Jianwen Chen, Xinyu Yang, Peng Xia, Arian Azarang, Yueh Z Lee, Gang Li, Hongtu Zhu, Yun Li, Beidi Chen, Huaxiu Yao. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Advection-diffusion equations describe a large family of natural transport processes, e.g., fluid flow, heat transfer, and wind transport. They are also used for optical flow and perfusion imaging computations. We develop a machine learning model, D2-SONATA, built upon a stochastic advection-diffusion equation, which predicts the velocity and diffusion fields that drive 2D/3D image time-series of transport. In particular, our proposed model incorporates a model of transport atypicality, which isolates abnormal differences between expected normal transport behavior and the observed transport. In a medical context such a normalabnormal decomposition can be used, for example, to quantify pathologies. Specifically, our model identifies the advection and diffusion contributions from the transport timeseries and simultaneously predicts an anomaly value field to provide a decomposition into normal and abnormal advection and diffusion behavior. To achieve improved estimation performance for the velocity and diffusion-tensor fields underlying the advection-diffusion process and for the estimation of the anomaly fields, we create a 2D/3D anomalyencoded advection-diffusion simulator, which allows for supervised learning. We further apply our model on a brain perfusion dataset from ischemic stroke patients via transfer learning. Extensive comparisons demonstrate that our model successfully distinguishes stroke lesions (abnormal) from normal brain regions, while reconstructing the underlying velocity and diffusion tensor fields.

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.

Perfusion imaging is of great clinical importance and is used to assess a wide range of diseases including strokes and brain tumors. Commonly used approaches for the quantitative analysis of perfusion images are based on measuring the effect of a contrast agent moving through blood vessels and into tissue. Contrast-agent free approaches, for example, based on intravoxel incoherent motion and arterial spin labeling, also exist, but are so far not routinely used clinically. Existing contrast-agent-dependent methods typically rely on the estimation of the arterial input function (AIF) to approximately model tissue perfusion. These approaches neglect spatial dependencies. Further, as reliably estimating the AIF is non-trivial, different AIF estimates may lead to different perfusion measures. In this work we therefore propose PIANO, an approach that provides additional insights into the perfusion process. PIANO estimates the velocity and diffusion fields of an advection-diffusion model best explaining the contrast dynamics without using an AIF. PIANO accounts for spatial dependencies and neither requires estimating the AIF nor relies on a particular contrast agent bolus shape. Specifically, we propose a convenient parameterization of the estimation problem, a numerical estimation approach, and extensively evaluate PIANO. Simulation experiments show the robustness and effectiveness of PIANO, along with its ability to distinguish between advection and diffusion. We further apply PIANO on a public brain magnetic resonance (MR) perfusion dataset of acute stroke patients, and demonstrate that PIANO can successfully resolve velocity and diffusion field ambiguities and results in sensitive measures for the assessment of stroke, comparing favorably to conventional measures of perfusion.

Conveying data uncertainty in visualizations is crucial for preventing viewers from drawing conclusions based on untrustworthy data points. This paper proposes a methodology for efficiently generating density plots of uncertain multivariate data sets that draws viewers to preattentively identify values of high certainty while not calling attention to uncertain values. We demonstrate how to augment scatter plots and parallel coordinates plots to incorporate statistically modeled uncertainty and show how to integrate them with existing multivariate analysis techniques, including outlier detection and interactive brushing. Computing high quality density plots can be expensive for large data sets, so we also describe a probabilistic plotting technique that summarizes the data without requiring explicit density plot computation. These techniques have been useful for identifying brain tumors in multivariate magnetic resonance spectroscopy data and we describe how to extend them to visualize ensemble data sets.