Physics-constrained robust learning of open-form partial differential equations from limited and noisy data

arXiv:2309.07672v2 Announce Type: replace
Abstract: Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise evaluations, which in turn result in redundant function terms or erroneous equations. This study proposes a framework to robustly uncover open-form partial differential equations (PDEs) from limited and noisy data. The framework operates through two alternating update processes: discovering and embedding. The discovering phase employs …

abstract arxiv challenge cs.lg cs.na data differential dynamic form function knowledge library math.na physics prior robust stat.ap systems terms type while