3 citations · 7 across the 7 of their papers we have counts for
8 papers
Lagrangian Flow Matching: A Least-Action Framework for Principled Path Design
Shukai Du, Junzhe Zhang, Yiming Li
Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the d…
Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer
Shukai Du, Samuel N. Stechmann
In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs)…
A note on devising HDG+ projections on polyhedral elements
Shukai Du, Francisco-Javier Sayas
In this note, we propose a simple way of constructing HDG+ projections on polyhedral elements. The projections enable us to analyze the Lehrenfeld-Schöberl HDG (HDG+) methods in a…
A unified error analysis of HDG methods for the static Maxwell equations
Shukai Du, Francisco-Javier Sayas
We propose a framework that allows us to analyze different variants of HDG methods for the static Maxwell equations using one simple analysis. It reduces all the work to the constr…
New analytical tools for HDG in elasticity, with applications to elastodynamics
Shukai Du, Francisco-Javier Sayas
We present some new analytical tools for the error analysis of hybridizable discontinuous Galerkin (HDG) method for linear elasticity. These tools allow us to analyze more variants…
Analysis of models for viscoelastic wave propagation
Thomas Brown, Shukai Du, Hasan Eruslu +1
We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time ver…
Calculation of Cauchy stress tensor in molecular dynamics system with a generalized Irving-Kirkwood formulism
Jerry Zhijian Yang, Shukai Du
Irving and Kirkwood formulism (IK formulism) provides a way to compute continuum mechanics quantities at certain location in terms of molecular variables. To make the approach more…
On the two mutually independent factors that determine the convergence of least-squares projection method
Shukai Du, Nailin Du
This paper investigates the least-squares projection method for bounded linear operators, which provides a natural regularization scheme by projection for many ill-posed problems.…