Machine learning and fluid mechanics

Recently Physical Review Fluids published an invited op-ed, "Perspective on machine learning for advancing fluid mechanics" by Brenner, Eldredge, and Freund.  As one who has dabbled in both fields, I found their comments illuminating and balanced, conveying both astonishment and excitement at the achievements and potential of machine learning methodology, as well as its potential pitfalls and limitations.  I share their astonishment that in some cases, deep neural networks have been able to generalize beyond the training data.  This remains an ill-understood phenomenon.  We do not know under what circumstances such generalization can reliably occur, and I believe any such claims about these generalizations must be validated with independent data sets.  Regardless, however, I am in broad agreement with the authors' views, including their conclusion that machine learning methods have potential for high impact "so long as outcomes are held to the long-standing critical standards that should guide studies of flow physics."

Reference

M. P. Brenner, J. D. Eldredge, and J. B. Freund, 2019:  Perspective on machine learning for advancing fluid mecanics.  Physical Review Fluids, 4:  100501 (7 pages).