Deep Learning of Turbulent Scalar Mixing
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Abstract (arXiv)
Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatio-temporal measurements of the probability density function (PDF). The models are for the conditional expected diffusion and the conditional expected dissipation of a Fickian scalar described by its transported single-point PDF equation. The discovered model are appraised against exact solution derived by the amplitude mapping closure (AMC)/ Johnsohn-Edgeworth translation (JET) model of binary scalar mixing in homogeneous turbulence.
Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Nov 2018.
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Citing papers per year: 2021: 7; 2022: 3; 2023: 1; 2024: 3; 2025: 2; 2026: 1.
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- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
- 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
- 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
- 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
- 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
- 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generationcited by 28
- 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
- 2021Fast PDE-constrained optimization via self-supervised operator learningcited by 24
- 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
- 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
- 2024ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learningcited by 7
5 more
- 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learningcited by 6
- 2021PINNs for the Solution of the Hyperbolic Buckley-Leverett Problem with a Non-convex Flux Functioncited by 3
- 2025Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEscited by 3
- 2021Physics-informed neural networks for improving cerebral hemodynamics predictionscited by 1
- 2026Graph-Instructed Neural Networks for parametric problems with varying boundary conditionscited by 0
- 2026Graph-Instructed Neural Networks for parametric problems with varying boundary conditions9 Mar 2026
- 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning17 Sep 2025
- 2025Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs23 May 2025
- 2024ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning14 Dec 2024
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning17 Oct 2024
- 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications5 Jun 2024
- 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation14 Nov 2023
- 2022Partial Differential Equations Meet Deep Neural Networks: A Survey27 Oct 2022
- 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic13 Apr 2022
- 2022Respecting causality is all you need for training physics-informed neural networks14 Mar 2022
- 2021PINNs for the Solution of the Hyperbolic Buckley-Leverett Problem with a Non-convex Flux Function29 Dec 2021
- 2021Fast PDE-constrained optimization via self-supervised operator learning25 Oct 2021
5 more
- 2021Physics-informed neural networks for improving cerebral hemodynamics predictions25 Aug 2021
- 2021A novel meta-learning initialization method for physics-informed neural networks23 Jul 2021
- 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks2 Jul 2021
- 2021Long-time integration of parametric evolution equations with physics-informed DeepONets9 Jun 2021
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets19 Mar 2021
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
- 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
- 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
- 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
- 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
- 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
- 2021Fast PDE-constrained optimization via self-supervised operator learningcited by 24
- 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
- 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
- 2024ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learningcited by 7
- 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learningcited by 6
12 most cited of 16 All 16 (JSON)
- 2026Graph-Instructed Neural Networks for parametric problems with varying boundary conditions9 Mar 2026
- 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning17 Sep 2025
- 2025Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs23 May 2025
- 2024ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning14 Dec 2024
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning17 Oct 2024
- 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications5 Jun 2024
- 2022Partial Differential Equations Meet Deep Neural Networks: A Survey27 Oct 2022
- 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic13 Apr 2022
- 2022Respecting causality is all you need for training physics-informed neural networks14 Mar 2022
- 2021PINNs for the Solution of the Hyperbolic Buckley-Leverett Problem with a Non-convex Flux Function29 Dec 2021
- 2021Fast PDE-constrained optimization via self-supervised operator learning25 Oct 2021
- 2021Physics-informed neural networks for improving cerebral hemodynamics predictions25 Aug 2021
12 newest of 16 All 16 (JSON)