mlsanityData to 13 Oct 2026

Multi-fidelity wavelet neural operator with application to uncertainty quantification

arXiv 2208.05606 ↗First posted 11 Aug 2022cs.LG physics.comp-phcited by 12

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Abstract (arXiv)

Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in the field of applied machine learning. Although these frameworks are extremely capable when it comes to modeling complex phenomena, they require an extensive amount of data for successful training which is often not available or is too expensive. However, this issue can be alleviated with the use of multi-fidelity learning, where a model is trained by making use of a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. To this end, we develop a new framework based on the wavelet neural operator which is capable of learning from a multi-fidelity dataset. The developed model's excellent learning capabilities are demonstrated by solving different problems which require effective correlation learning between the two fidelities for surrogate construction. Furthermore, we also assess the application of the developed framework for uncertainty quantification. The results obtained from this work illustrate the excellent performance of the proposed framework.

Key facts. Cited by 12 papers in the map (data through 13 Oct 2026). Builds on 19 of its 45 references that are in the map. First posted on arXiv 11 Aug 2022.

Builds on

19 of 45 references.

References · 19

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,857
  2. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 728
  3. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  4. 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
  5. 2022Wavelet neural operator: a neural operator for parametric partial differential equationscited by 77
  6. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
  7. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  8. 2022Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Networkcited by 45
  9. 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
  10. 2016Inferring solutions of differential equations using noisy multi-fidelity datacited by 38
  11. 2021Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domainscited by 37
  12. 2018A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factorscited by 30
7 more
  1. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
  2. 2020On transfer learning of neural networks using bi-fidelity data for uncertainty propagationcited by 26
  3. 2021Latent Map Gaussian Processes for Mixed Variable Metamodelingcited by 23
  4. 2021Transfer Learning on Multi-Fidelity Datacited by 18
  5. 2021Neural Network Training Using ℓ1-Regularization and Bi-fidelity Datacited by 16
  6. 2021Data Fusion with Latent Map Gaussian Processescited by 16
  7. 2022Deep Capsule Encoder-Decoder Network for Surrogate Modeling and Uncertainty Quantificationcited by 2

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 7; 2024: 2; 2025: 2.

12 papers.

  1. 2023Physics informed WNOcited by 27
  2. 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twincited by 19
  3. 2022Adaptive physics-informed neural operator for coarse-grained non-equilibrium flowscited by 7
  4. 2023Randomized prior wavelet neural operator for uncertainty quantificationcited by 4
  5. 2024Neural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equationscited by 4
  6. 2023Enhanced multi-fidelity modelling for digital twin and uncertainty quantificationcited by 2
  7. 2023DPA-WNO: A gray box model for a class of stochastic mechanics problemcited by 2
  8. 2024Generative flow induced neural architecture search: Towards discovering optimal architecture in wavelet neural operatorcited by 2
  9. 2023Neuroscience inspired scientific machine learning (Part-2): Variable spiking wavelet neural operatorcited by 1
  10. 2025Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosionscited by 1
  11. 2023A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systemscited by 0
  12. 2025Discretization-independent operator learning for partial differential equationscited by 0