Astani Civil and Environmental Engineering Seminar
Thu, Feb 20, 2020
4:00 PM - 5:00 PM
Location: KAP 209
Speaker: Dr. Subhayan De , Postdoctoral Associate, Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder
Talk Title: Design Optimization under Uncertainty using a Stochastic Gradient Approach
Abstract: Design optimization of complex engineering systems requires understanding and modeling the underlying physical phenomena and their interactions. In addition, uncertainties and their influences on both the design objective and the design constraints must be considered to achieve a robust design. Such uncertainties are typically due to intrinsic variabilities in the system or manufacturing processes, as well as the lack of knowledge in precisely describing the governing physics in terms of mathematical/computational models. However, accounting for uncertainty in the optimization process requires, for example, computing the statistical moments of the objective, which may lead to high computational costs. For example, a Monte Carlo approach based on random sampling in such cases requires many forward and adjoint solves, thus requiring significant computational resources. To alleviate this computational burden, in this talk, a stochastic gradient-based approach will be discussed. In this approach, stochastic approximations of the gradients, using only a handful of random samples of the uncertainty, are constructed at every design optimization iteration. Popular variants of stochastic gradient descent algorithms (e.g., AdaGrad and Adam) are used with this approach. In practical engineering settings, often models with different levels of fidelity are employed to describe the problem at hand. Lower-fidelity models (e.g., using coarser grid discretizations) can be simulated cheaply but may lead to inaccurate solutions relative to high-fidelity models (e.g., using fine grid discretizations) that are often expensive to simulate. To reduce the design optimization cost further, these low-fidelity models are incorporated in the optimization process to propose bi-fidelity versions of stochastic gradient descent algorithms with a linear rate of convergence. The stochastic gradient approach for design optimization is illustrated using numerical examples from shape and topology optimizations. These examples show that the use of stochastic gradients along with bi-fidelity approaches can reduce the computational cost of design optimization under uncertainty significantly. In the presence of uncertainty in the microscale properties of the structure, homogenization methods like FE2 require solving boundary value problems to quantify the effect of microscopic heterogeneity at the macroscale for all random samples in a Monte Carlo approach. Instead, the stochastic gradient-based approach is applied to this multiscale optimization problem to reduce the computational effort of design under microstructural uncertainty. The design of a fiber composite beam with uncertain microstructural properties is used to illustrate the proposed stochastic gradient approach. Ongoing work will introduce the application of this approach to 3D structural components with microstructural uncertainty and the limitations applying it to large-scale realistic aerospace structures, such as solid rocket fuel design.
Biography: Bio: Dr. Subhayan De is a postdoctoral associate in the Aerospace Engineering Sciences at the University of Colorado Boulder (CU-Boulder). His research at CU focuses on design optimization under uncertainty and physics-based machine learning. Subhayan received his Ph.D. in Civil Engineering from the University of Southern California in 2018, where he was supported by a Viterbi Ph.D. Fellowship, a Gammel Scholarship and several NSF grants. At USC, he worked on probabilistic model validation, machine learning, uncertainty quantification, and structural control design. Subhayan also holds an MS in Electrical Engineering from USC and an MEng in Structural Engineering from the Indian Institute of Science, Bangalore. He received his B.Eng. in Civil Engineering from Jadavpur University, Kolkata.
Host: Dr. Erik Johnson