A scalable framework for learning the geometry-dependent solution operators of partial differential equations.

Solving partial differential equations (PDEs) using numerical methods is a ubiquitous task in engineering and medicine. However, the computational costs can be prohibitively high when many-query evaluations of PDE solutions on multiple geometries are needed. Here we aim to address this challenge by introducing Diffeomorphic Mapping Operator Learning (DIMON), a generic artificial intelligence framework that learns geometry-dependent solution operators of different types of PDE on a variety of geometries.

Imaging features of vertebral artery fenestration.

Purpose: Vertebral artery fenestration (VAF) is a rare congenital vascular anomaly which has been associated with intracranial aneurysm. VAF can share some similar imaging features with vertebral artery dissection (VAD), which may confound diagnosis of the latter on CT and MR angiography. The purpose of this investigation is to assess the prevalence of VAF, evaluate its association with other vascular anomalies, and identify imaging features to help in distinguishing VAF and VAD.