Recent work in scientific machine learning (SciML) has focused on incorporating partial
differential equation (PDE) information into the learning process. Much of this work has …

Existing work in scientific machine learning (SciML) has shown that data-driven learning of
solution operators can provide a fast approximate alternative to classical numerical partial …

Abstract The degenerate parabolic Generalized Porous Medium Equation (GPME) poses
numerical challenges due to self-sharpening and its sharp corner solutions. For these …

Two-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used
to approximately describe the evolution of radiation energy within a multimaterial system …

Existing work in scientific machine learning (SciML) has shown that data-driven learning of
solution operators can provide a fast approximate alternative to classical numerical partial …

To draw rigorous conclusions from scientific data, Bayesian statistics requires
computationally efficient methods for posterior inference as well as models that are both …

The discovery of meningeal lymphatic vessels [Louveau et al, 2015] is one of the most
impressive breakthroughs of neurophysiology of last years, and the problem of its …

The Stefan problem is introduced and discretized. The problem is then solved using three
different numerical schemes; arithmetic averaging (AA), shock-based averaging (SAM) with …

Abstract The degenerate parabolic Generalized Porous Medium Equation (GPME) poses
numerical challenges due to self-sharpening and its sharp corner solutions. Spurious …