Discovering Hidden Physics Behind Transport Dynamics

Abstract

Transport processes are ubiquitous. They are, for example, at the heart of optical flow approaches; or of perfusion imaging, where blood transport is assessed, most com- monly by injecting a tracer. An advection-diffusion equation is widely used to describe these transport phenomena. Our goal is estimating the underlying physics of advection-diffusion equations, expressed as velocity and diffusion tensor fields. We propose a learning framework (YETI) building on an auto-encoder structure between 2D and 3D image time-series, which incorporates the advection-diffusion model. To help with identifiability, we develop an advection-diffusion simulator which allows pre-training of our model by supervised learning using the velocity and diffusion tensor fields. Instead of directly learning these velocity and diffusion tensor fields, we introduce representations that assure incompressible flow and symmetric positive semi-definite diffusion fields and demonstrate the additional benefits of these representations on improving estimation accuracy. We further use transfer learning to apply YETI on a public brain magnetic resonance (MR) perfusion dataset of stroke patients and show its ability to successfully distinguish stroke lesions from normal brain regions via the estimated velocity and diffusion tensor fields.

Publication
IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, virtual, June 19-25, 2021
Peirong Liu
Peirong Liu
Graduate Student in Computer Science

My research interests include machine learning, computer vision, partial differential equations, and perfusion imaging.

Lin Tian
Lin Tian
Graduate Student in Computer Science

My research interests include image registration and machine learning.

Marc Niethammer
Marc Niethammer
Professor of Computer Science

My research interests include image registration, image segmentation, shape analysis, machine learning, and biomedical applications.

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