Complex Physics-Informed Neural Network

Physics-Informed Neural Networks (PINNs) have emerged as a powerful method for solving both forward and inverse problems involving Partial Differential Equations (PDEs) [1-4]. PINNs leverage the expressive power of neural networks to minimize a loss function that enforces the governing PDEs and boundary/initial conditions. This approach has been widely applied across various domains, including heat transfer [5-7], solid mechanics [8-10], incompressible flows [11-13], stochastic differential equations [14, 15], and uncertainty quantification [16, 17]. Despite their success, PINNs face significant challenges and often struggle to solve certain classes of problems [18, 19]. One major difficulty arises in scenarios where the solution exhibits rapid changes, such as in'stiff' PDEs [20], leading to issues with convergence and accuracy.