Yibo Yang

TL;DR: In this paper, a machine learning framework is proposed to constrain the output of deep neural networks such that their predictions satisfy the conservation of mass and momentum principles, which can return physically consistent predictions for velocity, pressure and wall displacement pulse wave propagation.

TL;DR: A deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks uses latent variable models to construct probabilistic representations for the system states, and puts forth an adversarial inference procedure for training them on data.

TL;DR: A physics-informed neural network for cardiac activation mapping that accounts for the underlying wave propagation dynamics and quantifies the epistemic uncertainty associated with these predictions to open the door toward physics-based electro-anatomic mapping.

TL;DR: A machine learning framework is put forth that enables the seamless synthesis of non-invasive in-vivo measurement techniques and computational flow dynamics models derived from first physical principles and is illustrated by showing how one-dimensional models of pulsatile flow can be used to constrain the output of deep neural networks such that their predictions satisfy the conservation of mass and momentum principles.

TL;DR: An implicit variational inference formulation that constrains the generative model output to satisfy given physical laws expressed by partial differential equations provide a regularization mechanism for effectively training deep probabilistic models for modeling physical systems in which the cost of data acquisition is high and training data-sets are typically small.