Phase-IDENT: Identification of Two-phase PDEs with Uncertainty Quantification

TL;DR

Phase-IDENT is a new method for identifying PDEs in systems with phase transitions, accurately locating phase boundaries and quantifying uncertainty despite noisy data.

Contribution

It introduces a joint approach to identify PDEs and phase boundaries with uncertainty quantification, addressing challenges in systems with phase transitions.

Findings

Successfully identifies PDEs in two-phase systems

Accurately detects phase boundaries under noise

Provides uncertainty estimates for boundary locations

Abstract

We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phenomena are prevalent in fluid dynamics and materials science, where they can be modeled mathematically as functions satisfying different PDEs within distinct regions separated by phase boundaries. Our approach simultaneously identifies the underlying PDEs in each regime and accurately reconstructs the phase boundaries. Furthermore, by incorporating change point detection techniques, we provide uncertainty quantification for the detected boundaries, enhancing the interpretability and robustness of our method. We conduct numerical experiments on a variety of two-phase PDE systems under different noise levels, and the results demonstrate the effectiveness of the proposed approach.