A comparative investigation of a time-dependent mesh method and physics-informed neural networks to analyze the generalized Kolmogorov-Petrovsky-Piskunov equation

Cites Work

Title not available (Why is that?)
Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method
Traveling pulse solutions to Fitzhugh-Nagumo equations
Stability of travelling fronts of the Fisher-KPP equation in \(\mathbb {R}^{N}\)
A Jacobi-Gauss-Lobatto collocation method for solving generalized Fitzhugh-Nagumo equation with time-dependent coefficients
Variational mesh adaptation. II: Error estimates and monitor functions
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
A generalized FitzHugh-Nagumo equation
Numerical investigation of the solution of Fisher's equation via the B-spline Galerkin method
Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing
Traveling Waves of a Kinetic Transport Model for the KPP-Fisher Equation
Two meshless methods based on pseudo spectral delta-shaped basis functions and barycentric rational interpolation for numerical solution of modified Burgers equation
On the exact and numerical solutions to the FitzHugh–Nagumo equation
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh
Adaptive mesh movements -- the MMPDE approach and its applications
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations