Adjoint-Based Deep Learning for Flow Prediction and Control

Prediction and control of complex flows remain a significant challenge for engineering systems. Turbulent flow predictions generally require Reynolds-Averaged Navier–Stokes (RANS) simulations and Large-Eddy Simulation (LES), though their predictive accuracy can be insufficient for flow control optimization, and non-Boussinesq turbulence and/or unresolved multiphysical phenomena can preclude qualitative fidelity in certain regimes. For example, in turbulent combustion, flame–turbulence interactions can lead to inverse-cascade energy transfer, which violates the assumptions of many RANS and LES closures. We develop adjoint-based, solver-embedded data assimilation methods to augment the RANS and LES equations using trusted data and embedded higher-fidelity simulations. This is accomplished using Python-native flow solvers that leverage differentiable programming techniques to construct the adjoint equations needed for optimization.

We present applications to canonical turbulence, shock-dominated flows, aerothermodynamics, and flow control and discuss the potential of adjoint-based approaches for future machine learning applications.