mlsanityData to 7 Oct 2026

CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation

arXiv 2410.20072 ↗First posted 26 Oct 2024cs.LG math.DScited by 7

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Abstract (arXiv)

Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data assimilation (DA), which is a crucial technique for state estimation, model identification, and reconstructing missing data. Integrating ensemble-based DA methods with nonlinear deep learning models is computationally expensive and may suffer from large sampling errors. To address these challenges, we introduce a deep learning framework designed to simultaneously provide accurate forecasts and efficient DA. It is named Conditional Gaussian Koopman Network (CGKN), which transforms general nonlinear systems into nonlinear neural differential equations with conditional Gaussian structures. CGKN aims to retain essential nonlinear components while applying systematic and minimal simplifications to facilitate the development of analytic formulae for nonlinear DA. This allows for seamless integration of DA performance into the deep learning training process, eliminating the need for empirical tuning as required in ensemble methods. CGKN compensates for structural simplifications by lifting the dimension of the system, which is motivated by Koopman theory. Nevertheless, CGKN exploits special nonlinear dynamics within the lifted space. This enables the model to capture extreme events and strong non-Gaussian features in joint and marginal distributions with appropriate uncertainty quantification. We demonstrate the effectiveness of CGKN for both prediction and DA on three strongly nonlinear and non-Gaussian turbulent systems: the projected stochastic Burgers-Sivashinsky equation, the Lorenz 96 system, and the El Ni~no-Southern Oscillation. The results justify the robustness and computational efficiency of CGKN.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 29 of its 118 references that are in the map. First posted on arXiv 26 Oct 2024.

Builds on

29 of 118 references.

References · 29

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17 more
  1. 2019How Entropic Regression Beats the Outliers Problem in Nonlinear System Identificationcited by 14
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 5; 2026: 2.

7 papers.

  1. 2025Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Networkcited by 6
  2. 2025Active Learning of Model Discrepancy with Bayesian Experimental Designcited by 5
  3. 2025RL-DAUNCE: Reinforcement Learning-Driven Data Assimilation with Uncertainty-Aware Constrained Ensemblescited by 2
  4. 2025Uncertainty Propagation Networks for Neural Ordinary Differential Equationscited by 1
  5. 2026Pathwise Learning of Stochastic Dynamical Systems with Partial Observationscited by 1
  6. 2025DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecastingcited by 0
  7. 2026Omega: Operator-based Mixture Ensemble for Generative Assimilationcited by 0