# Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian

arXiv: https://arxiv.org/abs/2210.00090 · HTML: https://mlsanity.com/paper/2210.00090/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 20 of 20)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks](https://mlsanity.com/paper/1810.00825/) (2018)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps](https://mlsanity.com/paper/2103.05632/) (2021)
- [Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data](https://mlsanity.com/paper/2012.02334/) (2020)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Symplectic Learning for Hamiltonian Neural Networks](https://mlsanity.com/paper/2106.11753/) (2021)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
- [Nonseparable Symplectic Neural Networks](https://mlsanity.com/paper/2010.12636/) (2020)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (2021)
- [Sparse Symplectically Integrated Neural Networks](https://mlsanity.com/paper/2006.12972/) (2020)
- [ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias](https://mlsanity.com/paper/2206.12325/) (2022)

## Built on by (most cited first, 1 of 1)

- [Hamiltonian Neural Networks with Automatic Symmetry Detection](https://mlsanity.com/paper/2301.07928/) (2023)

## Abstract (arXiv)

Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their extension to the Lie group manifold is needed when rotations form a key component of the dynamics, such as the higher-order physics beyond simple point-mass dynamics for N-body celestial interactions. Moreover, the multiscale nature of these processes presents a challenge to existing methods as a long time horizon is required. By leveraging a symplectic Lie-group manifold preserving integrator, we present a method for data-driven discovery of non-Newtonian astronomy. Preliminary results show the importance of both these properties in training stability and prediction accuracy.