### Hidden Fluid Mechanics – (with JHU) DARPA/AIRA

**Full Title: **Hidden Fluid Mechanics: Discovering non-local closure models for wall-bounded turbulent and transitional flows using physics-informed neural networks (PINNs) (with Johns Hopkins University) sponsored by DARPA Artificial Intelligence Research Associate Program

**Abstract:** Predicting turbulence is still an open problem, a last frontier in classical physics. This project employs fractional operators in conjunction with physics-informed neural networks (PINNs) to discover new governing equations for modeling and simulating wall-bounded turbulent flows at high Reynolds number. The concept of the physics-informed learning machines (PhILMs), both for Gaussian process regression and for deep neural networks (DNN), has been developed by Karniadakis’s group. In particular, prior physics-based information in the form of conservation laws, physical principles, governing equations, initial/boundary conditions, and constraints (e.g., divergence-free condition) regularizes a learning machine in such a way that it can then learn from “small” and noisy data that could evolve in time. We have effectively applied PhILMs to a number of nonlinear problems ranging from fluid mechanics, to liquid mixing, combustion and quantum mechanics. We have demonstrated that PhILMs converge to accurate solutions of Partial Differential Equations (PDEs) by leveraging or discovering the “hidden physics” of the data without using any grids or discretization in space-time either for forward or for inverse problems. Moreover, PhILMs can effectively solve ill-posed (in the classical sense) forward and inverse problems, where no boundary conditions are specified or some of the parameters in the PDEs are unknown — scenarios where classical numerical methods may fail. Here, we aim to discover non-local functional relationships for Reynolds Averaged Navier-Stokes equations (RANS) and for large eddy simulations (LES) of hydrodynamic turbulence, to model the subgrid stress tensor (SGS) in terms of the resolved field. This is the fundamental “closure” problem in RANS and LES of turbulence. We will target fully-developed turbulent channel flows and developing turbulent boundary layers for which we will use the extensive database at JHU (JHTDB) from direct numerical simulations (DNS) as well as well-established experimental data sets. We will first demonstrate the effectiveness of both fractional operators in discovering truly new equations and of PINNs in obtaining known scaling laws in fluid mechanics. Subsequently, we will discover new subgrid functional relationships for laboratory wall-bounded flows and demonstrate how such findings can be used in other domains, e.g. geophysical flows.