Discovering Hidden Physics Behind Transport Dynamics

TL;DR

This paper introduces YETI, a novel learning framework that estimates the hidden physics of transport phenomena by inferring velocity and diffusion tensor fields from image time-series, with applications in medical imaging.

Contribution

It presents a new auto-encoder based method incorporating physical constraints and a simulator for pre-training, improving estimation accuracy of transport physics from imaging data.

Findings

Successfully distinguishes stroke lesions from normal brain regions.

Demonstrates improved estimation accuracy with physical constraints.

Applies transfer learning to real medical data.

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 commonly 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.