Conformal Online Learning of Deep Koopman Linear Embeddings
This addresses the challenge of efficient and robust online learning in dynamical systems modeling, which is incremental as it builds on existing Koopman embedding methods.
The paper tackles the problem of adaptively updating Koopman-invariant representations for nonlinear dynamical systems from streaming data, resulting in maintained long-term predictive accuracy with reduced unnecessary updates and overfitting avoidance.
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.