在线更新非线性系统表示，减少无效调整并防止过拟合
Conformal Online Learning of Deep Koopman Linear Embeddings
- 结合深度特征学习与升维空间的多步预测一致性
- 仅当预测误差超动态阈值时才更新模型，减少冗余调整
- 适合需要长期稳定预测的实时系统建模
我们提出一种名为COLoKe的新框架，用于从流式数据中自适应更新非线性动力系统的柯普曼不变表示。该方法将深度特征学习与升维空间中的多步预测一致性相结合，使动力学在升维空间中呈线性演化。为防止过拟合，COLoKe采用类似置信区间的方法，不再关注新状态的符合度，而是评估当前柯普曼模型的一致性。仅当当前模型预测误差超过动态校准的阈值时才触发更新，从而实现对柯普曼算子和嵌入的有选择性优化。在基准动力系统上的实验表明，COLoKe能有效保持长期预测精度，显著减少不必要的更新并避免过拟合。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。