# Identifying Physical Law of Hamiltonian Systems via Meta-Learning

arXiv: https://arxiv.org/abs/2102.11544 · HTML: https://mlsanity.com/paper/2102.11544/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 23 Feb 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [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)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [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)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Meta-Learning Representations for Continual Learning](https://mlsanity.com/paper/1905.12588/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Meta-Gradient Reinforcement Learning](https://mlsanity.com/paper/1805.09801/) (2018)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [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)
- [Meta-Learning with Warped Gradient Descent](https://mlsanity.com/paper/1909.00025/) (2019)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)

## Built on by (most cited first, 8 of 8)

- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [Learning Trajectories of Hamiltonian Systems with Neural Networks](https://mlsanity.com/paper/2204.05077/) (2022)
- [Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning](https://mlsanity.com/paper/2212.01168/) (2022)
- [Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics](https://mlsanity.com/paper/2306.11435/) (2023)
- [Meta-learning Structure-Preserving Dynamics](https://mlsanity.com/paper/2508.11205/) (2025)

## Abstract (arXiv)

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related phenomena that are governed by the same physical law. However, in general, identifying a functional or shared expression of the Hamiltonian is very difficult. It requires carefully designed experiments and the researcher's insight that comes from years of experience. We propose that meta-learning algorithms can be potentially powerful data-driven tools for identifying the physical law governing Hamiltonian systems without any mathematical assumptions on the representation, but with observations from a set of systems governed by the same physical law. We show that a well meta-trained learner can identify the shared representation of the Hamiltonian by evaluating our method on several types of physical systems with various experimental settings.