# Generalizing to New Physical Systems via Context-Informed Dynamics Model

arXiv: https://arxiv.org/abs/2202.01889 · HTML: https://mlsanity.com/paper/2202.01889/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 65 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 30 of 43)

- [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)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (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)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)

## Built on by (most cited first, 30 of 50)

- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction](https://mlsanity.com/paper/2504.19496/) (2025)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Zebra: In-Context Generative Pretraining for Solving Parametric PDEs](https://mlsanity.com/paper/2410.03437/) (2024)
- [Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data](https://mlsanity.com/paper/2410.04814/) (2024)
- [Masked Autoencoders are PDE Learners](https://mlsanity.com/paper/2403.17728/) (2024)
- [SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2403.19507/) (2024)
- [Strategies for Pretraining Neural Operators](https://mlsanity.com/paper/2406.08473/) (2024)
- [Interpretable Meta-Learning of Physical Systems](https://mlsanity.com/paper/2312.00477/) (2023)
- [Test-time Generalization for Physics through Neural Operator Splitting](https://mlsanity.com/paper/2602.00884/) (2026)
- [Neural Context Flows for Meta-Learning of Dynamical Systems](https://mlsanity.com/paper/2405.02154/) (2024)
- [Meta-Dynamical State Space Models for Integrative Neural Data Analysis](https://mlsanity.com/paper/2410.05454/) (2024)
- [GEPS: Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning](https://mlsanity.com/paper/2410.23889/) (2024)
- [Continual Learning of Dynamical Systems with Competitive Federated Reservoir Computing](https://mlsanity.com/paper/2206.13336/) (2022)
- [MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning](https://mlsanity.com/paper/2303.03181/) (2023)
- [Phase2vec: Dynamical systems embedding with a physics-informed convolutional network](https://mlsanity.com/paper/2212.03857/) (2022)
- [Discovering Physics Laws of Dynamical Systems via Invariant Function Learning](https://mlsanity.com/paper/2502.04495/) (2025)
- [Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Experts](https://mlsanity.com/paper/2502.05335/) (2025)
- [Weight-Space Linear Recurrent Neural Networks](https://mlsanity.com/paper/2506.01153/) (2025)
- [Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning](https://mlsanity.com/paper/2212.01168/) (2022)
- [SpReME: Sparse Regression for Multi-Environment Dynamic Systems](https://mlsanity.com/paper/2302.05942/) (2023)
- [CONFIDE: Contextual Finite Differences Modelling of PDEs](https://mlsanity.com/paper/2303.15827/) (2023)
- [Learning Efficient Surrogate Dynamic Models with Graph Spline Networks](https://mlsanity.com/paper/2310.16397/) (2023)
- [Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulation](https://mlsanity.com/paper/2410.01655/) (2024)
- [Tailored Forecasting from Short Time Series via Meta-learning](https://mlsanity.com/paper/2501.16325/) (2025)
- [Meta-learning Structure-Preserving Dynamics](https://mlsanity.com/paper/2508.11205/) (2025)
- [Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning](https://mlsanity.com/paper/2509.24332/) (2025)

## Abstract (arXiv)

Data-driven approaches to modeling physical systems fail to generalize to unseen systems that share the same general dynamics with the learning domain, but correspond to different physical contexts. We propose a new framework for this key problem, context-informed dynamics adaptation (CoDA), which takes into account the distributional shift across systems for fast and efficient adaptation to new dynamics. CoDA leverages multiple environments, each associated to a different dynamic, and learns to condition the dynamics model on contextual parameters, specific to each environment. The conditioning is performed via a hypernetwork, learned jointly with a context vector from observed data. The proposed formulation constrains the search hypothesis space to foster fast adaptation and better generalization across environments. We theoretically motivate our approach and show state-of-the-art generalization results on a set of nonlinear dynamics, representative of a variety of application domains. We also show, on these systems, that new system parameters can be inferred from context vectors with minimal supervision. Code is available at https://github.com/yuan-yin/CoDA .