Traveling wave solutions of partial differential equations via neural networks
DOI10.1007/s10915-021-01621-wzbMath1503.65273arXiv2101.08520OpenAlexW3197436794WikidataQ115382659 ScholiaQ115382659MaRDI QIDQ1983171
Sung Woong Cho, Hwijae Son, Hyung-Ju Hwang
Publication date: 15 September 2021
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.08520
Artificial neural networks and deep learning (68T07) Neural networks for/in biological studies, artificial life and related topics (92B20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Chemical kinetics in thermodynamics and heat transfer (80A30) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Cell movement (chemotaxis, etc.) (92C17) Traveling wave solutions (35C07) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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- Uniqueness and exponential stability of traveling wave fronts for a multi-type SIS nonlocal epidemic model
- The existence of minimum speed of traveling wave solutions to a non-KPP isothermal diffusion system
- Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
- Traveling bands of chemotactic bacteria: a theoretical analysis
- Exp-function method for nonlinear wave equations
- Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity
- New traveling wave exact and approximate solutions for the nonlinear Cahn-Allen equation: evolution of a nonconserved quantity
- Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation
- Steadily propagating waves of a chemotaxis model
- The sign of the wave speed for the Lotka-Volterra competition-diffusion system
- Rogue waves, bright-dark solitons and traveling wave solutions of the \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation
- DGM: a deep learning algorithm for solving partial differential equations
- Exact minimum speed of traveling waves in a Keller-Segel model
- Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach
- Deep neural network approach to forward-inverse problems
- Sharp bounds for the ratio of two zeta functions
- The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
- Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay
- Spreading speeds and traveling waves of a parabolic-elliptic chemotaxis system with logistic source on \(\mathbb{R}^N\)
- Traveling wave solutions of a nonlinear reaction-diffusion-chemotaxis model for bacterial pattern formation
- A new Riccati equation rational expansion method and its application to \((2+1)\)-dimensional Burgers equation
- Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer
- Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation
- Solitary wave solutions of nonlinear wave equations
- Transient Bounds and Time-Asymptotic Behavior of Solutions to Nonlinear Equations of Fisher Type
- Parameter Dependence of Propagation Speed of Travelling Waves for Competition-Diffusion Equations
- The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations
- Traveling Wave and Multiple Traveling Wave Solutions of Parabolic Equations
- DeepXDE: A Deep Learning Library for Solving Differential Equations
