Abstract: Topological optimization (TO) is a mathematical method that optimizes material layout within a given set of constraints with the goal of maximizing the performance of the system. Different from size and shape optimization, TO, enables the creation, merging and splitting of the interior solids and voids during the structural evolution and therefore, a much larger design space can be explored. The recent development of additive manufacturing (AM) technologies allows the production of complex topological design that was not feasible before, permitting the use of TO in wide range of applications in aerospace, nuclear, mechanical and biomedical engineering.
The conventional TO formulation uses a physical simulation (e.g. finite element method) to evaluate the design performance. The design is optimized using gradient-based mathematical programming approaches such as the method of moving asymptotes (MMA). The grand challenges in TO mainly include: 1) high-dimensional design space; 2) computationally expensive simulation; 3) non-parallelizable optimization algorithm and 4) non-convex and multiple local minima exist. In this work, we construct a low-dimensional ML model that can explore the optimal search path. To this end, we developed a sequence of local deep neural networks (DNN), each of which only covers a segment of the search path. We further designed a new sampling strategy that can concentrate the training samples along the gradient descent direction. Moreover, we investigate the use of the Directional Gaussian Smoothing Evaluation Strategy (DGS-ES) in topology optimization to move from a poor local minimum to a better one. We demonstrate this approach via numerical examples and show that the coupling of the DGS-ES with topology optimization leads to a better and more robust design that does not depend on the initial design.
Speaker’s Bio: Dr. Jiaxin Zhang is a Research Staff in Computational and Applied Mathematics (CAM) Group at Computational Science and Mathematics Division (CSMD). He earned his B.S. and M.S. in Computational Mechanics in 2011 and 2014 at Dalian University of Technology, China. He received his Ph.D. in Computational Science and Engineering with a dual M.S. in Applied Mathematics & Statistics at Johns Hopkins University in 2018. He joined ORNL in 2018 as a postdoc in Scientific Computing Group in National Center for Computational Science (NCCS). His research focuses on probabilistic data-driven modeling, robust and scalable machine learning (ML) and artificial intelligence (AI), computational design and optimization with uncertainty, with an interest in applications of UQ, ML and optimization for computational mechanics, materials design, advanced manufacturing and robotic systems.
Host: Eirik Endeve, firstname.lastname@example.org
About the Seminar: The Computational and Applied Math Seminar features talks by invited speakers, local mathematicians, and domain scientists working on problems of mathematical interest. The seminar is held weekly, every Thursday from 3:00pm-4:00pm. If you are interested in giving a seminar, please contact Eirik Endeve, email@example.com. To subscribe to the CAM Seminar mailing list, please contact Kasi Arnold, firstname.lastname@example.org. To see the full list of previous and upcoming seminars, go to https://csmd.ornl.gov/events/9/seminars.
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Last Updated: May 28, 2020 - 4:00 pm