Past Event: Oden Institute Seminar

Fast algorithms for nonlinear optimal control of geodesic flows of diffeomorphisms

Andreas Mang, Assistant Professor, Department of Mathematics, University of Houston

Abstract

In this talk, we will discuss optimal control formulations for diffeomorphic registration and algorithms for their solution. Our contributions are in the design of numerical methods and computational kernels that scale on high-performance computing platforms. Diffeomorphic registration is an infinite-dimensional, nonlinear inverse problem. The inputs are two views of the same object. Given these views, we seek a spatial transformation $y$ that relates points in one view to its corresponding points in the other. We consider an optimal control formulation; we introduce a pseudo-time variable $t$ and parameterize the sought-after mapping $y$ by its velocity $v$. Prescribing suitable regularity requirements for $v$ allows us to ensure that $y$ is a diffeomorphism. We will consider formulations with ODE-constraints to model the flow of the diffeomorphism $y$, hyperbolic PDE constraints to model the transport of the data, and initial value control formulations subject to the EPDiff equation.

Our solvers are based on state-of-the-art algorithms to enable fast convergence and short runtime. The applications of our methodology are in medical imaging. We will showcase results on real and synthetic data to study the rate of convergence, time-to-solution, numerical accuracy, and scalability of our solvers. As a highlight, we will showcase results for a GPU-accelerated implementation termed CLAIRE that allows us to solve clinically relevant 3D image registration problems to high accuracy in well under 10 seconds on a single GPU and scales up to 100s of GPUs.

This is joint work with Robert Azencott, George Biros, Jiwen He, Miriam Mehl, and others.

Biography

Andreas Mang is a member of the Numerical Analysis & Scientific Computing group at the Department of Mathematics of the University of Houston. I am the head of the SCOPA (Scientific Computing, Optimization, and Parallel Algorithms) group. A  list for some of the publications of his research groups and their collaborators here. The key areas of his research include:

• scientific computing and numerical methods
• numerical optimization and variational techniques
• non-linear optimal control
• inverse problems
• parallel and distributed-memory algorithms

His primary academic interest is the design, analysis, and deployment of computational methods that integrate data with simulation and optimization. His research targets applications in computational medicine to (i) aid data analysis, (ii) improve understanding, (iii) support decision-making, and (iv) aid design and control of clinical intervention with the ultimate aspiration to (v) improve and predict clinical outcome.