European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

Physics-Informed Neural Networks for Solving and Calibrating the Fisher-KPP Equation in Spatiotemporal Pathogen Dynamics

14 Jul 2026, 18:30

2h

University of Graz

Poster Numerical, Computational, and Data-Driven Methods Poster Presentations

Speaker

Jayrah Bena Riñon (Data Science Program, College of Science, University of the Philippines Diliman; Department of Mathematics, College of Science, Bicol University)

Description

Reaction-diffusion equations are central in ecological modeling for describing how biological populations, such as pathogens, propagate through space and time. While standard numerical methods such as finite difference and finite element schemes are well established for solving these equations, they can be difficult to integrate with data-driven inverse problems, particularly when estimating model parameters from noisy experimental observations. In this study, we employ Physics-Informed Neural Networks (PINNs) to solve and calibrate the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation, which models the logistic growth and homogeneous diffusion of biological populations \cite{Raissi_2019, Leclerc_2023}. We specifically investigate the spread of Peyronellaea pinodes on pea stipules using sequential daily imagery obtained from an experimental setup \cite{pea_dataset_2022}. By integrating the Fisher-KPP equation into the neural network’s loss function, our framework enables the simultaneous prediction of the probability of infection and the identification of key biological parameters, including the growth rate and diffusion coefficient, directly from the image dataset. This approach demonstrates the potential of PINNs to provide efficient solutions to both forward and inverse problems in complex biological systems.

Bibliography

@article{Raissi_2019,
    title = {Physics-informed neural networks: {A} deep learning framework for solving forward and
inverse problems involving nonlinear partial differential equations},
    volume = {378},
    issn = {00219991},
    shorttitle = {Physics-informed neural networks},
    url = {https://linkinghub.elsevier.com/retrieve/pii/S0021999118307125},
    doi = {10.1016/j.jcp.2018.10.045},
    language = {en},
    urldate = {2026-03-10},
    journal = {Journal of Computational Physics},
    author = {Raissi, M. and Perdikaris, P. and Karniadakis, G.E.},
    month = feb,
    year = {2019},
    pages = {686--707},
}

@article{Leclerc_2023,
    title = {Imaging with spatio-temporal modelling to characterize the dynamics of plant-pathogen
lesions},
    volume = {19},
    issn = {1553-7358},
    url = {https://dx.plos.org/10.1371/journal.pcbi.1011627},
    doi = {10.1371/journal.pcbi.1011627},
    language = {en},
    number = {11},
    urldate = {2026-03-10},
    journal = {PLOS Computational Biology},
    author = {Leclerc, Melen and Jumel, Stéphane and Hamelin, Frédéric M. and Treilhaud, Rémi and
Parisey, Nicolas and Mammeri, Youcef},
    editor = {Althouse, Benjamin},
    month = {11},
    year = {2023},
    pages = {1-15},
}

@misc{pea_dataset_2022,
    title = {Image sequences of growing lesions - {Ascochyta} blight of pea},
    url = {https://entrepot.recherche.data.gouv.fr/citation?persistentId=doi:10.57745/MQXKCP},
    doi = {10.57745/MQXKCP},
    abstract = {Image sequences showing the spread of lesions caused by the fungal pathogen P. pinodes
on inoculated pea stipules.},
    urldate = {2026-03-10},
    publisher = {Recherche Data Gouv},
    author = {Leclerc, Melen and Jumel, Stéphane and Hamelin, Frédéric and Treilhaud, Rémi and Parisey,
Nicolas and Mammeri, Youcef},
    collaborator = {Leclerc, Melen},
    year = {2022},
}