https://doi.org/10.1140/epjp/s13360-025-06220-4
Regular Article
Combining finite volume method and physics-informed neural networks for parameter identification and model selection in cell invasion models
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914, Tehran, Iran
Received:
26
September
2024
Accepted:
16
March
2025
Published online:
4
April
2025
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.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjp/s13360-025-06220-4.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
