mlsanityData to 14 Oct 2026

Data-driven Discovery of Closure Models

arXiv 1803.09318 ↗First posted 25 Mar 2018math.DS nlin.CD stat.MLcited by 20

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Abstract (arXiv)

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this work, we present a framework of operator inference to extract the governing dynamics of closure from data in a compact, non-Markovian form. We employ sparse polynomial regression and artificial neural networks to extract the underlying operator. For a special class of non-linear systems, observability of the closure in terms of the resolved dynamics is analyzed and theoretical results are presented on the compactness of the memory. The proposed framework is evaluated on examples consisting of linear to nonlinear systems with and without chaotic dynamics, with an emphasis on predictive performance on unseen data.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 Mar 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 3; 2024: 2; 2025: 2; 2026: 3.

20 papers.

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  1. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  2. 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 58
  3. 2022Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal datacited by 37
  4. 2024On the Benefits of Memory for Modeling Time-Dependent PDEscited by 31
  5. 2022Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation datacited by 18
  6. 2021Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inferencecited by 16
  7. 2023Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equationscited by 13
  8. 2023A Multifidelity deep operator network approach to closure for multiscale systemscited by 11
  9. 2022Deep Learning of Chaotic Systems from Partially-Observed Datacited by 9
  10. 2023Generalized Neural Closure Models with Interpretabilitycited by 8
  11. 2021Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectoriescited by 5
  12. 2021Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Ito Diffusionscited by 5
8 more
  1. 2022Physics Guided Machine Learning for Variational Multiscale Reduced Order Modelingcited by 4
  2. 2024Systematic construction of continuous-time neural networks for linear dynamical systemscited by 1
  3. 2025Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulationscited by 1
  4. 2022Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systemscited by 0
  5. 2025Attention-Enhanced Convolutional Autoencoder and Structured Delay Embeddings for Weather Predictioncited by 0
  6. 2026The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flowscited by 0
  7. 2026Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEscited by 0
  8. 2026Counterfactual Predictions in Scientific Emulators Without Controlled Experimentscited by 0