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math.NA2024★ 2 cited
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…
math.NA2023
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…