8 papers
Non-Uniform Quantum Fourier Transform
Junaid Aftab, Yuehaw Khoo, Haizhao Yang
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Unifor…
FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction
Jiaxin Yuan, Haizhao Yang, Maria Cameron
Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off bet…
Curse of Dimensionality in Neural Network Optimization
Sanghoon Na, Haizhao Yang
This paper demonstrates that when a shallow neural network with a Lipschitz continuous activation function is trained using either empirical or population risk to approximate a tar…
AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing
Jianda Du, Youran Sun, Haizhao Yang
PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent ne…
Protocode: Prototype-Driven Interpretability for Code Generation in LLMs
Krishna Vamshi Bodla, Haizhao Yang
Since the introduction of Large Language Models (LLMs), they have been widely adopted for various tasks such as text summarization, question answering, speech-to-text translation,…
Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces
Yahong Yang, Yue Wu, Haizhao Yang +1
This paper introduces deep super ReLU networks (DSRNs) as a method for approximating functions in Sobolev spaces measured by Sobolev norms for with $m\ge…