# Discovering Hidden Physics Behind Transport Dynamics

arXiv: https://arxiv.org/abs/2011.12222 · HTML: https://mlsanity.com/paper/2011.12222/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2020.

## Built on by (most cited first, 8 of 8)

- [Brain-ID: Learning Contrast-agnostic Anatomical Representations for Brain Imaging](https://mlsanity.com/paper/2311.16914/) (2023)
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- [PEPSI: Pathology-Enhanced Pulse-Sequence-Invariant Representations for Brain MRI](https://mlsanity.com/paper/2403.06227/) (2024)
- [A Modality-agnostic Multi-task Foundation Model for Human Brain Imaging](https://mlsanity.com/paper/2509.00549/) (2025)
- [HelmFluid: Learning Helmholtz Dynamics for Interpretable Fluid Prediction](https://mlsanity.com/paper/2310.10565/) (2023)
- [Deep Decomposition for Stochastic Normal-Abnormal Transport](https://mlsanity.com/paper/2111.14777/) (2021)
- [Unraveling Normal Anatomy via Fluid-Driven Anomaly Randomization](https://mlsanity.com/paper/2501.13370/) (2025)
- [Differential Motion Evolution for Fine-Grained Motion Deformation in Unsupervised Image Animation](https://mlsanity.com/paper/2110.04658/) (2021)

## Abstract (arXiv)

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.