Turbulence is an exceptionally complex and high-dimensional phenomena, exhibiting spatio-temporal dynamics, non-linearity and chaos. In an era where vast quantities of such DNS data are generated; building practical, physics-driven reduced order models (ROM) of such phenomena are crucial. While Deep neural networks for spatio-temporal data have shown considerable promise, they face severe computational bottlenecks in learning extremely high dimensional datasets, often with > 10^9 degrees of freedom. These application-agnostic networks may also lack physical constraints and interpretability that is desired in scientific ROMs. In this work, we present our efforts in integrating the strong mathematical and physical foundations underlying numerical methods and wavelet theory with deep neural networks. In this talk, we demonstrate computationally efficient learning of 3D turbulence with embedded physics constraints for improved interpretability and physics guarantees, and outline ongoing efforts.
Dr. Arvind Mohan is a Postdoctoral Researcher in the Center for Nonlinear Studies and the Computational Physics and Methods group at Los Alamos National Laboratory. He obtained his PhD in Aeronautical and Astronautical Engineering from The Ohio State University with research in Computational Fluid Dynamics, data-driven aerodynamics and stall failure for aircraft wings. His current research is focused on embedding domain knowledge and physics for deep learning algorithms in turbulence and fluid mechanics, with high-performance computing. His other research efforts are deep learning collaborations at Los Alamos in nuclear physics, earth sciences, and astrophysics. Dr. Mohan has also organized two international conferences in physics-informed machine learning at LANL, with hundreds of attendees from all over the globe. He has consistently presented his work at leading engineering, physics and machine learning conferences such as AIAA, APS, and NeurIPS among others.