# Meta-Learning for Koopman Spectral Analysis with Short Time-series

arXiv: https://arxiv.org/abs/2102.04683 · HTML: https://mlsanity.com/paper/2102.04683/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 61 references that are in the map.
- First posted on arXiv 9 Feb 2021.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [A Survey on Deep Transfer Learning](https://mlsanity.com/paper/1808.01974/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Transfer Learning from Speaker Verification to Multispeaker Text-To-Speech Synthesis](https://mlsanity.com/paper/1806.04558/) (2018)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks](https://mlsanity.com/paper/1810.00825/) (2018)
- [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)
- [Meta-learning framework with applications to zero-shot time-series forecasting](https://mlsanity.com/paper/2002.02887/) (2020)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [MetaFun: Meta-Learning with Iterative Functional Updates](https://mlsanity.com/paper/1912.02738/) (2019)
- [Robust and Efficient Transfer Learning with Hidden-Parameter Markov Decision Processes](https://mlsanity.com/paper/1706.06544/) (2017)
- [Few-shot Learning for Time-series Forecasting](https://mlsanity.com/paper/2009.14379/) (2020)
- [Recurrent Attentive Neural Process for Sequential Data](https://mlsanity.com/paper/1910.09323/) (2019)
- [Recurrent Neural Processes](https://mlsanity.com/paper/1906.05915/) (2019)
- [Energy Predictive Models with Limited Data using Transfer Learning](https://mlsanity.com/paper/1906.02646/) (2019)
- [Zero-shot Domain Adaptation without Domain Semantic Descriptors](https://mlsanity.com/paper/1807.02927/) (2018)

## Built on by (most cited first, 1 of 1)

- [Multi-Task Learning of Conditional Mean Operators: applications to dynamical systems and uncertainty quantification](https://mlsanity.com/paper/2609.35429/) (2026)

## Abstract (arXiv)

Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find appropriate embedding functions. Although several neural network-based methods have been proposed for learning embedding functions, existing methods require long time-series for training neural networks. This limitation prohibits performing Koopman spectral analysis in applications where only short time-series are available. In this paper, we propose a meta-learning method for estimating embedding functions from unseen short time-series by exploiting knowledge learned from related but different time-series. With the proposed method, a representation of a given short time-series is obtained by a bidirectional LSTM for extracting its properties. The embedding function of the short time-series is modeled by a neural network that depends on the time-series representation. By sharing the LSTM and neural networks across multiple time-series, we can learn common knowledge from different time-series while modeling time-series-specific embedding functions with the time-series representation. Our model is trained such that the expected test prediction error is minimized with the episodic training framework. We experimentally demonstrate that the proposed method achieves better performance in terms of eigenvalue estimation and future prediction than existing methods.