arXiv：cs.LG· Joel-Pascal Ntwali N'konzi, Feliks N\"{u}ske, Stefan Klus·· 3 小时前
EDMD-kDL：用核自编码器与双层优化从数据中学习 Koopman 嵌入
Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders
AI 导读
研究人员提出 EDMD-kDL，一种基于核方法的 Koopman 嵌入学习框架，通过结合配点法与双层优化，同时学习核字典与对应的 Koopman 近似，无需预先指定字典。在全球海表温度预测和直接从视频数据学习等数值实验中，EDMD-kDL 的表现与基于 ANN 的先进方法相当或更优。该方法具备良好的可扩展性，其核矩阵规模取决于配点数量而非训练数据集大小。
正文
Abstract:Koopman operator theory provides a linear framework for analyzing nonlinear dynamical systems and has become a major tool for data-driven modeling. A central challenge, however, is that finite-dimensional approximations computed by methods such as extended dynamic mode decomposition (EDMD) require the dictionary to be specified a priori. Recent machine-learning approaches address this limitation by learning the dictionary from data, predominantly using artificial neural network (ANN) autoencoder architectures. Although kernel methods offer an alternative with greater interpretability and tractability for theoretical analysis, they have received little attention in this setting. We introduce extended dynamic mode decomposition with kernel-based dictionary learning (EDMD-kDL), a kernel-based method for learning finite-dimensional Koopman embeddings directly from data. The method combines ideas from collocation methods and bilevel optimization to simultaneously learn a kernel dictionary and the corresponding Koopman approximation. We evaluate EDMD-kDL against state-of-the-art ANN-based approaches on a range of numerical experiments, including global sea-surface-temperature forecasting and learning directly from video data. Across all tested settings, EDMD-kDL achieves performance comparable to or better than the ANN-based methods. Moreover, in contrast to standard kernel methods, the proposed approach is scalable to large datasets by design since the size of the required kernel matrices depends on the number of collocation points rather than the size of the training dataset.
| Subjects: | Machine Learning (cs.LG); Dynamical Systems (math.DS); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.12370 [cs.LG] |
| (or arXiv:2610.12370v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12370 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Joel-Pascal Ntwali N'konzi [view email]
[v1]
Thu, 8 Oct 2026 17:30:23 UTC (10,226 KB)
来源：arXiv：cs.LG · arxiv.org