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Center for Nonlinear Studies |
The purpose of this talk is threefold: (i) a deep dive into numerical methods for optimal design of porous structures and optimal control of electromagnetic waves, which motivate (ii) algorithmic advances in optimization with differential equations, and require (iii) new matrix-free software for large-scale optimization.
We begin with a new perspective on permeability optimization for porous media, with the goal to control flow patterns. This research is motivated by recent advances in additive manufacturing, which facilitate precise control of the geometry of each pore. We analyze an optimization problem constrained by Darcy’s law, to design porous media columns that achieve uniform transit times of fluid particles, despite having nonuniform geometries. We prove existence of solutions to this optimization problem, as well as differentiability, which enables the use of rapidly converging, derivative-based optimization methods.
We continue the talk by highlighting recent advances in the simulation and optimization of electromagnetic devices and systems. We motivate new research challenges, such as the theoretical analysis of optimal control formulations for Maxwell's equations and the development of parallel-in-time optimization methods. We then focus on the robust and scalable handling of general constraints, such as inequalities, through augmented Lagrangian methods. Our methods have recently enabled novel mesh optimization techniques for solving partial differential equations and high-precision trajectory optimization using low-precision analog co-processors.
We conclude with an overview of the Rapid Optimization Library (ROL), https://rol.sandia.gov, a high-performance C++ library that brings an extensive collection of state-of-the-art optimization algorithms to any application, owing to its matrix-free interfaces and customizable linear algebra.
Bio: Denis Ridzal is a Distinguished Member of Technical Staff in the Center for Computing Research at Sandia National Labs. Denis joined Sandia in 2006 as the Von Neumann Postdoctoral Fellow, after receiving his PhD in computational and applied mathematics from Rice University. Denis's research interests include numerical optimization, numerical analysis, optimal control, partial differential equations, high-performance computing, and applications in physical science and engineering. Denis is the project lead for the Rapid Optimization Library (ROL), a high-performance software for simulation-based optimization, https://rol.sandia.gov. Denis's recent contributions span algorithms for matrix-free optimization with general constraints, novel property-preserving numerical methods for hyperbolic conservation laws, and extreme-scale simulation and optimization of electromagnetic meta-surfaces, for which he received two R&D100 awards.
Host: Mikhail Shashkov (XCP-4)