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.

翻译：本文提出了保形在线学习库普曼嵌入（COLoKe）框架，这是一种从流数据中自适应更新非线性动力系统库普曼不变表示的新方法。我们的建模方法将深度特征学习与提升空间中的多步预测一致性相结合，其中动力学呈线性演化。为防止过拟合，COLoKe采用了一种保形式机制，该机制将评估重点从新状态的符合性转向评估当前库普曼模型的一致性。仅当当前模型的预测误差超过动态校准的阈值时才会触发更新，从而实现对库普曼算子与嵌入的选择性优化。在基准动力系统上的实证结果表明，COLoKe在保持长期预测精度的同时，能显著减少不必要的更新并避免过拟合。