A deep learning method for solving third-order nonlinear evolution equations
Jun Li, Yong Chen
Abstract
Abstract It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.
Topics & Concepts
Nonlinear systemComputer scienceOrder (exchange)Applied mathematicsStatistical physicsPhysicsMathematicsQuantum mechanicsFinanceEconomicsModel Reduction and Neural NetworksFractional Differential Equations SolutionsNumerical methods for differential equations