New high performance computational strategies for inverse problems with application to analytical ultracentrifugation

In the physical sciences experimental data are often analyzed to determine model parameters by solving inverse problems. Solving such problems is complicated by the presence of random noise in the data. Traditional regularization methods used to eliminate the effects of noise introduce a bias which smooths the solution. In the problems considered here, the answer is sharp, containing a sparse set of parameters. We introduce high-performance techniques to find the correct set of parameters through the sequential application of our new methods. The first method is a novel divide and conquer technique for parallelizing a large scale multivariate linear optimization problem, which is commonly solved using a sequential algorithm with the entire parameter space as the input. By partitioning the parameters and the associated computations, our technique overcomes memory constraints when used in the context of a single workstation and is scalable with high processor utilization when clusters are used. We describe this technique and present an analytical model for performance prediction which is validated on a cluster of 512 processors. The second method uses a Genetic Algorithm and the results of the first method to find the simplest set of model parameters for the data with an equivalent goodness-of-fit. A method of representation, initialization and mutation is introduced to efficiently find this model. Analysis of analytical ultracentrifugation sedimentation velocity experimental data is the primary example application, where these methods are currently being used by researchers worldwide.