which includes machine learning algorithms provides significant insights into the training process, norm selection, and kernel choice, and shows that Matérn-based methods emerge as a choice to be considered for regression problems.

Key words: Numerical modelling, Parallel programming, Matérn kernels, Machine learning

中图分类号:

Violeta Migallón, Héctor Penadés, José Penadés. Design and Comparison of Parallel Dynamic Matérn Kernel-Based Regression Models and Machine Learning Approaches: Application to Bias Correction in Numerical Weather Prediction[J]. Communications on Applied Mathematics and Computation, 2026, 8(3): 1115-1156.

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Design and Comparison of Parallel Dynamic Matérn Kernel-Based Regression Models and Machine Learning Approaches: Application to Bias Correction in Numerical Weather Prediction

Design and Comparison of Parallel Dynamic Matérn Kernel-Based Regression Models and Machine Learning Approaches: Application to Bias Correction in Numerical Weather Prediction

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