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We consider a quadcopter operating in a turbulent windy environment. The turbulent environment may be imposed on a quadcopter by structures, landscapes, terrains and most importantly by the unique physical phenomena in the lower atmosphere. Turbulence can negatively impact quadcopter's performance and operations. Modeling turbulence as a stochastic random input, we investigate control designs that can reduce the turbulence effects on the quadcopter's motion. In particular, we design a minimum cost variance (MCV) controller aiming to minimize the cost in terms of its weighted sum of mean and variance. We linearize the quadcopter dynamics and examine the MCV controller derived from a set of coupled algebraic Riccati equations (CARE) with full-state feedback. Our preliminary simulation results show reduction in variance and in mean trajectory tracking error compared to a traditional linear quadratic regulator (LQR).

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational entities. To this end, we present a robust hybrid analysis and modeling approach combining a physics-based full order model (FOM) and a data-driven reduced order model (ROM) to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive digital twin technologies. At the interface, we introduce a long short-term memory network to bridge these high and low-fidelity models in various forms of interfacial error correction or prolongation. The proposed interface learning approaches are tested as a new way to address ROM-FOM coupling problems solving nonlinear advection-diffusion flow situations with a bifidelity setup that captures the essence of a broad class of transport processes.

Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach based on memory embedding to provide physically correct boundary conditions at the interface. To enable the interface learning for hyperbolic systems by considering the domain of influence and wave structures into account, we put forth the concept of upwind learning towards a physics-informed domain decomposition. The promise of the proposed approach is shown for a set of canonical illustrative problems. We highlight that high-performance computing environments can benefit from this methodology to reduce communication costs among processing units in emerging machine learning ready heterogeneous platforms toward exascale era.

The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.