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Conformal Online Learning of Deep Koopman Linear Embeddings

arXiv 2511.12760 ↗First posted 16 Nov 2025cs.LG stat.MLcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 25 of its 49 references that are in the map. First posted on arXiv 16 Nov 2025.

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References · 25

  1. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  2. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 792
  3. 2019Conformalized Quantile Regressioncited by 629
  4. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  5. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 375
  6. 2021Modern Koopman Theory for Dynamical Systemscited by 276
  7. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 158
  8. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 145
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  10. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 127
  11. 2023Conformal PID Control for Time Series Predictioncited by 88
  12. 2023Improved Online Conformal Prediction via Strongly Adaptive Online Learningcited by 78
13 more
  1. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 67
  2. 2017Time-lagged autoencoders: Deep learning of slow collective variables for molecular kineticscited by 65
  3. 2023Sharp Spectral Rates for Koopman Operator Learningcited by 36
  4. 2019Online Non-Convex Learning: Following the Perturbed Leader is Optimalcited by 32
  5. 2020Kernel-based approximation of the Koopman generator and Schr"odinger operatorcited by 31
  6. 2017Online dynamic mode decomposition for time-varying systemscited by 23
  7. 2022Deep Koopman Learning of Nonlinear Time-Varying Systemscited by 11
  8. 2025ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residualscited by 6
  9. 2022Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approachcited by 3
  10. 2019Online Learning of Dynamical Systems: An Operator Theoretic Approachcited by 2
  11. 2021Online Learning Koopman operator for closed-loop electrical neurostimulation in epilepsycited by 2
  12. 2021Finite-time Koopman Identifier: A Unified Batch-online Learning Framework for Joint Learning of Koopman Structure and Parameterscited by 1
  13. 2024Online learning of Koopman operator using streaming data from different dynamical regimescited by 1

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