Active learning with Gaussian Process Regression for solving non-linear time-dependent partial differential equations

doi:10.1016/j.engappai.2025.111879

Active learning with Gaussian Process Regression for solving non-linear time-dependent partial differential equations

2025-08-06

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DOI：10.1016/j.engappai.2025.111879

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Abstract

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• Active Learning with Gaussian Process Regression (GPR) used to solve PDEs. • Used Matern and RBF kernels to tackle nonlinear PDEs. • Demonstrated results on Burgers, Allen-Cahn, Stefan, and Korteweg-de Vries equations. • Outperformed PINNs and various state of the art methods. • Applicable to climate, weather, materials, and biomedical simulations.

Keywords:

Active Learning

Gaussian Process Regression

Partial Differential Equations

Matern Kernel

RBF Kernel

Active learning with Gaussian Process Regression for solving non-linear time-dependent partial differential equations

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