Conformal Online Learning of Deep Koopman Linear Embeddings

2025-11-16

AI Summary

To address the degradation of long-term forecasting accuracy for nonlinear dynamical systems under streaming data, this paper proposes an online learning framework that adaptively updates Koopman-invariant representations. The method integrates deep feature learning with Koopman operator theory and introduces a multi-step prediction consistency regularization. Crucially, it devises a novel conformal consistency test: model updates are triggered only when prediction errors exceed a dynamically calibrated threshold. This mechanism effectively suppresses redundant updates and overfitting. Experiments on multiple benchmark dynamical systems demonstrate that the proposed approach achieves superior long-term prediction accuracy—averaging a 12.7% improvement—while reducing update frequency by up to 68%. Moreover, it significantly enhances model stability and generalization capability under continuous data streams.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Adaptively updating Koopman-invariant representations from streaming data
• Preventing overfitting in nonlinear dynamical system modeling
• Maintaining predictive accuracy while reducing unnecessary model updates

Innovation

• Conformal online learning updates Koopman embeddings adaptively
• Combines deep features with multistep prediction consistency
• Triggers updates when error exceeds dynamic threshold