Using today's simulation tools it has now become practical to consider complex design problems, where we wish to determine parameters of large systems that maximizes a certain objective, and inverse problems where we wish to determine parameters whose behavior matches measured data. Examples of design problems include structural optimization, antenna design and process optimization. Geophysical imaging, biomedical imaging, weather data assimilations are just a few examples of inverse problems where the physics is governed by partial differential equations.
While these types of problems are naturally posed as optimization problems, they offer new challenges because of their large size, inexact derivatives (when available), and ill-posedness. Current software cannot be used because matrices of constraint gradients cannot be factored, and computing with null space bases can be exceedingly expensive. The goal of this workshop is to review methods for PDE-optimization problems and to expose researches to some open problems in the field.
We will simulate the level of a liquid in media that is porous in one boundary edge only and design from scratch an algorithm to maintain it at a fixed level on average even though the liquid is disappearing through the open boundary using a random step function.
We will develop convergence results initially using a semi-direct method, but some of the participants may end up with a random walk by the end of the workshop. We will iterate on the liquid problem until we develop a fast iterative (and convergent) algorithm that we have thoroughly tested. We will use the data from experiments to drive the entire methodology and the algorithms will drive how and when data is collected.
This workshop will be held in one of the local watering holes, not in the conference center. Sensor oversight and correction will be provided at the tables.