A Cell-Division Search Technique for Inversion with Application to Picture-Discovery and Magnetotellurics

Solving inverse problems in natural sciences often requires a search pro- cess to find explanatory models that match collected field data. Inverse problems are often under-determined meaning that there are many poten- tial explanatory models for the same data. In such cases using stochastic search, through providing multiple solutions, can help characterise which model features that are most persistent and therefore likely to be real. Unfortunately, in some fields, large parameter spaces can make stochas- tic search intractable. In this work we improve upon previous work by defining a compact and expressive representation and search process able to describe and discover two and three dimensional spatial models. The search process takes place in stages starting with greedy search, followed by alternating stages of evolutionary search and a novel model-splitting process inspired by cell-division. We apply this framework to two prob- lems - magnetotellurics and picture discovery. We show that our improved representation and search process is able to produce detailed models with low error residuals.