Computational Aerosciences Laboratory

About the lab

We are a computational modeling group. We identify and work on critical modeling challenges relevant to real-world problems from a variety of perspectives. This includes innovations in physics-based modeling, data-driven paradigms, mathematical formalisms, algorithms, numerical methods, computer science, etc.

Our applications are centered around fluid flows, but we are continually expanding our domains (such as combustion, materials, fluid structure interaction, etc.) Our work targets modeling applications at a fundamental level as well as in an integrated system-level setting.

An overarching theme in our lab involves the development and application of ``appropriate'' fidelity simulation and data-driven methods to answer a spectrum of scientific and engineering questions.

Featured projects (1)

The purpose of the center is to investigate and develop new algorithms, architectures, and operational procedures for unmanned aircraft systems. The center will contribute to the advancement of the UAS community through cutting-edge, industrially-relevant research at the center’s universities. Five main thrusts have been identified for research within C-UAS • Advanced autonomous capabilities for UAS • UAS-based communication networks • Multi-agent cooperative control of UAS • Human interfaces for UAS • UAS integration into the National Airspace System

Featured research (7)

This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying levels of input are considered : a) The data, likelihood and prior distributions are given, b) The data and likelihood are given; c) The data and prior are given; d) the data and the dimensionality of the parameters is specified. The first two problems seek encoders (or the posterior) and the latter two seek autoencoders (i.e. the posterior and the likelihood). A variational Bayesian setting is pursued, and detailed derivations are provided for the optimization problem. Following this, a linear Gaussian setting is adopted, and closed form solutions are derived. Numerical experiments are also performed to verify expected behavior and assess convergence properties. Explicit connections are made to rate-distortion theory, information bottleneck theory, and the related concept of sufficiency of statistics is also explored. One of the motivations of this work is to present the theory and learning dynamics associated with variational inference and autoencoders, and to expose information theoretic concepts from a computational science perspective.
The variational multiscale (VMS) formulation formally segregates the evolution of the coarse-scales from the fine-scales. VMS modeling requires the approximation of the impact of the fine scales in terms of the coarse scales. For the purpose of this approximation, this work introduces a VMS framework with a special neural-network (N-N) structure, which we call the variational super-resolution N-N (VSRNN). The VSRNN constructs a super-resolved model of the unresolved scales as a sum of the products of individual functions of coarse scales and physics-informed parameters. Combined with a set of locally non-dimensional features obtained by normalizing the input coarse-scale and output sub-scale basis coefficients, the VSRNN provides a general framework for the discovery of closures for both the continuous and the discontinuous Galerkin discretizations. By training this model on a sequence of $L_2-$projected data and using the super-resolved state to compute the discontinuous Galerkin fluxes, we improve the optimality and the accuracy of the method for both the linear advection problem and turbulent channel flow. Finally, we demonstrate that - in the investigated examples - that the present model allows generalization to out-of-sample initial conditions and Reynolds numbers. Perspectives are provided on data-driven closure modeling, limitations of the present approach, and opportunities for improvement.
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the conservative form of the governing equations. Least-squares-based minimization is leveraged to guarantee symmetrization and discrete consistency with the full-order model (FOM) at the sub-iteration level. Two levels of scaling are used to achieve the conditioning required to effectively handle problems with extremely disparate physical phenomena, characterized by extreme stiffness in the system of equations. The formulation - referred to as structure-preserving least-squares with variable transformation (SP-LSVT) - provides global stabilization for both implicit and explicit time integration schemes. In addition, physical realizability is promoted by enforcing limiters in both temperature and species mass fractions, thus contributing to local stability enhancement. These limiters are demonstrated to be important eliminating regions of spurious burning, thus enabling the ROMs to provide accurate representation of the heat release rate and flame propagation speed. To achieve computational efficiency, a pivoted QR decomposition is used with oversampling, and adapted to the SP-LSVT method. The framework is demonstrated in representative two- and three-dimensional reacting flow problems, and the SP-LSVT is shown to exhibit improved stability and accuracy over standard projection-based ROM techniques. In the 3D application, it is shown that more than two orders of magnitude acceleration in computational efficiency can be achieved, while also providing reasonable future-state predictions. A key contribution of this work is the development and demonstration of a comprehensive ROM formulation that targets highly challenging multi-scale transport-dominated problems.
Koopman decomposition is a non-linear generalization of eigen decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its variants provide approximations to the Koopman operator, and have been applied extensively in many fluid dynamic problems. Despite being endowed with a richer dictionary of nonlinear observables, nonlinear variants of the DMD, such as extended/kernel dynamic mode decomposition (EDMD/KDMD) are seldom applied to large-scale problems primarily due to the difficulty of discerning the Koopman invariant subspace from thousands of resulting Koopman triplets: eigenvalues, eigenvectors, and modes. To address this issue, we revisit the formulation of EDMD and KDMD, and propose an algorithm based on multi-task feature learning to extract the most informative Koopman invariant subspace by removing redundant and spurious Koopman triplets. These algorithms can be viewed as sparsity promoting extensions of EDMD/KDMD and are presented in an open-source package. Further, we extend KDMD to a continuous-time setting and show a relationship between the present algorithm, sparsity-promoting DMD and an empirical criterion from the viewpoint of non-convex optimization. The effectiveness of our algorithm is demonstrated on examples ranging from simple dynamical systems to two-dimensional cylinder wake flows at different Reynolds numbers and a three-dimensional turbulent ship air-wake flow. The latter two problems are designed such that very strong transients are present in the flow evolution, thus requiring accurate representation of decaying modes.

Lab head

Karthik Duraisamy
  • Department of Aerospace Engineering

Members (8)

Cheng Huang
  • University of Kansas
Behdad Davoudi
  • University of Michigan
Mehdi Khalloufi
  • Dow Chemical Company
Jiayang Xu
  • University of Michigan
Nicholas Arnold-Medabalimi
  • University of Michigan
Aniruddhe Pradhan
  • University of Michigan
James Duvall
  • University of Michigan
Bernardo Pacini
  • University of Michigan
Ayoub Gouasmi
Ayoub Gouasmi
  • Not confirmed yet

Alumni (1)

Shaowu Pan
  • Rensselaer Polytechnic Institute