# Deep Learning of Turbulent Scalar Mixing

arXiv: https://arxiv.org/abs/1811.07095 · HTML: https://mlsanity.com/paper/1811.07095/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2018.

## Built on by (most cited first, 17 of 17)

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- [A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning](https://mlsanity.com/paper/2509.14198/) (2025)
- [Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs](https://mlsanity.com/paper/2505.17575/) (2025)
- [PINNs for the Solution of the Hyperbolic Buckley-Leverett Problem with a Non-convex Flux Function](https://mlsanity.com/paper/2112.14826/) (2021)
- [Physics-informed neural networks for improving cerebral hemodynamics predictions](https://mlsanity.com/paper/2108.11498/) (2021)
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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.