Surrogate-based modeling and dimension reduction techniques for multi-scale mechanics problems

Successful modeling and/or design of engineering systems often requires one to address the impact of multiple "design variables" on the prescribed outcome. There are often multiple, competing objectives based on which we assess the outcome of optimization. Since accurate, high fidelity models are typically time consuming and computationally expensive, comprehensive evaluations can be conducted only if an efficient framework is available. Furthermore, informed decisions of the model/hardware's overall performance rely on an adequate understanding of the global, not local, sensitivity of the individual design variables on the objectives. The surrogate-based approach, which involves approximating the objectives as continuous functions of design variables from limited data, offers a rational framework to reduce the number of important input variables, i.e., the dimension of a design or modeling space. In this paper, we review the fundamental issues that arise in surrogate-based analysis and optimization, highlighting concepts, methods, techniques, as well as modeling implications for mechanics problems. To aid the discussions of the issues involved, we summarize recent efforts in investigating cryogenic cavitating flows, active flow control based on dielectric barrier discharge concepts, and lithium (Li)-ion batteries. It is also stressed that many multi-scale mechanics problems can naturally benefit from the surrogate approach for "scale bridging."