mlsanityData to 14 Oct 2026

A Multifidelity deep operator network approach to closure for multiscale systems

arXiv 2303.08893 ↗First posted 15 Mar 2023physics.comp-ph cs.LG cs.NAcited by 11

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Abstract (arXiv)

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due to the improper accounting of the interaction between the resolved and unresolved scales of the multiscale system (known as the closure problem). In the current work, we interpret closure as a multifidelity problem and use a multifidelity deep operator network (DeepONet) framework to address it. In addition, to enhance the stability and accuracy of the multifidelity-based closure, we employ the recently developed "in-the-loop" training approach from the literature on coupling physics and machine learning models. The resulting approach is tested on shock advection for the one-dimensional viscous Burgers equation and vortex merging using the two-dimensional Navier-Stokes equations. The numerical experiments show significant improvement of the predictive ability of the closure-corrected PROM over the un-corrected one both in the interpolative and the extrapolative regimes.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 18 of its 68 references that are in the map. First posted on arXiv 15 Mar 2023.

Builds on

18 of 68 references.

References · 18

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  4. 2021Machine learning accelerated computational fluid dynamicscited by 471
  5. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 205
  6. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  7. 2021Improved architectures and training algorithms for deep operator networkscited by 86
  8. 2021Physics-based Deep Learningcited by 68
  9. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  10. 2022Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equationscited by 56
  11. 2022Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systemscited by 50
  12. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
6 more
  1. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
  2. 2020Neural Closure Models for Dynamical Systemscited by 22
  3. 2018Data-driven Discovery of Closure Modelscited by 20
  4. 2020On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flowscited by 6
  5. 2021On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifoldscited by 6
  6. 2021On the Stochastic Stability of Deep Markov Modelscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 4; 2024: 1; 2025: 4; 2026: 2.

11 papers.

  1. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  2. 2023PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformerscited by 16
  3. 2023A multifidelity approach to continual learning for physical systemscited by 13
  4. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 6
  5. 2024Multifidelity linear regression for scientific machine learning from scarce datacited by 3
  6. 2025Stabilizing PDE--ML coupled systemscited by 1
  7. 2025Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systemscited by 1
  8. 2025Bridging quantum and classical computing for partial differential equations through multifidelity machine learningcited by 1
  9. 2023A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systemscited by 0
  10. 2026Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flowscited by 0
  11. 2026From Classification to Regression: Using a Fruitfly to Solve Equationscited by 0