Session: 12-03-02: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 120350

120350 - Self-Directed Online Machine Learning 

Distributing materials in a domain to optimize performance is a significant topic in many fields, such as solid mechanics, heat transfer, acoustics, fluid mechanics, materials design and various multiphysics disciplines. Many numerical approaches have been developed since 1988, where the problems are formulated by density, level set, phase field, topological derivative, or other methods. Typically, these approaches use gradient-based optimizers, such as the Method of Moving Asymptotes (MMA), and thus have various restrictions on the properties of governing equations and optimization constraints to allow for fast computation of gradients. Because of the intrinsic limitation of gradient-based algorithms, the majority of existing approaches have only been applied to simple problems, since they would fail as soon as the problem becomes complicated such as involving varying signs on gradients or non-linear constraints. To address these difficulties, non-gradient methods have been developed which play a significant role in overcoming the tendency to be trapped in a local minimum. Non-gradient optimizers, also known as gradient-free or derivative-free methods, do not use the gradient or derivative of the objective function and have been attempted by several researchers, most of which are stochastic and heuristic methods. However, the major disadvantage of the methods is their high computational cost from calling the objective functions, which becomes prohibitively expensive for large systems. As a trade-off, sometimes searching space can be reduced in order for less computation. For instance, pattern search has been applied, which is a non-heuristic method with a smaller searching space but is more likely to be trapped in local minima.

Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report a new approach of Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations [1]. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN’s prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

1.   C. Deng, Y. Wang, C. Qin, Y. Fu, and W. Lu, “Self-directed online machine learning for topology optimization,” Nature Communications, 13, 388, 2022.

Presenting Author: Wei Lu University of Michigan

Presenting Author Biography: Dr. Wei Lu is Professor at the Mechanical Engineering Department, University of Michigan, Ann Arbor, and Director of Research Center: Advanced Battery Coalition for Drivetrains. He uses multi-scale and multi-physics approaches to address mechanics and electrochemistry in energy storage and battery degradation. He has more than 180 journal publications in high impact peer-reviewed journals and 200 presentations and invited talks in international conferences, universities and national labs including Harvard, MIT and Stanford. He also has plenty of publications in conference proceedings, encyclopedias and book chapters. Prof. Lu was the recipient of many awards including the CAREER award by the US National Science Foundation; the Robert J. McGrattan Award by the American Society of Mechanical Engineers; Elected Fellow of the American Society of Mechanical Engineers; Robert M. Caddell Memorial Research Achievement Award; Faculty Recognition Award; Department Achievement Award; Novelis/CoE Distinguished Professor Award; CoE Ted Kennedy Family Faculty Team Excellence Award; CoE Creative, Innovative, Daring Award; CoE George J. Huebner, Jr. Research Excellence Award; and the Gustus L Larson Memorial Award by American Society of Mechanical Engineers. He was recognized as academics in the top 2% in the discipline of energy (a study from Stanford University science-wide author databases of standardized citation indicators and top 2% is the highest in the study). He was invited to the National Academies Keck Futures Initiative Conference multiple times.

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