I³MS - van Bloemen Waanders Seminar
Dr. Bart van Bloemen Waanders - Multiscale Optimization under Uncertainty For Additive Manufacturing
Sandia National Laboratories, Albuquerque, New Mexico
Additive manufacturing (AM) enables new and innovative designs that are not realizable using standard procedures. Unfortunately, AM-produced parts often exhibit significant variability in their material properties. For engineering systems with strict reliability requirements, these uncertainties render AM-based subassemblies of limited use. In an attempt to address reliability, improvements are continuously being made to the controlability and observability of AM processes. However these improvements need to be coupled to numerical optimization and uncertainty quantification methods to help navigate the large design spaces and manage uncertainties inherent in these problems. In particular, design, control, and inversion problems must be solved at each stage of the overall design process. This presentation outlines an approach that leverages techniques from partial differential equation (PDE) constrained optimization, stochastic optimization, and multiscale (in particular mortar) finite element methods. We endow PDE-constrained optimization formulations with risk measures to steer the solution towards satisfaction of reliability and robustness criteria while accounting for model-based uncertainties. Because the optimization problem is constrained by PDEs and can contain millions of design variables, a significant software foundation is required to obtain solutions in a flexible and efficient manner. To that end, we leverage several components from the Trilinos framework. In particular, the Rapid Optimization Library (ROL) provides Newton-based optimization, line search, trust region, and stochastic optimization algorithms. ROL enables special interfaces that carefully map the underlying linear algebra of the simulation software to function space requirements for optimization. Furthermore, to approximate disparate PDE constraints, a finite element framework has been developed that leverages other Trilinos packages and automates discretizations, adjoints, and the optimization interfaces to ROL. This Multiscale Interface for Large scale Optimization (MILO) provides a convenient prototyping capability whereby the weak form of any set of PDEs is directly mapped to the underlying finite element matrices and vectors through automatic differentiation, thus creating a fully functional 3D parallel optimization solver. Although this approach is not unique, our development enables novel optimization under uncertainty capabilities and provides a framework to tackle multiscale and multiphysics problems. Several numerical examples are demonstrated including a convection-diffusion-reaction problem motivated by the control of trace gases in atmospheric transport.