# Multi-Task Learning based Convolutional Models with Curriculum Learning for the Anisotropic Reynolds Stress Tensor in Turbulent Duct Flow

arXiv: https://arxiv.org/abs/2111.00328 · HTML: https://mlsanity.com/paper/2111.00328/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 75 references that are in the map.
- First posted on arXiv 30 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Understanding and Improving Information Transfer in Multi-Task Learning](https://mlsanity.com/paper/2005.00944/) (2020)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Trace Norm Regularised Deep Multi-Task Learning](https://mlsanity.com/paper/1606.04038/) (2016)
- [Massively Multitask Networks for Drug Discovery](https://mlsanity.com/paper/1502.02072/) (2015)
- [Multi-directional Geodesic Neural Networks via Equivariant Convolution](https://mlsanity.com/paper/1810.02303/) (2018)
- [Learning rotation invariant convolutional filters for texture classification](https://mlsanity.com/paper/1604.06720/) (2016)
- [A Brief Review of Deep Multi-task Learning and Auxiliary Task Learning](https://mlsanity.com/paper/2007.01126/) (2020)
- [A Survey on Curriculum Learning](https://mlsanity.com/paper/2010.13166/) (2020)
- [Geodesic convolutional neural networks on Riemannian manifolds](https://mlsanity.com/paper/1501.06297/) (2015)

## Built on by (most cited first, 1 of 1)

- [Airfoil2Vec: Spectral Geometry-Conditioned Neural Surrogate Models for Airfoil Aerodynamics and a Downforce-Generating CFD Dataset](https://mlsanity.com/paper/2609.38213/) (2026)

## Abstract (arXiv)

The Reynolds-averaged Navier-Stokes (RANS) equations require accurate modeling of the anisotropic Reynolds stress tensor. Traditional closure models, while sophisticated, often only apply to restricted flow configurations. Researchers have started using machine learning approaches to tackle this problem by developing more general closure models informed by data. In this work we build upon recent convolutional neural network architectures used for turbulence modeling and propose a multi-task learning-based fully convolutional neural network that is able to accurately predict the normalized anisotropic Reynolds stress tensor for turbulent duct flows. Furthermore, we also explore the application of curriculum learning to data-driven turbulence modeling.