212 citations · 568 across the 48 of their papers we have counts for
11 papers · 1 filter
Controlling conservation laws I: entropy-entropy flux
Wuchen Li, Siting Liu, Stanley Osher
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on con…
Heavy Ball Neural Ordinary Differential Equations
Hedi Xia, Vai Suliafu, Hangjie Ji +4
We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural OD…
Improving Transformers with Probabilistic Attention Keys
Tam Nguyen, Tan M. Nguyen, Dung D. Le +5
Multi-head attention is a driving force behind state-of-the-art transformers, which achieve remarkable performance across a variety of natural language processing (NLP) and compute…
Computational Mean-field information dynamics associated with Reaction diffusion equations
Wuchen Li, Wonjun Lee, Stanley Osher
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapu…
Operator Splitting for Learning to Predict Equilibria in Convex Games
Daniel McKenzie, Howard Heaton, Qiuwei Li +3
Systems of competing agents can often be modeled as games. Assuming rationality, the most likely outcomes are given by an equilibrium (e.g. a Nash equilibrium). In many practical s…
Direct observation of 3D topological spin textures and their interactions using soft x-ray vector ptychography
Arjun Rana, Chen-Ting Liao, Ezio Iacocca +21
Magnetic topological defects are energetically stable spin configurations characterized by symmetry breaking. Vortices and skyrmions are two well-known examples of 2D spin textures…