Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs
Genming Bai, Ujjwal Koley, Siddhartha Mishra, Roberto Molinaro
Abstract
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions of these dispersive PDEs is leveraged to prove rigorous bounds on the resulting error. We present several numerical experiments to demonstrate that PINNs can approximate solutions of these dispersive PDEs very accurately.
Topics & Concepts
Artificial neural networkPhysicsNonlinear systemApplied mathematicsStatistical physicsArtificial intelligenceComputer scienceMathematicsQuantum mechanicsModel Reduction and Neural NetworksMeteorological Phenomena and SimulationsFluid Dynamics and Turbulent Flows