In this talk I will present an PDE-constrained approach to optimizing
the electrostatic interactions between biological molecules, a problem
relevant to the analysis and design of new drugs as well as to advancing
our understanding of the design strategies employed by biological
systems. Our research in this area serves as a case study to highlight
some of the conceptual challenges involved in coupling modeling
approaches such as simulation and optimization. Here, the simulations
are partial-differential equation (PDE)-based mathematical models and
the objective function is a relatively simple quadratic. Re-engineering
the interface between simulation and optimization drastically reduces
the time required to find an optimal solution, but complicates the task
of regularization. The need to address this complication has led, in
turn, to our recent discovery of a promising new approach for modeling
electrostatic interactions between molecules.
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