# Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigm

arXiv: https://arxiv.org/abs/2511.06585 · HTML: https://mlsanity.com/paper/2511.06585/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 103 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://mlsanity.com/paper/2103.01436/) (2021)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials](https://mlsanity.com/paper/2310.03121/) (2023)
- [Koopman operator-based model reduction for switched-system control of PDEs](https://mlsanity.com/paper/1710.06759/) (2017)
- [Learning stiff chemical kinetics using extended deep neural operators](https://mlsanity.com/paper/2302.12645/) (2023)
- [Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations](https://mlsanity.com/paper/2402.07465/) (2024)
- [Stochastic Physics-Informed Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.01621/) (2021)
- [Deep Operator Learning Lessens the Curse of Dimensionality for PDEs](https://mlsanity.com/paper/2301.12227/) (2023)
- [TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations](https://mlsanity.com/paper/2402.17660/) (2024)
- [PyDEns: a Python Framework for Solving Differential Equations with Neural Networks](https://mlsanity.com/paper/1909.11544/) (2019)

## Abstract (arXiv)

The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with physical constraints, resulting in models that are accurate, mechanistic, generalizable, and able to extrapolate beyond observed domains. This review surveys recent advances in physics-informed neural networks and operator learning, differentiable molecular simulation, and hybrid physics-ML potentials, with emphasis on long-timescale kinetics, rare events, and free-energy estimation. We frame these approaches as solutions to the "biomolecular closure problem", recovering unresolved interactions beyond classical force fields while preserving thermodynamic consistency and mechanistic interpretability. We examine theoretical foundations, tools and frameworks, computational trade-offs, and unresolved issues, including model expressiveness and stability. We outline prospective research avenues at the intersection of machine learning, statistical physics, and computational chemistry, contending that future advancements will depend on mechanistic inductive biases, and integrated differentiable physical learning frameworks for biomolecular simulation and discovery.