Deep Learning for Efficient Modeling of High Dimensional Spatiotemporal Physics
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.