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

arXiv: https://arxiv.org/abs/2510.25368 · HTML: https://mlsanity.com/paper/2510.25368/

## 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 (most cited first, 30 of 45)

- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers](https://mlsanity.com/paper/2212.12474/) (2022)
- [Application-Driven Innovation in Machine Learning](https://mlsanity.com/paper/2403.17381/) (2024)
- [AutoIP: A United Framework to Integrate Physics into Gaussian Processes](https://mlsanity.com/paper/2202.12316/) (2022)
- [Variational Inference with Gaussian Score Matching](https://mlsanity.com/paper/2307.07849/) (2023)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [Physics-informed machine learning as a kernel method](https://mlsanity.com/paper/2402.07514/) (2024)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response](https://mlsanity.com/paper/2402.17233/) (2024)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [LLM-Lasso: A Robust Framework for Domain-Informed Feature Selection and Regularization](https://mlsanity.com/paper/2502.10648/) (2025)
- [Neural Context Flows for Meta-Learning of Dynamical Systems](https://mlsanity.com/paper/2405.02154/) (2024)
- [Uncovering differential equations from data with hidden variables](https://mlsanity.com/paper/2002.02250/) (2020)
- [MAGMA: Inference and Prediction with Multi-Task Gaussian Processes](https://mlsanity.com/paper/2007.10731/) (2020)
- [Learning Governing Equations of Unobserved States in Dynamical Systems](https://mlsanity.com/paper/2404.18572/) (2024)
- [Physics-Informed Variational State-Space Gaussian Processes](https://mlsanity.com/paper/2409.13876/) (2024)

## Built on by (most cited first, 4 of 4)

- [Validating Interpretability in siRNA Efficacy Prediction: A Perturbation-Based, Dataset-Aware Protocol](https://mlsanity.com/paper/2602.10152/) (2026)
- [Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes](https://mlsanity.com/paper/2605.13088/) (2026)
- [Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots](https://mlsanity.com/paper/2607.01749/) (2026)
- [An Investigation of the NeurIPS and ICML 2025 Position Tracks](https://mlsanity.com/paper/2608.16894/) (2026)

## 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.