Physics-Informed Machine Learning in Biomedical Science and Engineering

TL;DR

This paper reviews physics-informed machine learning frameworks like PINNs, NODEs, and NOs, highlighting their applications, benefits, and future challenges in modeling complex biomedical systems.

Contribution

It provides a comprehensive overview of PIML methods in biomedical science, emphasizing their roles, applications, and open challenges for future research.

Findings

PINNs successfully applied to biosolid and biofluid mechanics.

NODEs effectively model dynamic physiological systems.

Deep neural operators enable efficient multiscale biological simulations.

Abstract

Physics-informed machine learning (PIML) is emerging as a potentially transformative paradigm for modeling complex biomedical systems by integrating parameterized physical laws with data-driven methods. Here, we review three main classes of PIML frameworks: physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and neural operators (NOs), highlighting their growing role in biomedical science and engineering. We begin with PINNs, which embed governing equations into deep learning models and have been successfully applied to biosolid and biofluid mechanics, mechanobiology, and medical imaging among other areas. We then review NODEs, which offer continuous-time modeling, especially suited to dynamic physiological systems, pharmacokinetics, and cell signaling. Finally, we discuss deep NOs as powerful tools for learning mappings between function spaces, enabling efficient simulations across multiscale and spatially heterogeneous biological domains. Throughout, we emphasize applications where physical interpretability, data scarcity, or system complexity make conventional black-box learning insufficient. We conclude by identifying open challenges and future directions for advancing PIML in biomedical science and engineering, including issues of uncertainty quantification, generalization, and integration of PIML and large language models.