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

arXiv: https://arxiv.org/abs/2603.15331 · HTML: https://mlsanity.com/paper/2603.15331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 29 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior](https://mlsanity.com/paper/2406.06287/) (2024)
- [Approximating Families of Sharp Solutions to Fisher's Equation with Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.08313/) (2024)

## Abstract (arXiv)

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.