Forecasting Sequential Data Using Consistent Koopman Autoencoders

Omri Azencot, N. Benjamin Erichson, Vanessa Lin, Michael Mahoney
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:475-485, 2020.

Abstract

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-azencot20a, title = {Forecasting Sequential Data Using Consistent Koopman Autoencoders}, author = {Azencot, Omri and Erichson, N. Benjamin and Lin, Vanessa and Mahoney, Michael}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {475--485}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/azencot20a/azencot20a.pdf}, url = {https://proceedings.mlr.press/v119/azencot20a.html}, abstract = {Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.} }
Endnote
%0 Conference Paper %T Forecasting Sequential Data Using Consistent Koopman Autoencoders %A Omri Azencot %A N. Benjamin Erichson %A Vanessa Lin %A Michael Mahoney %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-azencot20a %I PMLR %P 475--485 %U https://proceedings.mlr.press/v119/azencot20a.html %V 119 %X Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.
APA
Azencot, O., Erichson, N.B., Lin, V. & Mahoney, M.. (2020). Forecasting Sequential Data Using Consistent Koopman Autoencoders. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:475-485 Available from https://proceedings.mlr.press/v119/azencot20a.html.

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