LINFA: a Python library for variational inference with normalizing flow and annealing

Variational inference is an increasingly popular method in statistics and machine learning for approximating probability distributions. We developed LINFA (Library for Inference with Normalizing Flow and Annealing), a Python library for variational inference to accommodate computationally expensive models and difficult-to-sample distributions with dependent parameters. We discuss the theoretical background, capabilities, and performance of LINFA in various benchmarks. LINFA is publicly available on GitHub at https://github.com/desResLab/LINFA

Direct estimation of wall shear stress from aneurysmal morphology: A statistical approach

Computational fluid dynamics (CFD) is a valuable tool for studying vascular diseases, but requires long computational time. To alleviate this issue, we propose a statistical framework to predict the aneurysmal wall shear stress patterns directly from the aneurysm shape. A database of 38 complex intracranial aneurysm shapes is used to generate aneurysm morphologies and CFD simulations. The shapes and wall shear stresses are then converted to clouds of hybrid points containing both types of information. These are subsequently used to train a joint statistical model implementing a mixture of principal component analyzers. Given a new aneurysmal shape, the trained joint model is firstly collapsed to a shape only model and used to initialize the missing shear stress values. The estimated hybrid point set is further refined by projection to the joint model space. We demonstrate that our predicted patterns can achieve significant similarities to the CFD-based results

A matching pursuit approach to solenoidal filtering of three-dimensional velocity measurements

Methodologies to acquire three-dimensional velocity fields are becoming increasingly available, generating large datasets of steady state and transient flows of engineering and/or biomedical interest. This paper presents a novel linear filter for three-dimensional velocity acquisitions, which eliminates the spurious velocity divergence due to measurement errors. The noise reduction properties of the associated linear operator are discussed together with the treatment of boundary conditions. Examples show the application of the technique to real velocity fields acquired through volumetric Particle Image Velocimetry. The effectiveness of the filter is demonstrated by application to synthetic velocity fields obtained from analytical solutions and computations. The filter eliminates about half of the noise, without artificial smoothing of the original data, and conserves localized flow features