# Learning Physics-Consistent Particle Interactions

arXiv: https://arxiv.org/abs/2202.00299 · HTML: https://mlsanity.com/paper/2202.00299/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 21 of 21)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://mlsanity.com/paper/2103.01436/) (2021)
- [Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture](https://mlsanity.com/paper/2011.13511/) (2020)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [PIGNet: A physics-informed deep learning model toward generalized drug-target interaction predictions](https://mlsanity.com/paper/2008.12249/) (2020)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)

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

- [Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamics](https://mlsanity.com/paper/2411.11467/) (2024)
- [Collective Relational Inference for learning heterogeneous interactions](https://mlsanity.com/paper/2305.00557/) (2023)
- [Physics-tailored machine learning reveals unexpected physics in dusty plasmas](https://mlsanity.com/paper/2310.05273/) (2023)
- [On the Convergence and Size Transferability of Continuous-depth Graph Neural Networks](https://mlsanity.com/paper/2510.03923/) (2025)

## Abstract (arXiv)

Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the particle interaction hidden in many cases. Machine learning methods have the potential to learn the behavior of interacting particle systems by combining experiments with data analysis methods. However, most existing algorithms focus on learning the kinetics at the particle level. Learning pairwise interaction, e.g., pairwise force or pairwise potential energy, remains an open challenge. Here, we propose an algorithm that adapts the Graph Networks framework, which contains an edge part to learn the pairwise interaction and a node part to model the dynamics at particle level. Different from existing approaches that use neural networks in both parts, we design a deterministic operator in the node part that allows to precisely infer the pairwise interactions that are consistent with underlying physical laws by only being trained to predict the particle acceleration. We test the proposed methodology on multiple datasets and demonstrate that it achieves superior performance in inferring correctly the pairwise interactions while also being consistent with the underlying physics on all the datasets. The proposed framework is scalable to larger systems and transferable to any type of particle interactions, contrary to the previously proposed purely data-driven solutions. The developed methodology can support a better understanding and discovery of the underlying particle interaction laws, and hence guide the design of materials with targeted properties.