Constrained optimization in fluid mechanics and medical imaging

Abstract
This talk will explore how techniques from constrained optimization have proven useful in both fluid mechanics and medical imaging research. On the fluid mechanics side, sharp interface methods for the multi-material Euler equations based on volume-of-fluid (VOF) interface tracking will be discussed, and it will be shown how the application of the Karush-Kuhn-Tucker conditions to volume fraction updates can enable more general update schemes. On the medical imaging side, improvements to digital subtraction angiography using a simple constraint on neural network outputs, and inference of hidden velocity field components in hemodynamic flows using physics informed neural networks will be discussed.

Speaker Bio
Dr. Murray Cutforth is a research scientist on the PSAAP III project at the Stanford. He works with Professor Eric Darve on uncertainty quantification of laser-ignited turbulent combustion. During his PhD at the University of Cambridge, Murray studied sharp interface methods for multi-material flow, and subsequently has worked on applications of machine learning in medical image and text analysis at Canon Medical Research.