Stochastic Partial Differential Equation

Stochastic partial differential equations (SPDEs) model systems evolving in space and time under random influences, aiming to capture complex phenomena with inherent uncertainty. Current research heavily focuses on developing efficient numerical solutions, particularly for singularly perturbed SPDEs exhibiting rapid changes in solution behavior, employing methods like physics-informed neural networks (PINNs) and Fourier neural operators, often enhanced with asymptotic analysis for improved accuracy and efficiency. These advancements are crucial for diverse applications, including uncertainty quantification in geophysical data assimilation, modeling complex dynamical systems, and discovering underlying SPDEs from limited data, ultimately improving the accuracy and interpretability of models across various scientific disciplines.