Inversion Based on Computational Simulations

Abstract

A standard approach to solving inversion problems that involve many pa- rameters uses gradient-based optimization to find the parameters that best match the data. We will discuss enabling techniques that facilitate application of this approach to large-scale computational simulations, which are the only way to investigate many complex physical phenomena. Such simulations may not seem to lend themselves to calculation of the gradient with respect to numerous parameters. However, adjoint dif- ferentiation allows one to efficiently compute the gradient of an objective function with respect to all the variables of a simulation. When combined with advanced gradient-based optimization algorithms, adjoint differentiation permits one to solve very large problems of optimization or parameter estimation. These techniques will be illustrated through the simulation of the time-dependent diffusion of infrared light through tissue, which has beenusedtoperformopticaltomography.Thetechniquesdiscussedhaveawiderange of applicability to modeling including the optimization of models to achieve a desired design goal.