4 papers
A Probabilistic Approach to Trajectory-Based Optimal Experimental Design
Ahmed Attia
We present a novel probabilistic approach for optimal experimental path design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and tr…
Path-OED for infinite-dimensional Bayesian linear inverse problems governed by PDEs
J. Nicholas Neuberger, Alen Alexanderian, Bart van Bloemen Waanders +1
We consider infinite-dimensional Bayesian linear inverse problems governed by time-dependent partial differential equations (PDEs) and develop a mathematical and computational fram…
Optimal experimental design with k-space data: application to inverse hemodynamics
Miriam Löcke, Ahmed Attia, Dariusz UcÃnski +1
Subject-specific cardiovascular models rely on parameter estimation using measurements such as 4D Flow MRI data. However, acquiring high-resolution, high-fidelity functional flow d…
Distributional Sensitivity Analysis: Enabling Differentiability in Sample-Based Inference
Pi-Yueh Chuang, Ahmed Attia, Emil Constantinescu
This work introduces a mathematical framework for estimating the space-parameter sensitivity of random samples in arbitrary dimensions. Such sensitivity effectively acts as gradien…