End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates viability this approach and presents an end-to-end framework for neural networks learn eddy viscosity from observations derived velocity pressure fields. consists a Reynolds-averaged Navier–Stokes (RANS) solver neural-network-represented model, each accompanied by its derivative computations. For sensitivities Reynolds stress field, we use continuous adjoint equations RANS equations, while gradient network obtained via built-in automatic differentiation capability. We demonstrate ability true underlying closure when one exists synthetic data linear nonlinear closures. also train model measurements direct numerical simulations which no exists. trained deep-neural-network showed predictive capability on similar flows.