Inversion Based on Complex Computational Simulations

Experimental data often can only be interpreted by means of a computational simulation that approximately models the physical situation. We will discuss techniques that facilitate application to complex, large-scale simulations of the standard approach to inversion in which gradient-based optimization is used to nd the parameters that best match the data. The fundamental enabling techniques are adjoint di erentiation to efciently compute the gradient of an objective function with respect to all the variables of a simulation and relatively new gradient-based optimization algorithms. These techniques will be illustrated through the simulation of the time-dependent di usion of infrared light through tissue, which has been used to perform optical tomography [1]. The techniques discussed have a wide range of applicability to modeling including the optimization of models to achieve a desired design goal.