arXiv:2510.05433cs.LGcs.AI2025-10中稿 · publication in the…被引 14

将物理定律融入机器学习,提升生物医学建模的准确性与可解释性。

Physics-Informed Machine Learning in Biomedical Science and Engineering

  • 用物理方程约束神经网络,融合先验知识与数据。
  • 在生物力学、药代动力学等场景中显著提升小样本建模效果。
  • 适合数据少、机制复杂或需可解释性的生物医学研究者。

物理信息机器学习(PIML)正成为建模复杂生物医学系统的一种变革性范式,通过将参数化物理定律与数据驱动方法相结合。本文综述三类主要PIML框架:物理信息神经网络(PINNs)、神经微分方程(NODEs)和神经算子(NOs),并强调其在生物医学科学与工程中的日益重要作用。首先介绍PINNs,其将控制方程嵌入深度学习模型,已成功应用于生物固体力学、生物流体力学、机械生物学及医学影像等领域。随后回顾NODEs,其提供连续时间建模,特别适用于动态生理系统、药代动力学和细胞信号传导。最后讨论深层神经算子,作为学习函数空间映射的强大工具,可实现多尺度与空间异质生物域的高效模拟。文中强调在物理可解释性、数据稀缺或系统复杂性背景下,传统黑箱学习难以胜任的应用场景。最后指出当前挑战与未来方向,包括不确定性量化、泛化能力提升,以及PIML与大语言模型的融合。

原文摘要 · Abstract (English)

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.

物理信息生物医学神经网络可解释性

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