mlsanityData to 7 Oct 2026

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

arXiv 2302.12682 ↗First posted 24 Feb 2023math.NA cs.LG cs.NAcited by 14

Not on the map. Why?

Abstract (arXiv)

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 20 of its 87 references that are in the map. First posted on arXiv 24 Feb 2023.

Builds on

20 of 87 references.

References · 20

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2018Survey of multifidelity methods in uncertainty propagation, inference, and optimizationcited by 141
  5. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  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. 2020Multi-fidelity Bayesian Neural Networks: Algorithms and Applicationscited by 59
  8. 2017Data-Driven Sparse Sensor Placement for Reconstructioncited by 57
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8 more
  1. 2018Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decompositioncited by 14
  2. 2021The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equationscited by 14
  3. 2014Progressive construction of a parametric reduced-order model for PDE-constrained optimizationcited by 13
  4. 2021PySensors: A Python Package for Sparse Sensor Placementcited by 8
  5. 2020A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problemscited by 6
  6. 2022Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximationcited by 4
  7. 2021Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secantscited by 3
  8. 2022Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantificationcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 2; 2026: 6.

14 papers.

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  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2023A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Samplingcited by 10
  3. 2023Generative Adversarial Reduced Order Modellingcited by 7
  4. 2025Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsamplingcited by 5
  5. 2024Alpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantificationcited by 4
  6. 2024Multifidelity linear regression for scientific machine learning from scarce datacited by 3
  7. 2025PODNO: Proper Orthogonal Decomposition Neural Operatorscited by 2
  8. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  9. 2024Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networkscited by 1
  10. 2026Multifidelity Surrogate Modeling of Depressurized Loss of Forced Cooling in High-temperature Gas Reactorscited by 1
  11. 2026Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurementscited by 1
  12. 2026The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositionscited by 0
2 more
  1. 2026Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applicationscited by 0
  2. 2026A Residual Learning Approach for Unsteady Aerodynamic Load Predictioncited by 0