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Physics-Informed Machine Learning in Biomedical Science and Engineering.

Nazanin Ahmadi1, Qianying Cao2, Jay D Humphrey3

  • 1Center for Biomedical Engineering, Brown University, Providence, Rhode Island, USA.

Annual Review of Biomedical Engineering
|May 1, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

Physics-informed machine learning (PIML) integrates physical laws with data for complex biomedical modeling. This review covers physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and neural operators (NOs) for enhanced scientific discovery.

Keywords:
gray-box discoveryinverse problemsneural ODEsneural operatorsphysics-informed neural networks

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Area of Science:

  • Biomedical Science and Engineering
  • Computational Biology
  • Medical Physics

Background:

  • Traditional machine learning often struggles with data scarcity and complexity in biomedical systems.
  • Integrating physical laws into machine learning offers improved interpretability and accuracy.
  • Physics-informed machine learning (PIML) is an emerging paradigm addressing these limitations.

Purpose of the Study:

  • To review and categorize the main classes of PIML frameworks used in biomedical science.
  • To highlight the applications and potential of PIML in modeling complex biological systems.
  • To identify challenges and future directions for PIML in biomedical research.

Main Methods:

  • Review of three PIML frameworks: physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and neural operators (NOs).
  • Discussion of their underlying principles and mathematical formulations.
  • Emphasis on their integration of physical laws with data-driven approaches.

    • Main Results:

    • PINNs embed governing equations into deep learning for applications in biomechanics and medical imaging.
    • NODEs provide continuous-time modeling suitable for dynamic physiological systems and pharmacokinetics.
    • Deep NOs efficiently learn function space mappings for multiscale biological simulations.

    Conclusions:

    • PIML frameworks like PINNs, NODEs, and NOs are crucial for biomedical applications where interpretability and data scarcity are concerns.
    • Advancements in uncertainty quantification, generalization, and integration with large language models are key future directions.
    • PIML offers a powerful approach to overcome limitations of conventional black-box learning in biomedical science.