Optimization of Systems Governed by PDEs: Algorithms and Applications in Computational Science and Engineering

Omar Ghattas, CMU

Many problems in computational science and engineering can be expressed ultimately as optimization problems that are governed by partial differential equations (PDEs). Such “PDE-constrained optimization problems” arise as inverse problems (in which model parameters characterizing a simulation are estimated based on observations), control problems (in which optimal control strategies are generated based on simulations of the system to be controlled), and design problems (in which an optimal design is sought based on a simulation of the system). The size, complexity, and infinite-dimensional nature of the PDE simulations often present significant challenges for general-purpose optimization algorithms. Recent years have seen sustained progress in PDE solvers and large-scale optimization algorithms, and the rapid rise in computing capability. Accompanying these advances is a growing interest in simulation-based optimization in diverse scientific and engineerings areas.

I will discuss the challenges and opportunities presented by the confluence of terascale computing, high-resolution simulations, and scalable optimization methods, drawing on examples of inverse problems and design optimization from the earth sciences, bioengineering, medicine, and infrastructure security. I will then focus on the problem of shape optimization of next generation accelerators, and discuss results of a collaboration among the AST, TOPS, and TSTT SciDAC centers aimed at creating a general-purpose capability for scalable gradient-based high-resolution electromagnetics-based shape optimization of accelerator structures.