# Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation

arXiv: https://arxiv.org/abs/2510.24216 · HTML: https://mlsanity.com/paper/2510.24216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 69 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 30 of 41)

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- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
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- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
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- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
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- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction](https://mlsanity.com/paper/2305.11421/) (2023)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Learning Neural PDE Solvers with Parameter-Guided Channel Attention](https://mlsanity.com/paper/2304.14118/) (2023)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [A probabilistic model for the numerical solution of initial value problems](https://mlsanity.com/paper/1610.05261/) (2016)
- [Domain Adaptation under Open Set Label Shift](https://mlsanity.com/paper/2207.13048/) (2022)
- [Respecting Domain Relations: Hypothesis Invariance for Domain Generalization](https://mlsanity.com/paper/2010.07591/) (2020)

## Abstract (arXiv)

In dynamical system modeling, traditional numerical methods are limited by high computational costs, while modern data-driven approaches struggle with data scarcity and distribution shifts. To address these fundamental limitations, we first propose SPARK, a physics-guided quantitative augmentation plugin. Specifically, SPARK utilizes a reconstruction autoencoder to integrate physical parameters into a physics-rich discrete state dictionary. This state dictionary then acts as a structured dictionary of physical states, enabling the creation of new, physically-plausible training samples via principled interpolation in the latent space. Further, for downstream prediction, these augmented representations are seamlessly integrated with a Fourier-enhanced Graph ODE, a combination designed to robustly model the enriched data distribution while capturing long-term temporal dependencies. Extensive experiments on diverse benchmarks demonstrate that SPARK significantly outperforms state-of-the-art baselines, particularly in challenging out-of-distribution scenarios and data-scarce regimes, proving the efficacy of our physics-guided augmentation paradigm.