A Hybrid Spectral Deferred Correction Method With Physics-informed Neural Network Initialization
Year: 2026
Type: article
Abstract: Spectral Deferred Correction (SDC) methods are iterative methods used to solve ordinary differential equations. The SDC method can achieve high-order convergence by adjusting the initial guess, quadrature nodes, and the number of iterations. Therefore, its convergence strongly depends on the initial approximation. In this work, we introduce a hybrid method in which a Physics-Informed Neural Network (PINN) provides the initial guess for SDC iterations. We present a rigorous formulation of both SDC and PINN, along with a convergence analysis of the proposed method. Finally, we validate our results using numerical examples. The proposed method significantly reduces the number of SDC sweeps required to achieve high-order accuracy.
Institution: Bukhara State University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7204886780