A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients

• URL: http://arxiv.org/abs/2603.15331v1
• Date: Mon, 16 Mar 2026 14:21:38 GMT
• Title: A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
• Abstract summary: We propose an efficient and generalizable physics-informed neural network (PINN) framework for computing traveling wave solutions.<n>A single PINN solver trained on a scaled equation is reused for different coefficient choices and spatial dimensions.<n> Numerical experiments in one and two dimensions, together with a comparison to the existing wave-PINN method, demonstrate the accuracy, flexibility, and superior performance of scaled TW-PINN.
• Score: 7.459187887558538
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We propose an efficient and generalizable physics-informed neural network (PINN) framework for computing traveling wave solutions of $n$-dimensional reaction-diffusion equations with various reaction and diffusion coefficients. By applying a scaling transformation with the traveling wave form, the original problem is reduced to a one-dimensional scaled reaction-diffusion equation with unit reaction and diffusion coefficients. This reduction leads to the proposed framework, termed scaled TW-PINN, in which a single PINN solver trained on the scaled equation is reused for different coefficient choices and spatial dimensions. We also prove a universal approximation property of the proposed PINN solver for traveling wave solutions. Numerical experiments in one and two dimensions, together with a comparison to the existing wave-PINN method, demonstrate the accuracy, flexibility, and superior performance of scaled TW-PINN. Finally, we explore an extension of the framework to the Fisher's equation with general initial conditions.

Related papers

• A Two-Stage Learning PINN Approach for Solving the Inverse Problem of the 1D Porous Medium Equation [0.0]
  The Porous Medium Equation (PME) arises in various physical applications such as fluid flow in porous media, heat transfer in plasmas, and population dynamics.<n>We study numerical solutions of the one-dimensional direct and inverse PME using Physics-Informed Neural Networks (PINNs)
  arXiv  Detail & Related papers  (2026-08-17T12:13:22Z)
• Quantum Physics-Informed Neural Networks for Solving Integro and Fractional PDEs [5.658353995249502]
  This work introduces a quantum physics-informed neural network (QPINN) framework that combines a quantum neural network with the governing equations of general nonlinear equations.<n>A series of numerical experiments demonstrates that the proposed QPINN framework accurately captures the behavior of nonlinearIDEs and FIPDEs.
  arXiv  Detail & Related papers  (2026-06-25T10:51:47Z)
• Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations [42.57657519369106]
  This work establishes rigorous first-of-its-kind upper bounds on the generalization error for the method of approximating solutions to Navier-Stokes equations.<n>We trained depth-2 neural networks trained via the unsupervised Physics-Informed Neural Network framework.<n>We provide empirical validation of the suggested activation functions and the corresponding bounds on a PINN setup solving the Taylor-Green vortex benchmark.
  arXiv  Detail & Related papers  (2026-03-24T11:08:34Z)
• Discovery of Quasi-Integrable Equations from traveling-wave data using the Physics-Informed Neural Networks [0.0]
  We apply PINNs to investigate vortex-type solutions of quasi-integrable equations in two spatial dimensions.<n>These equations are toy models for geostrophic shallow water dynamics in planetary atmospheres.<n>We introduce conservation law-enhanced PINNs, initial condition variations, and a friction-based perturbation approach to improve identification accuracy.
  arXiv  Detail & Related papers  (2024-10-23T08:29:13Z)
• Solving Poisson Equations using Neural Walk-on-Spheres [80.1675792181381]
  We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient solution of high-dimensional Poisson equations. We demonstrate the superiority of NWoS in accuracy, speed, and computational costs.
  arXiv  Detail & Related papers  (2024-06-05T17:59:22Z)
• Approximating Families of Sharp Solutions to Fisher's Equation with Physics-Informed Neural Networks [8.487185704099925]
  This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation. The focus is on investigating Fisher's equation under conditions of large reaction rate coefficients. A residual weighting scheme is introduced in the network training to mitigate the difficulties associated with standard PINN approaches.
  arXiv  Detail & Related papers  (2024-02-13T09:17:20Z)
• Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmas [0.06316710659541969]
  PINN is first tested as a compression method for the solution of the Vlasov-Poisson system. The application of PINN to solving the Vlasov-Poisson system is also presented with the special emphasis on the integral part.
  arXiv  Detail & Related papers  (2023-08-23T07:00:56Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Quantum-inspired optimization for wavelength assignment [51.55491037321065]
  We propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. Our results pave the way to the use of quantum-inspired algorithms for practical problems in telecommunications.
  arXiv  Detail & Related papers  (2022-11-01T07:52:47Z)
• Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions [68.8204255655161]
  We develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. Localized large gradients in the ADE solution make the (common in PINN) Latin hypercube sampling of the equation's residual highly inefficient. We propose criteria for weights in the loss function that produce a more accurate PINN solution than those obtained with the weights selected via other methods.
  arXiv  Detail & Related papers  (2022-08-18T05:00:24Z)
• Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations [63.8376359764052]
  We propose an approach to solving partial differential equations (PDEs) using a set of neural networks. We regress a set of neural networks onto a reduced order Proper Orthogonal Decomposition (POD) basis. These networks are then used in combination with a branch network that ingests the parameters of the prescribed PDE to compute a reduced order approximation to the PDE.
  arXiv  Detail & Related papers  (2022-08-02T18:27:13Z)
• Learning Physics-Informed Neural Networks without Stacked Back-propagation [82.26566759276105]
  We develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is two orders of magnitude faster.
  arXiv  Detail & Related papers  (2022-02-18T18:07:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.