Robust Adjoint-based Closure Training for Particle-laden Turbulence Simulation

Neural networks are known for their ability to fit complex data effective fits of data, which makes them attractive tools for modeling complex subgrid-scale interactions in large-eddy simulations. The presence of dispersed particles makes the modeling task even more challenging, due to additional unresolved physics. However, there is no guarantee that a trained model will be robust, and the sub-grid-scale data required for training are rarely available. It is therefore appealing to train using limited statistical data that is available from experiments, although this introduces its own difficulties: limited observability, measurement noise, and coarse spatial or temporal resolution. The proposed adjoint optimization framework addresses these challenges. It computes sensitivities of statistical targets with respect to network weights by solving the discrete-exact adjoint of the coupled system---both the resolved governing equations and the neural network closure. This provides closure models that remain grounded in the governing dynamics while aligning with experimentally observed behavior and without need for closure data itself. The approach is demonstrated for simulations of particle-laden turbulence.