PDE MODELING OF POPULATION DYNAMICS USING PHYSICS INFORMED NEURAL NETWORKS (PINNS)
DOI:
https://doi.org/10.60787/apjcasr.vol9no1.57Keywords:
PDE Modelling, Population dynamics, Physics informed neural network, machine learning, Biological laws, Disease spreadAbstract
In recent years, artificial intelligence (AI) has transformed scientific inquiry and technological innovation significantly in almost all facets of life.. This paper presents a study of Physics-Informed Neural Networks (PINNs) solution techniques applied to Partial Differential Equation (PDE) models in population dynamics. Specifically, the paper focuses on modelling disease spread using an advection–diffusion–reaction partial differential equations (PDEs), with the solution sought through Physics-Informed Neural Networks (PINNs) technique. The community is being modelled as a bounded spatial domain where the disease density evolves over time and space. By embedding the underlying physical and biological laws into the network architecture, PINNs offer a robust and accurate framework to simulate infectious disease dynamics. Furthermore, numerical simulations, were implemented using the MATLAB ODE45 scheme, which provided insights into the interplay between disease progression, recovery , birth and death rate as parameter of interest in the transmission dynamics.
References
Chin,C. & Mckay,A.,(2019) Model verification and validation strategies: An Application Case Study.The 8th International Symposium on Computational Intelligence and Industrial Applications .(ISCHA2018).
Christou, K. (2022). Application of partial differential equations in population dynamics: Fixed-mesh and adaptive mesh approaches (Doctoral dissertation, University of Cyprus).
Jagtap, A. D., Kawaguchi, K., & Karniadakis, G. E. (2020). Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2239), 20200334. https://doi.org/10.1098/rspa.2020.0334
Lalić, B., Cuong, D. V., Petrić, M., Pavlović, V., Sremac, A. F., & Roantree, M. (2024). Physics-based dynamic models hybridisation using physics-informed neural networks. arXiv preprint arXiv:2412.07514
Lin, S., & Chen, Y. (2023). Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions. Physica D: Nonlinear Phenomena, 445, 133629. https://doi.org/10.1016/j.physd.2022.133629
Lin, S., & Chen, Y. (2024). Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations. Physica D: Nonlinear Phenomena, 459, 134023. https://doi.org/10.1016/j.physd.2023.134023
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
Rodrigues, J. A. (2024). Using physics-informed neural networks (PINNs) for tumor cells growth modeling [Preprint]. Preprints.org. https://doi.org/10.20944/preprints202403.1013.v1
Wu, Y., Sicard, B., & Gadsden, S. A. (2024). Physics-informed machine learning: A comprehensive review on applications in anomaly detection and condition monitoring. Expert Systems with Applications, 255, 124678. https://doi.org/10.1016/j.eswa.2024.124678
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Akwapoly Journal of Communication & Scientific Research
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
