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 language | English |
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Article number | 109422 |
Number of pages | 9 |
Journal | Computer Physics Communications |
Volume | 307 |
Early online date | 6 Nov 2024 |
DOIs | |
Publication status | Published - 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