Martins’ research is on algorithms for multidisciplinary design optimization (MDO) that can take advantage of high-fidelity simulations and high-performance parallel computing. He has been focusing on applying these algorithms to the design optimization of new aircraft configurations. In the design of an aircraft wing in particular, since it is flexible, it is crucial to consider the coupling of the aerodynamics and the structure. In addition, when performing design optimization, it is important to simultaneously account for the aerodynamic performance and the structural failure constraints. In the MDO Lab, Martins’ team has developed ways to perform design optimization based a Reynolds-averaged Navier-Stokes model for the aerodynamics that is tightly coupled to a detailed structural finite-element model. The optimization of the coupled system is done with a gradient-based algorithm, where the gradients of the coupled system are computed using a two-field adjoint system of equations. This enables the high-fidelity aerostructural design of aircraft configurations with respect to thousands of design variables.
In order to understand the relationship between molecular structure and dynamics and biological function, the Frank research group seeks to develop and deploy integrative modeling tools to elucidate the structure and dynamics of biologically relevant molecules. Our methods will utilize readily accessible experimental observables from a variety of sources to first guide structure prediction efforts and then guide atomistic simulations to map the entire conformational landscape of these molecules. We are primarily interested in using our methods to understand how functional ribonucleic acids, either by themselves or in concert with other molecules, achieve specific cellular functions. Our research makes heavy use of advanced machine learning and optimization techniques.