Koopman Learning with Episodic Memory
arXiv:2311.12615 · doi:10.1063/5.0245244
Abstract
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to traditional machine learning methodologies, make Koopman learning an especially appealing approach. Despite this, little work has been performed on endowing Koopman learning with the ability to leverage its own failures. To address this, we equip Koopman methods -- developed for predicting non-autonomous time-series -- with an episodic memory mechanism, enabling global recall of (or attention to) periods in time where similar dynamics previously occurred. We find that a basic implementation of Koopman learning with episodic memory leads to significant improvements in prediction on synthetic and real-world data. Our framework has considerable potential for expansion, allowing for future advances, and opens exciting new directions for Koopman learning.
17 pages, 7 figures
References in corpus (19)
- Neural Machine Translation by Jointly Learning to Align and Translate
- A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
- On Dynamic Mode Decomposition: Theory and Applications
- Deep learning for universal linear embeddings of nonlinear dynamics
- Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
- Chaos as an Intermittently Forced Linear System
- A Time Series is Worth 64 Words: Long-term Forecasting with Transformers
- Ergodic theory, Dynamic Mode Decomposition and Computation of Spectral Properties of the Koopman operator
- Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator
- Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
- Transformers for Modeling Physical Systems
- Adaptive, locally-linear models of complex dynamics
- Delay-coordinate maps and the spectra of Koopman operators
- Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors
- Non-stationary Online Learning with Memory and Non-stochastic Control
- Identifying Equivalent Training Dynamics
- Koopman Reduced Order Modeling with Confidence Bounds
- Learning Nonautonomous Systems via Dynamic Mode Decomposition
- Delay Embedding Theory of Neural Sequence Models