# Generalizing to New Dynamical Systems via Frequency Domain Adaptation

arXiv: https://arxiv.org/abs/2507.00025 · HTML: https://mlsanity.com/paper/2507.00025/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 64 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Domain Agnostic Learning with Disentangled Representations](https://mlsanity.com/paper/1904.12347/) (2019)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Regularizing Deep Networks with Semantic Data Augmentation](https://mlsanity.com/paper/2007.10538/) (2020)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [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)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [Training for the Future: A Simple Gradient Interpolation Loss to Generalize Along Time](https://mlsanity.com/paper/2108.06721/) (2021)
- [Transform Once: Efficient Operator Learning in Frequency Domain](https://mlsanity.com/paper/2211.14453/) (2022)
- [Generalizing to Evolving Domains with Latent Structure-Aware Sequential Autoencoder](https://mlsanity.com/paper/2205.07649/) (2022)
- [Inferring halo masses with Graph Neural Networks](https://mlsanity.com/paper/2111.08683/) (2021)

## Abstract (arXiv)

Learning the underlying dynamics from data with deep neural networks has shown remarkable potential in modeling various complex physical dynamics. However, current approaches are constrained in their ability to make reliable predictions in a specific domain and struggle with generalizing to unseen systems that are governed by the same general dynamics but differ in environmental characteristics. In this work, we formulate a parameter-efficient method, Fourier Neural Simulator for Dynamical Adaptation (FNSDA), that can readily generalize to new dynamics via adaptation in the Fourier space. Specifically, FNSDA identifies the shareable dynamics based on the known environments using an automatic partition in Fourier modes and learns to adjust the modes specific for each new environment by conditioning on low-dimensional latent systematic parameters for efficient generalization. We evaluate our approach on four representative families of dynamic systems, and the results show that FNSDA can achieve superior or competitive generalization performance compared to existing methods with a significantly reduced parameter cost. Our code is available at https://github.com/WonderSeven/FNSDA.