Approximating families of sharp solutions to Fisher’s equation with physics-informed neural networks

Franz Martin Rohrhofer*, Stefan Posch, Clemens Gößnitzer, Bernhard Geiger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large reaction rate coefficients, where solutions exhibit steep traveling waves that often present challenges for traditional numerical methods. To address these challenges, a residual weighting scheme is introduced in the network training to mitigate the difficulties associated with standard PINN approaches. Additionally, a specialized network architecture designed to capture traveling wave solutions is explored. The paper also assesses the ability of PINNs to approximate a family of solutions by generalizing across multiple reaction rate coefficients. The proposed method demonstrates high effectiveness in solving Fisher's equation with large reaction rate coefficients and shows promise for meshfree solutions of generalized reaction-diffusion systems.

Original languageEnglish
Article number109422
Number of pages9
JournalComputer Physics Communications
Volume307
Early online date6 Nov 2024
DOIs
Publication statusPublished - Feb 2025

Keywords

  • Continuous parameter space
  • Fisher's equation
  • Physics-informed neural network
  • Reaction-diffusion system
  • Sharp solution
  • Traveling wave

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy

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