Mohammad Nooraiepour

Partial differential equations in the age of machine learning: a critical synthesis of classical, machine learning, and hybrid methods

Abstract Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature but epistemologically distinct...

Bridging Nanoscopic Surface Heterogeneity and MacroscopicNucleation Rates: A Perspective on Probabilistic Approaches

Abstract Predicting the number of newly formed crystals and their spatial distribution on surfaces or within pore spaces matters across many fields, from structural biology to coupled fluid flow and reactive transport in porous media to atmospheric physics. Nucleation occurs at m...