Conformal Online Learning of Deep Koopman Linear Embeddings
Ben Gao, Jordan Patracone, Olivier Alata, Stephane Chretien
We introduce Conformal Online Learning (COL), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multi-step prediction consistency in the lifted space, where the dynamics evolve linearly. To prevent overfitting, COL 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 calibrated threshold, allowing selective refinement of the Koopman operator and embedding. Empirical results on benchmark dynamical systems demonstrate the effectiveness of COL in maintaining long-term predictive accuracy while significantly reducing unnecessary updates.