Deep Learning Approaches for Solving Differential Equations in Scientific Computing

作者：Dr. A. Prashanthi · 发表于：International Journal for Research in Applied Science and Engineering Technology · 年份：2025 · DOI：10.22214/ijraset.2025.71980

Differential equations are fundamental in modeling dynamic systems across physics, engineering, and finance. Traditional numerical methods, while robust, often struggle with high-dimensional problems and computational complexity. Recent advances in deep learning have introduced novel frameworks such as Physics-Informed Neural Networks (PINNs), Deep Operator Networks (DeepONets), and neural ordinary differential equations (Neural ODEs), offering efficient and scalable alternatives. This paper explores the integration of deep learning with differential equation solvers, comparing their accuracy, computational efficiency, and application scope. We provide theoretical insights, mathematical formulations, and implementation details to demonstrate how these models outperform traditional solvers in various scientific computing scenarios