30 citations · 39 across the 15 of their papers we have counts for
11 papers · 1 filter
Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations
Dai Shi, Luke Thompson, Andi Han +3
In this paper, we explore how our recently developed Wiener Chaos Expansion (WCE)-based neural operator (NO) can be applied to singular stochastic partial differential equations, e…
RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data
Peiyan Hu, Haodong Feng, Hongyuan Liu +13
Predicting the evolution of complex physical systems remains a central problem in science and engineering. Despite rapid progress in scientific Machine Learning (ML) models, a crit…
On the Design of One-step Diffusion via Shortcutting Flow Paths
Haitao Lin, Peiyan Hu, Minsi Ren +5
Recent advances in few-step diffusion models have demonstrated their efficiency and effectiveness by shortcutting the probabilistic paths of diffusion models, especially in trainin…
From Uncertain to Safe: Conformal Adaptation of Diffusion Models for Safe PDE Control
Peiyan Hu, Xiaowei Qian, Wenhao Deng +8
The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requi…
On the Guidance of Flow Matching
Ruiqi Feng, Chenglei Yu, Wenhao Deng +2
Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where generation under energy guidance (abbrevia…
Wavelet Diffusion Neural Operator
Peiyan Hu, Rui Wang, Xiang Zheng +7
Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative mode…
Multi-modal Policies with Physics-informed Representations in Complex Fluid Environments
Haodong Feng, Peiyan Hu, Yue Wang +1
Control in fluid environments is an important research area with numerous applications across various domains, including underwater robotics, aerospace engineering, and biomedical…
Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey
Haixin Wang, Yadi Cao, Zijie Huang +13
This paper explores the recent advancements in enhancing Computational Fluid Dynamics (CFD) tasks through Machine Learning (ML) techniques. We begin by introducing fundamental conc…
DiffPhyCon: A Generative Approach to Control Complex Physical Systems
Long Wei, Peiyan Hu, Ruiqi Feng +7
Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computati…
Better Neural PDE Solvers Through Data-Free Mesh Movers
Peiyan Hu, Yue Wang, Zhi-Ming Ma
Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system ev…
Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs
Peiyan Hu, Qi Meng, Bingguang Chen +6
Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generation…