# Interpretable Meta-Learning of Physical Systems

arXiv: https://arxiv.org/abs/2312.00477 · HTML: https://mlsanity.com/paper/2312.00477/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 1 Dec 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [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)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Multi-Task Reinforcement Learning with Context-based Representations](https://mlsanity.com/paper/2102.06177/) (2021)
- [Bridging Multi-Task Learning and Meta-Learning: Towards Efficient Training and Effective Adaptation](https://mlsanity.com/paper/2106.09017/) (2021)
- [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)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Improved Active Multi-Task Representation Learning via Lasso](https://mlsanity.com/paper/2306.02556/) (2023)
- [Interpretable machine learning in Physics](https://mlsanity.com/paper/2203.08021/) (2022)
- [FLEX: an Adaptive Exploration Algorithm for Nonlinear Systems](https://mlsanity.com/paper/2304.13426/) (2023)

## Built on by (most cited first, 11 of 11)

- [DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction](https://mlsanity.com/paper/2504.19496/) (2025)
- [Zebra: In-Context Generative Pretraining for Solving Parametric PDEs](https://mlsanity.com/paper/2410.03437/) (2024)
- [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)
- [Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Experts](https://mlsanity.com/paper/2502.05335/) (2025)
- [Disentangled Representation Learning for Parametric Partial Differential Equations](https://mlsanity.com/paper/2410.02136/) (2024)
- [Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulation](https://mlsanity.com/paper/2410.01655/) (2024)
- [PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems](https://mlsanity.com/paper/2605.25353/) (2026)
- [Meta-learning of shared linear representations beyond well-specified linear regression](https://mlsanity.com/paper/2501.18975/) (2025)
- [Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2606.22969/) (2026)
- [Cross-Domain Pretraining for Steady-State Neural CFD Surrogates](https://mlsanity.com/paper/2610.10398/) (2026)

## Abstract (arXiv)

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.