2 citations · 5 across the 5 of their papers we have counts for
6 papers
A Mathematical Explanation of Transformers
Xue-Cheng Tai, Hao Liu, Lingfeng Li +1
The Transformer architecture has revolutionized the field of sequence modeling and underpins the recent breakthroughs in large language models (LLMs). However, a comprehensive math…
Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping
Han Zhang, Xue-Cheng Tai, Jean-Michel Morel +1
Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. Howev…
A Mathematical Explanation of UNet
Xue-Cheng Tai, Hao Liu, Raymond H. Chan +1
The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine lea…
BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet
Lingfeng Li, Xue-Cheng Tai, Raymond Chan
Cardiovascular diseases (CVDs) are the leading cause of death worldwide, with blood pressure serving as a crucial indicator. Arterial blood pressure (ABP) waveforms provide continu…
Double-well Net for Image Segmentation
Hao Liu, Jun Liu, Raymond H. Chan +1
In this study, our goal is to integrate classical mathematical models with deep neural networks by introducing two novel deep neural network models for image segmentation known as…
A Meshless Solver for Blood Flow Simulations in Elastic Vessels Using Physics-Informed Neural Network
Han Zhang, Raymond Chan, Xue-Cheng Tai
Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood…