Efficient navigation of parameter landscapes

Abstract

Optimization techniques can have difficulty navigating long valleys that are oriented obliquely to the parameter axes. Efficiency may be improved by rotating coordinates so that the most prominent valleys are optimally aligned with the parameter axes. The rotated axes are parallel to the eigenvectors of the covariance matrix of the gradient of the cost function, which may be estimated efficiently by Monte Carlo integration. The information in the covariance matrix may also be used to obtain an improved parametrization, which corresponds to the rotated coordinates associated with the largest eigenvalues. The approach is illustrated for the inverse problem of estimating ocean bottom parameters from acoustic data using simulated annealing. For multifrequency inverse problems, the resolution for each frequency is optimized.