|
Abstract:
|
Level set methods have been widely used as a tool for the analysis of the change in surfaces, shapes, and boundaries. In particular, a signed distance function used in level set methods can readily be interpreted and can represent complicated boundaries and their changes in time quite effectively. While there is a substantial literature on level set methods in applied mathematics and computer science, these implementations have not focused on uncertainty quantification for complex spatio-temporal data. Here, we present a Bayesian spatio-temporal dynamic model based on level sets, which can be utilized for prediction and forecasting the boundary of interest in the presence of uncertain data and lack of knowledge about the boundary velocity. We show the effectiveness of our method by applying it to the evolution of the fire front boundary of a classic megafire – the 2017-2018 Thomas fire in southern California.
|
