# Generalizing across Temporal Domains with Koopman Operators

arXiv: https://arxiv.org/abs/2402.07834 · HTML: https://mlsanity.com/paper/2402.07834/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 30 of 39)

- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [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)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [Domain Generalization for Object Recognition with Multi-task Autoencoders](https://mlsanity.com/paper/1508.07680/) (2015)
- [Domain Randomization and Pyramid Consistency: Simulation-to-Real Generalization without Accessing Target Domain Data](https://mlsanity.com/paper/1909.00889/) (2019)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [Feature-Critic Networks for Heterogeneous Domain Generalization](https://mlsanity.com/paper/1901.11448/) (2019)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [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)
- [Learning Invariant Representations and Risks for Semi-supervised Domain Adaptation](https://mlsanity.com/paper/2010.04647/) (2020)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [A Century of Portraits: A Visual Historical Record of American High School Yearbooks](https://mlsanity.com/paper/1511.02575/) (2015)
- [Domain Invariant Representation Learning with Domain Density Transformations](https://mlsanity.com/paper/2102.05082/) (2021)
- [Near-Optimal Linear Regression under Distribution Shift](https://mlsanity.com/paper/2106.12108/) (2021)
- [Multi-component Image Translation for Deep Domain Generalization](https://mlsanity.com/paper/1812.08974/) (2018)
- [AdaGraph: Unifying Predictive and Continuous Domain Adaptation through Graphs](https://mlsanity.com/paper/1903.07062/) (2019)

## Built on by (most cited first, 13 of 13)

- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [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)
- [Homophily Enhanced Graph Domain Adaptation](https://mlsanity.com/paper/2505.20089/) (2025)
- [Learning Time-Aware Causal Representation for Model Generalization in Evolving Domains](https://mlsanity.com/paper/2506.17718/) (2025)
- [Non-stationary Domain Generalization: Theory and Algorithm](https://mlsanity.com/paper/2405.06816/) (2024)
- [Full spectrum Unlearnable Examples via Spectral Equalization](https://mlsanity.com/paper/2606.26719/) (2026)
- [Continuous Domain Generalization](https://mlsanity.com/paper/2505.13519/) (2025)
- [Optimal Empirical Risk Minimization under Temporal Distribution Shifts](https://mlsanity.com/paper/2507.13287/) (2025)
- [Parameter-Efficient Temporal Domain Generalization](https://mlsanity.com/paper/2602.11965/) (2026)
- [Cross-Machine Anomaly Detection Leveraging Pre-trained Time-series Model](https://mlsanity.com/paper/2604.05335/) (2026)
- [FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2608.22224/) (2026)
- [Adaptive Spectral-Koopman Dynamics Modeling for Temporal Domain Generalization](https://mlsanity.com/paper/2610.02822/) (2026)

## Abstract (arXiv)

In the field of domain generalization, the task of constructing a predictive model capable of generalizing to a target domain without access to target data remains challenging. This problem becomes further complicated when considering evolving dynamics between domains. While various approaches have been proposed to address this issue, a comprehensive understanding of the underlying generalization theory is still lacking. In this study, we contribute novel theoretic results that aligning conditional distribution leads to the reduction of generalization bounds. Our analysis serves as a key motivation for solving the Temporal Domain Generalization (TDG) problem through the application of Koopman Neural Operators, resulting in Temporal Koopman Networks (TKNets). By employing Koopman Operators, we effectively address the time-evolving distributions encountered in TDG using the principles of Koopman theory, where measurement functions are sought to establish linear transition relations between evolving domains. Through empirical evaluations conducted on synthetic and real-world datasets, we validate the effectiveness of our proposed approach.