  This study proposes a novel framework for learning the underlying physics of
phenomena with moving boundaries. The proposed approach combines Ensemble SINDy
and Peridynamic Differential Operator (PDDO) and imposes an inductive bias
assuming the moving boundary physics evolve in its own corotational coordinate
system. The robustness of the approach is demonstrated by considering various
levels of noise in the measured data using the 2D Fisher-Stefan model. The
confidence intervals of recovered coefficients are listed, and the
uncertainties of the moving boundary positions are depicted by obtaining the
solutions with the recovered coefficients. Although the main focus of this
study is the Fisher-Stefan model, the proposed approach is applicable to any
type of moving boundary problem with a smooth moving boundary front without a
mushy region. The code and data for this framework is available at:
https://github.com/alicanbekar/MB_PDDO-SINDy.
