# Graph network for learning bi-directional physics

arXiv: https://arxiv.org/abs/2112.07054 · HTML: https://mlsanity.com/paper/2112.07054/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [TossingBot: Learning to Throw Arbitrary Objects with Residual Physics](https://mlsanity.com/paper/1903.11239/) (2019)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [GResNet: Graph Residual Network for Reviving Deep GNNs from Suspended Animation](https://mlsanity.com/paper/1909.05729/) (2019)
- [Unsupervised Learning of Latent Physical Properties Using Perception-Prediction Networks](https://mlsanity.com/paper/1807.09244/) (2018)

## Built on by (most cited first, 2 of 2)

- [Decomposing heterogeneous dynamical systems with graph neural networks](https://mlsanity.com/paper/2407.19160/) (2024)
- [Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks](https://mlsanity.com/paper/2207.08927/) (2022)

## Abstract (arXiv)

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems through problem-specific regularization and loss functions. Such explicit learning biases the network to learn data specific patterns and may require a change in the loss function or neural network architecture hereby limiting their generalizabiliy. Our graph network is implicitly biased by learning to solve several tasks, thereby sharing representations between tasks in order to learn the forward dynamics as well as infer the probability distribution of unknown particle specific properties. We evaluate our approach on one-step next state prediction tasks across diverse datasets. Our comparison against related data-driven physics learning approaches reveals that our model is able to predict the forward dynamics with at least an order of magnitude higher accuracy. We also show that our approach is able to recover multi-modal probability distributions of unknown physical parameters.