# Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational N-body Problem

arXiv: https://arxiv.org/abs/2111.15631 · HTML: https://mlsanity.com/paper/2111.15631/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 28 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [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)
- [HIGAN: Cosmic Neutral Hydrogen with Generative Adversarial Networks](https://mlsanity.com/paper/1904.12846/) (2019)

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

- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks](https://mlsanity.com/paper/2310.20398/) (2023)

## Abstract (arXiv)

The gravitational N-body problem, which is fundamentally important in astrophysics to predict the motion of N celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general analytical solution for N>2. Can an N-body problem be solved accurately by a neural network (NN)? Can a NN observe long-term conservation of energy and orbital angular momentum? Inspired by Wistom & Holman (1991)'s symplectic map, we present a neural N-body integrator for splitting the Hamiltonian into a two-body part, solvable analytically, and an interaction part that we approximate with a NN. Our neural symplectic N-body code integrates a general three-body system for 105 steps without diverting from the ground truth dynamics obtained from a traditional N-body integrator. Moreover, it exhibits good inductive bias by successfully predicting the evolution of N-body systems that are no part of the training set.