Physics-Informed Machine Learning in Biomedical Science and Engineering.

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.