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Using Physics-Informed Neural Networks (PINNs) for Tumor Cell Growth Modeling

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  • José Alberto Rodrigues

    (CIMA and Department of Mathematics of ISEL—Higher Institute of Engineering of Lisbon, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisbon, Portugal)

Abstract

This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely, the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employed a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation.

Suggested Citation

  • José Alberto Rodrigues, 2024. "Using Physics-Informed Neural Networks (PINNs) for Tumor Cell Growth Modeling," Mathematics, MDPI, vol. 12(8), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1195-:d:1376879
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    References listed on IDEAS

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    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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