Combining finite volume method and physics-informed neural networks for parameter identification and model selection in cell invasion models

Accurate modeling of a phenomenon is essential for enhancing predictive capabilities and understanding its underlying mechanisms. The precision of model predictions is heavily influenced by the parameters of the model. Consequently, in addition to addressing problems framed as Partial Differential Equations or Ordinary Differential Equations, parameter estimation is crucial for improving solution accuracy and selecting the optimal model among alternatives. This study focuses on estimating the parameters of the Fisher-KPP (Ronald Fisher, Andrey Kolmogorov, Ivan Petrovsky, Nikolai Piskunov) model using physics-informed neural networks. The Fisher-KPP reaction–diffusion model, which explores cell invasion, has four variants depending on whether the parameters are free or fixed. We employ the finite volume method to simulate the model and obtain numerical solutions.