mlsanityData to 13 Oct 2026

Parametric Learning of Time-Advancement Operators for Unstable Flame Evolution

arXiv 2402.10238 ↗First posted 14 Feb 2024cs.LGcited by 5

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Abstract (arXiv)

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier-Stokes equations.

Key facts. Cited by 5 papers in the map (data through 13 Oct 2026). Builds on 12 of its 50 references that are in the map. First posted on arXiv 14 Feb 2024.

Builds on

12 of 50 references.

References · 12

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,656
  2. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,457
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,857
  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,989
  5. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 766
  6. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 728
  7. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  8. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
  9. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  10. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
  11. 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 145
  12. 2023Nonlocality and Nonlinearity Implies Universality in Operator Learningcited by 43

Built on by

Cited by year (2026 to 13 Oct)

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

5 papers.

  1. 2026CompNO: A Novel Foundation Model approach for solving Partial Differential Equationscited by 5
  2. 2024Learning Flame Evolution Operator under Hybrid Darrieus Landau and Diffusive Thermal Instabilitycited by 1
  3. 2025Data-driven quantum Koopman method for simulating nonlinear dynamicscited by 1
  4. 2025An Inverse Scattering Inspired Fourier Neural Operator for Time-Dependent PDE Learningcited by 1
  5. 2026Compositional Neural Operators for Multi-Dimensional Fluid Dynamicscited by 0