# Learning Contact Dynamics using Physically Structured Neural Networks

arXiv: https://arxiv.org/abs/2102.11206 · HTML: https://mlsanity.com/paper/2102.11206/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 22 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Variational Integrator Networks for Physically Structured Embeddings](https://mlsanity.com/paper/1910.09349/) (2019)
- [DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control](https://mlsanity.com/paper/2009.04278/) (2020)
- [Unsupervised Contact Learning for Humanoid Estimation and Control](https://mlsanity.com/paper/1709.07472/) (2017)
- [Learning a Structured Neural Network Policy for a Hopping Task](https://mlsanity.com/paper/1710.00022/) (2017)

## Built on by (most cited first, 10 of 10)

- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Neural Hybrid Automata: Learning Dynamics with Multiple Modes and Stochastic Transitions](https://mlsanity.com/paper/2106.04165/) (2021)
- [OSCAR: Data-Driven Operational Space Control for Adaptive and Robust Robot Manipulation](https://mlsanity.com/paper/2110.00704/) (2021)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics](https://mlsanity.com/paper/2410.18868/) (2024)
- [Forced Variational Integrator Networks for Prediction and Control of Mechanical Systems](https://mlsanity.com/paper/2106.02973/) (2021)
- [Learning Trajectories of Hamiltonian Systems with Neural Networks](https://mlsanity.com/paper/2204.05077/) (2022)
- [Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Models](https://mlsanity.com/paper/2609.19674/) (2026)

## Abstract (arXiv)

Learning physically structured representations of dynamical systems that include contact between different objects is an important problem for learning-based approaches in robotics. Black-box neural networks can learn to approximately represent discontinuous dynamics, but they typically require large quantities of data and often suffer from pathological behaviour when forecasting for longer time horizons. In this work, we use connections between deep neural networks and differential equations to design a family of deep network architectures for representing contact dynamics between objects. We show that these networks can learn discontinuous contact events in a data-efficient manner from noisy observations in settings that are traditionally difficult for black-box approaches and recent physics inspired neural networks. Our results indicate that an idealised form of touch feedback -- which is heavily relied upon by biological systems -- is a key component of making this learning problem tractable. Together with the inductive biases introduced through the network architectures, our techniques enable accurate learning of contact dynamics from observations.