Physical Review Fluids

Modeling the effect of subgrid-scale processes is one of the main obstacles in the accurate prediction of multiscale systems. An investigation considers how machine learning methods can be applied to model subgrid-scale processes and integrated within sequential data assimilation methods. It is found that the use of machine-learning-based closure modeling in conjunction with data assimilation improves the prediction of multiscale systems and can be considered a promising approach to numerical weather prediction tasks in the age of data.

The weights of a deep neural-network model are optimized over the governing flow equations to provide a model for the subgrid-scale stresses in a turbulent plane jet. The training, which is done in $aposteriori$ large-eddy simulations (LES), solves the adjoint Navier-Stokes equations to provide end-to-end sensitivities. Out-of-sample testing on multiple dual-jet configurations confirms that the required grid resolution is half that needed by dynamic models for comparable accuracy. The coupled formulation is generalized to train based only on the mean flow and Reynolds stresses, which are more readily available from experiments.

Investigations show that convolutional neural networks (CNNs) are able to reconstruct missing data in turbulence. Different types of input information impact the performance of the algorithm. CNNs are able to reconstruct original data with errors comparable to equation-informed tools such as nudging, even in the presence of large gaps.

Perspectives are presented on the use of machine learning to augment models of turbulent flows. Particular emphasis is placed on techniques that promote consistency of the machine learning model with the underlying physical model in view of the possibility of using sparse computational and experimental data. This is followed by a discussion of physics-informed and mathematical considerations on the choice of the feature space and imposition of constraints. Machine learning should be viewed as one tool in the turbulence modeler’s toolkit. The associated modeling endeavor requires multidisciplinary advances.

Fish swim by coordinating their shape changes with the fluid environment to produce forward swimming or turning gaits. We use model-free reinforcement learning to learn shape coordinations that lead to robust turning and forward swimming motions in the context of a simple three-link fish in a potential flow environment. We show that the optimal control policies arrived at by reinforcement learning are interpretable via shape space analysis in driftless environment and are robust to the presence of drift-related perturbations.

We use an ensemble Kalman filter (EnKF) to sequentially estimate low Reynolds number aerodynamic flows using an inviscid vortex model and distributed surface pressure readings. We look at two scenarios: an impulsively translating plate subject to flow actuation near the leading edge or placed in a cylinder wake. In each case, the ensemble transform Kalman filter (ETKF) - a deterministic version of the EnKF - is consistently more robust than the stochastic EnKF and is qualitatively better at representing the coherent structures of the true flow. We analyze the mapping from pressure discrepancies to state update through a singular value decomposition of the Kalman gain.

A rotating detonation engine displays complex nonlinear shock front propagation dynamics which impede effective dimensionality reduction. A novel optimization is used to discover separate low-rank modes and interpretable dynamics for each front’s propagation. Koopman autoencoders similarly enable separation and forecasting of shock wave interactions.