# Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts

arXiv: https://arxiv.org/abs/2210.03675 · HTML: https://mlsanity.com/paper/2210.03675/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 7 Oct 2022.

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

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [An introduction to domain adaptation and transfer learning](https://mlsanity.com/paper/1812.11806/) (2018)
- [Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks](https://mlsanity.com/paper/2107.07455/) (2021)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Meta-learning framework with applications to zero-shot time-series forecasting](https://mlsanity.com/paper/2002.02887/) (2020)
- [Domain Adaptation for Time Series Forecasting via Attention Sharing](https://mlsanity.com/paper/2102.06828/) (2021)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [Long Expressive Memory for Sequence Modeling](https://mlsanity.com/paper/2110.04744/) (2021)
- [Deep Learning of Koopman Representation for Control](https://mlsanity.com/paper/2010.07546/) (2020)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control](https://mlsanity.com/paper/1902.09742/) (2019)
- [Detecting and Adapting to Irregular Distribution Shifts in Bayesian Online Learning](https://mlsanity.com/paper/2012.08101/) (2020)
- [Learning Stable Koopman Embeddings](https://mlsanity.com/paper/2110.06509/) (2021)

## Built on by (most cited first, 30 of 37)

- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [Model scale versus domain knowledge in statistical forecasting of chaotic systems](https://mlsanity.com/paper/2303.08011/) (2023)
- [Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamics](https://mlsanity.com/paper/2402.12971/) (2024)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective](https://mlsanity.com/paper/2402.11463/) (2024)
- [Learning Robust Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2505.12585/) (2025)
- [LANISTR: Multimodal Learning from Structured and Unstructured Data](https://mlsanity.com/paper/2305.16556/) (2023)
- [Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems](https://mlsanity.com/paper/2507.07222/) (2025)
- [KODA: A Data-Driven Recursive Model for Time Series Forecasting and Data Assimilation using Koopman Operators](https://mlsanity.com/paper/2409.19518/) (2024)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting](https://mlsanity.com/paper/2502.12603/) (2025)
- [Deep Koopman operator framework for causal discovery in nonlinear dynamical systems](https://mlsanity.com/paper/2505.14828/) (2025)
- [SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting](https://mlsanity.com/paper/2506.14113/) (2025)
- [EventTSF: Event-Aware Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2508.13434/) (2025)
- [Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equations](https://mlsanity.com/paper/2311.04522/) (2023)
- [Hierarchical Ensemble-Based Feature Selection for Time Series Forecasting](https://mlsanity.com/paper/2310.17544/) (2023)
- [KoopAGRU: A Koopman-based Anomaly Detection in Time-Series using Gated Recurrent Units](https://mlsanity.com/paper/2501.17976/) (2025)
- [Wavelet-based Disentangled Adaptive Normalization for Non-stationary Times Series Forecasting](https://mlsanity.com/paper/2506.05857/) (2025)
- [DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecasting](https://mlsanity.com/paper/2508.02616/) (2025)
- [Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation](https://mlsanity.com/paper/2510.24216/) (2025)
- [Koopman Regularized Deep Speech Disentanglement for Speaker Verification](https://mlsanity.com/paper/2603.05577/) (2026)
- [Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction](https://mlsanity.com/paper/2605.12683/) (2026)
- [Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2606.22969/) (2026)
- [Learning the Koopman Operator using Attention Free Transformers](https://mlsanity.com/paper/2606.23957/) (2026)
- [A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems](https://mlsanity.com/paper/2607.14937/) (2026)

## Abstract (arXiv)

Temporal distributional shifts, with underlying dynamics changing over time, frequently occur in real-world time series and pose a fundamental challenge for deep neural networks (DNNs). In this paper, we propose a novel deep sequence model based on the Koopman theory for time series forecasting: Koopman Neural Forecaster (KNF) which leverages DNNs to learn the linear Koopman space and the coefficients of chosen measurement functions. KNF imposes appropriate inductive biases for improved robustness against distributional shifts, employing both a global operator to learn shared characteristics and a local operator to capture changing dynamics, as well as a specially-designed feedback loop to continuously update the learned operators over time for rapidly varying behaviors. We demonstrate that ours achieves superior performance compared to the alternatives, on multiple time series datasets that are shown to suffer from distribution shifts.