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arXiv · 2304.14088

Hyperparameter optimization of orthogonal functions in the numerical solution of differential equations

Alireza Afzal Aghaei·Kourosh Parand
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Abstract

This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm manner, are developed to find the optimal set of hyperparameters. Employing rational Jacobi functions, we ran these algorithms on two nonlinear benchmark differential equations on the semi-infinite domain. The configurations contain different rational mappings along with their length scale parameter and the Jacobi functions parameters. These trials are configured on the collocation Least-Squares Support Vector Regression (CLS-SVR), a novel numerical simulation approach based on spectral methods. In addition, we have addressed the sensitivity of these hyperparameters on the numerical stability and convergence of the CLS-SVR model. The experiments show that this technique can effectively improve state-of-the-art results.

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Alireza Afzal Aghaei, Kourosh Parand. 2023-04-27. Hyperparameter optimization of orthogonal functions in the numerical solution of differential equations. https://arxiv.org/abs/2304.14088

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