Many remote sensing applications encountered in astronomy and space sc
ience involve the solution of nonlinear inverse problems. These are of
ten difficult to solve because of nonlinearities, ill-behaved integrat
ion kernels, and amplification of data noise associated with the inver
sion of the integral operator. In some cases these difficulties are se
vere enough to warrant repeated evaluations of the forward problem as
an alternate approach to formal inversion. Because a forward approach
is intrinsically repetitive and time consuming, an efficient and flexi
ble forward technique is required for this avenue to be practical. We
show how a forward technique based on a genetic algorithm allows us to
fit magnetostatic models of the solar minimum corona to observations
in white light to a degree that would otherwise have been computationa
lly prohibitive. In addition, and perhaps equally important, the metho
d also allows the determination of global error estimates on the model
parameters defining the best fit solution.