mlsanityData to 14 Oct 2026

Neural Koopman prior for data assimilation

arXiv 2309.05317 ↗First posted 11 Sep 2023cs.LGcited by 10

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Abstract (arXiv)

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 34 of its 71 references that are in the map. First posted on arXiv 11 Sep 2023.

Builds on

34 of 71 references.

References · 34

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22 more
  1. 2022Self-supervised Learning in Remote Sensing: A Reviewcited by 137
  2. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 127
  3. 2020Forecasting Sequential Data using Consistent Koopman Autoencoderscited by 115
  4. 2019Data-driven approximation of the Koopman generator: Model reduction, system identification, and controlcited by 85
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  6. 2018Deep Dynamical Modeling and Control of Unsteady Fluid Flowscited by 68
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 2; 2026: 4.

10 papers.

  1. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 11
  2. 2025Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systemscited by 7
  3. 2024Learning Semilinear Neural Operators : A Unified Recursive Framework For Prediction And Data Assimilationcited by 4
  4. 2024KODA: A Data-Driven Recursive Model for Time Series Forecasting and Data Assimilation using Koopman Operatorscited by 4
  5. 2025Augmented Invertible Koopman Autoencoder for long-term time series forecastingcited by 4
  6. 2024Koopman Ensembles for Probabilistic Time Series Forecastingcited by 1
  7. 2026Pathwise Learning of Stochastic Dynamical Systems with Partial Observationscited by 1
  8. 2026ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiabilitycited by 1
  9. 2026Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecastingcited by 0
  10. 2026LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observationscited by 0