# Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning

arXiv: https://arxiv.org/abs/2212.01168 · HTML: https://mlsanity.com/paper/2212.01168/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Transfusion: Understanding Transfer Learning for Medical Imaging](https://mlsanity.com/paper/1902.07208/) (2019)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (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)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [Sequential Neural Processes](https://mlsanity.com/paper/1906.10264/) (2019)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [Variational Integrator Networks for Physically Structured Embeddings](https://mlsanity.com/paper/1910.09349/) (2019)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [The Impact of Reinitialization on Generalization in Convolutional Neural Networks](https://mlsanity.com/paper/2109.00267/) (2021)
- [Constants of motion network](https://mlsanity.com/paper/2208.10387/) (2022)
- [Identifying Physical Law of Hamiltonian Systems via Meta-Learning](https://mlsanity.com/paper/2102.11544/) (2021)

## Built on by (most cited first, 3 of 3)

- [System-Aware Neural ODE Processes for Few-Shot Bayesian Optimization](https://mlsanity.com/paper/2406.02352/) (2024)
- [Meta-learning Structure-Preserving Dynamics](https://mlsanity.com/paper/2508.11205/) (2025)
- [TLXML: Task-Level Explanation of Meta-Learning via Influence Functions](https://mlsanity.com/paper/2501.14271/) (2025)

## Abstract (arXiv)

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the system domain, where the type of system remains consistent and thus cannot ensure the adaptation to new, or unseen physical systems governed by different laws. For instance, a neural network trained on a mass-spring system cannot guarantee accurate predictions for the behavior of a two-body system or any other system with different physical laws. In this work, we take a significant leap forward by targeting cross domain generalization within the field of Hamiltonian dynamics. We model our system with a graph neural network (GNN) and employ a meta learning algorithm to enable the model to gain experience over a distribution of systems and make it adapt to new physics. Our approach aims to learn a unified Hamiltonian representation that is generalizable across multiple system domains, thereby overcoming the limitations of system-specific models. We demonstrate that the meta-trained model captures the generalized Hamiltonian representation that is consistent across different physical domains. Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning.