I wrote a couple previous posts on some interesting work using

deep learning to accelerate topology optimization, and a couple

neural network methods for accelerating computational fluid dynamics (with

source). This post is about a use of machine learning in computational fluid dynamics (CFD) with a slightly different goal: to improve the quality of solutions. Rather than a focus on getting to solutions more

*quickly*, this post covers work focused on getting

*better* solutions. A better solution is one that has more predictive capability. There is usually a trade-off between predictive capability, and how long it takes to get a solution. The most well-known area for improvement in predictive capability of state-of-the-practice, industrial CFD is in our turbulence and transition modeling. There are a proliferation of approaches to tackling that problem, but the overall strategy that seems to be paying off is for CFD'ers to follow the enormous investment being made by the large tech companies in techniques, open source libraries, and services for machine learning. How can those free / low-cost tools and techniques be applied to our problems?

The authors of

Machine Learning Models of Errors in Large Eddy Simulation Predictions of Surface Pressure Fluctuations used machine learning techniques to model the error in their LES solutions. See an illustration of the instantaneous density gradient magnitude of the developing boundary layer from that paper shown to the right. Here's the abstract,

We investigate a novel application of deep neural networks to modeling of errors in prediction of surface pressure fluctuations beneath a compressible, turbulent flow. In this context, the truth solution is given by Direct Numerical Simulation (DNS) data, while the predictive model is a wall-modeled Large Eddy Simulation (LES

). The neural network provides a means to map relevant statistical flow-features within the LES solution to errors in prediction of wall pressure spectra. We simulate a number of flat plate turbulent boundary layers using both DNS and wall-modeled LES to build up a database with which to train the neural network. We then apply machine learning techniques to develop an optimized neural network model for the error in terms of relevant flow features