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Randomized Neural Networks for Partial Differential Equation on Static and Evolving Surfaces
Jingbo Sun, Fei Wang
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due t…
Local Randomized Neural Networks with Discontinuous Galerkin Methods for KdV-type and Burgers Equations
Jingbo Sun, Fei Wang
The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in [42], were originally designed for solving linear partial differential equations.…
Local Randomized Neural Networks with Discontinuous Galerkin Methods for Diffusive-Viscous Wave Equation
Jingbo Sun, Fei Wang
The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geo…
Deep Petrov-Galerkin Method for Solving Partial Differential Equations
Yong Shang, Fei Wang, Jingbo Sun
Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural…