mlsanityData to 14 Oct 2026

Position: Biology is the Challenge Physics-Informed ML Needs to Evolve

arXiv 2510.25368 ↗First posted 29 Oct 2025cs.LG cs.AI cs.NEcited by 4

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Abstract (arXiv)

Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology, a field rich in dynamical systems but shaped by different constraints. Biological modeling, however, presents unique challenges: multi-faceted and uncertain prior knowledge, heterogeneous and noisy data, partial observability, and complex, high-dimensional networks. In this position paper, we argue that these challenges should not be seen as obstacles to PIML, but as catalysts for its evolution. We propose Biology-Informed Machine Learning (BIML): a principled extension of PIML that retains its structural grounding while adapting to the practical realities of biology. Rather than replacing PIML, BIML retools its methods to operate under softer, probabilistic forms of prior knowledge. We outline four foundational pillars as a roadmap for this transition: uncertainty quantification, contextualization, constrained latent structure inference, and scalability. Foundation Models and Large Language Models will be key enablers, bridging human expertise with computational modeling. We conclude with concrete recommendations to build the BIML ecosystem and channel PIML-inspired innovation toward challenges of high scientific and societal relevance.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 45 of its 127 references that are in the map. First posted on arXiv 29 Oct 2025.

Builds on

45 of 127 references.

References · 45

  1. 2023Retrieval-Augmented Generation for Large Language Models: A Surveycited by 2,212
  2. 2023A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questionscited by 1,601
  3. 2020WILDS: A Benchmark of in-the-Wild Distribution Shiftscited by 1,375
  4. 2024LLM-SR: Scientific Equation Discovery via Programming with Large Language Modelscited by 133
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33 more
  1. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 62
  2. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
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  4. 2022Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solverscited by 41
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  9. 2024Physics-informed machine learning as a kernel methodcited by 13
  10. 2024Zero-shot Imputation with Foundation Inference Models for Dynamical Systemscited by 13
  11. 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
  12. 2023Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlookcited by 11
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  18. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
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  20. 2018Constraining the Dynamics of Deep Probabilistic Modelscited by 5
  21. 2020Human Strategic Steering Improves Performance of Interactive Optimizationcited by 5
  22. 2024Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networkscited by 5
  23. 2025Al-Khwarizmi: Discovering Physical Laws with Foundation Modelscited by 5
  24. 2022Reactmine: a statistical search algorithm for inferring chemical reactions from time series datacited by 4
  25. 2024Bayesian Physics-informed Neural Networks for System Identification of Inverter-dominated Power Systemscited by 4
  26. 2025TEDDY: A Family Of Foundation Models For Understanding Single Cell Biologycited by 4
  27. 2024Assessment of Uncertainty Quantification in Universal Differential Equationscited by 3
  28. 2024A Primer on Large Language Models and their Limitationscited by 3
  29. 2024Efficient Fine-Tuning of Single-Cell Foundation Models Enables Zero-Shot Molecular Perturbation Predictioncited by 3
  30. 2022Bayesian Variable Selection in a Million Dimensionscited by 2
  31. 2023SpReME: Sparse Regression for Multi-Environment Dynamic Systemscited by 2
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  33. 2025Manifold-Constrained Gaussian Processes for Inference of Mixed-effects Ordinary Differential Equations with Application to Pharmacokineticscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.