# Adaptive Spectral-Koopman Dynamics Modeling for Temporal Domain Generalization

arXiv: https://arxiv.org/abs/2610.02822 · HTML: https://mlsanity.com/paper/2610.02822/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 49 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 30 of 36)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [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 via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [DLOW: Domain Flow for Adaptation and Generalization](https://mlsanity.com/paper/1812.05418/) (2018)
- [Wild-Time: A Benchmark of in-the-Wild Distribution Shift over Time](https://mlsanity.com/paper/2211.14238/) (2022)
- [Best sources forward: domain generalization through source-specific nets](https://mlsanity.com/paper/1806.05810/) (2018)
- [Continuously Indexed Domain Adaptation](https://mlsanity.com/paper/2007.01807/) (2020)
- [A Unified Feature Disentangler for Multi-Domain Image Translation and Manipulation](https://mlsanity.com/paper/1809.01361/) (2018)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [Temporal Domain Generalization with Drift-Aware Dynamic Neural Networks](https://mlsanity.com/paper/2205.10664/) (2022)
- [Training for the Future: A Simple Gradient Interpolation Loss to Generalize Along Time](https://mlsanity.com/paper/2108.06721/) (2021)
- [Sequential Learning for Domain Generalization](https://mlsanity.com/paper/2004.01377/) (2020)
- [Generalizing to Evolving Domains with Latent Structure-Aware Sequential Autoencoder](https://mlsanity.com/paper/2205.07649/) (2022)
- [Continuous Temporal Domain Generalization](https://mlsanity.com/paper/2405.16075/) (2024)
- [Learning Robust Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2505.12585/) (2025)

## Abstract (arXiv)

Temporal Domain Generalization (TDG) has emerged to address real-world streaming data with distribution shifts over time. However, existing methods are either prone to overfitting to domain-specific noise in the data space or become overly complex and less interpretable in the parameter space. To bridge these gaps, we propose AdaSpecK, a spectral-Koopman framework with adaptive context extraction for TDG. To mitigate noise fitting to irregularly sampled domains, we introduce spectral-regularized Koopman dynamics modeling, which applies spectral-aware filtering in the latent space to extract denoised low-frequency trajectories and learn a Koopman operator to model the system dynamics in a linearized space. To model complex historical environments under non-stationarity, we design a context-informed heterogeneous pattern extraction mechanism. Specifically, we employ a target-conditioned attention module to attend to distinct past windows, producing a dynamic, target-specific historical summary. By constructing an environmental signature from the current evolutionary pattern, our model adaptively perceives which aspects of the past context are most informative for future prediction via a learned router. Extensive experiments on eight diverse classification and regression benchmarks demonstrate that AdaSpecK achieves state-of-the-art performance. The code and datasets are available at hrefhttps://anonymous.4open.science/r/Ada-Spec-K.