Enhancing Computational Fluid Dynamics with Machine Learning

Abstract

In this video we discuss the recent article published in Nature Computational Science by Ricardo Vinuesa and Steve Brunton, where the potential of machine learning (ML) to improve numerical simulations of fluid flows is discussed. In particular, we show the possibilities enabled by ML in the context of 1) accelerating direct numerical simulations (DNSs); 2) improving turbulence modeling for large-eddy simulations (LESs) and Reynolds-averaged Navier–Stokes (RANS) simulations; and also enhancing the development of reduced-order models (ROMs). Focusing on the latter, we describe a deep-learning framework for learning a minimal and near-orthogonal set of non-linear modes in the context of turbulent flows. In particular, we focus on a high-fidelity numerical database of a simplified urban environment. The proposed technique relies on β-variational autoencoders (β-VAEs) and convolutional neural networks (CNNs), which enable extracting non-linear modes while encouraging the learning of statistically-independent latent variables and penalizing the size of the latent vector. We demonstrate that by constraining the shape of the latent space, it is possible to motivate orthogonality and extract a set of parsimonious modes which enable high-quality reconstruction. This method exhibits an excellent performance in the reconstruction against linear-theory-based decompositions, where the energy percentage captured by the proposed method from five modes is equal to 87.36% against 32.41% from proper-orthogonal decomposition (POD).