Conformal Online Learning of Deep Koopman Linear Embeddings

TL;DR

COLoKe is a novel framework that adaptively updates Koopman embeddings for nonlinear dynamical systems using conformal methods, improving long-term prediction accuracy and reducing overfitting in streaming data scenarios.

Contribution

It introduces a conformal online learning approach for Koopman embeddings, combining deep feature learning with adaptive updates based on prediction error thresholds.

Findings

Effective long-term predictions on benchmark systems.

Reduces unnecessary model updates and overfitting.

Maintains high accuracy with streaming data.

Abstract

We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multistep prediction consistency in the lifted space, where the dynamics evolve linearly. To prevent overfitting, COLoKe employs a conformal-style mechanism that shifts the focus from evaluating the conformity of new states to assessing the consistency of the current Koopman model. Updates are triggered only when the current model's prediction error exceeds a dynamically calibrated threshold, allowing selective refinement of the Koopman operator and embedding. Empirical results on benchmark dynamical systems demonstrate the effectiveness of COLoKe in maintaining long-term predictive accuracy while significantly reducing unnecessary updates and avoiding overfitting.