34 citations · 212 across the 40 of their papers we have counts for
5 papers · 1 filter
Wall laws for viscous flows in 3D randomly rough pipes: optimal convergence rates and stochastic integrability
Mitsuo Higaki, Yulong Lu, Jinping Zhuge
This paper is concerned with effective approximations and wall laws of viscous laminar flows in 3D pipes with randomly rough boundaries. The random roughness is characterized by th…
In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning
Frank Cole, Yulong Lu, Wuzhe Xu +1
We study theoretical guarantees for solving linear systems in-context using a linear transformer architecture. For in-domain generalization, we provide neural scaling laws that bou…
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^…
Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
Frank Cole, Yulong Lu
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we…