21 citations · 65 across the 18 of their papers we have counts for
8 papers · 1 filter
Improving Data Fidelity via Diffusion Model-based Correction and Super-Resolution
Wuzhe Xu, Yulong Lu, Sifan Wang +1
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. Fi…
Diffusion-based Models for Unpaired Super-resolution in Fluid Dynamics
Wuzhe Xu, Yulong Lu, Lian Shen +2
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, dire…
Generative downscaling of PDE solvers with physics-guided diffusion models
Yulong Lu, Wuzhe Xu
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be…
Fully discretized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem
Ziang Chen, Jianfeng Lu, Yulong Lu +1
This paper studies the numerical approximation of the ground state of the Gross-Pitaevskii (GP) eigenvalue problem with a fully discretized Sobolev gradient flow induced by the $H^…
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms
Yahong Yang, Yulong Lu
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionalit…
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu
Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments. This paper derives complexity estimates of t…