Zhongqiang Zhang

1. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
   2021/03/18 by Lu Lu, Pengzhan Jin, Guofei Pang +2 · 230 citations
   Computer Science · Physics and Astronomy · #Model Reduction and Neural Networks #Neural Networks and Applications #Stochastic Gradient Optimization Techniques
2. Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
   2019/11/27 by Ehsan Kharazmi, Kharazmi, E., Zhongqiang Zhang +3 · 24 citations
   Computer Science · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #Nuclear Engineering Thermal-Hydraulics #Numerical Analysis (math.NA)
3. hp-VPINNs: Variational physics-informed neural networks with domain decomposition
   2020/12/04 by Ehsan Kharazmi, Zhongqiang Zhang, George E.M. Karniadakis +1 · 27 citations
   Engineering · Materials Science · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Magnetic Properties and Applications #Model Reduction and Neural Networks
4. Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity
   2024/05/29 by Benjamin Shih, Ahmad Peyvan, Shih, Benjamin +5 · 14 citations
   Computer Science · #Neural Networks and Applications
5. Error estimates of residual minimization using neural networks for linear PDEs
   2020/10/15 by Yeonjong Shin, Zhongqiang Zhang, Shin, Yeonjong +3 · 7 citations
   Engineering · Physics and Astronomy · #35J25 #35S15 #41A46 #65M12 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering
6. Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses
   2024/01/11 by Siavash Jafarzadeh, Jafarzadeh, Siavash, Stewart Silling +7 · 4 citations
   Computer Science · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Materials Science (cond-mat.mtrl-sci) #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical methods in engineering
7. Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients
   2023/03/26 by Xiaojie Wang, Wang, Xiaojie, Yuying Zhao +3 · 3 citations
   Economics, Econometrics and Finance · Social Sciences · #60H15 #60H35 #65C30 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Stochastic processes and financial applications
8. Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk
   2021/03/24 by Zhaopeng Hao, Huiyuan Li, Zhimin Zhang +1 · 2 citations
   Mathematics · #Fractional Differential Equations Solutions #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems
9. A Modified Walk-on-sphere Method for High Dimensional Fractional Poisson Equation
   2022/08/13 by Caiyu Jiao, Changpin Li, Jiao, Caiyu +5 · 2 citations
   Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering
10. Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
    2024/02/12 by Zheyuan Hu, Zhongqiang Zhang, Hu, Zheyuan +5 · 2 citations
    Physics and Astronomy · Computer Science · #Model Reduction and Neural Networks #Gaussian Processes and Bayesian Inference #Statistical Mechanics and Entropy
11. Tensor neural networks for high-dimensional Fokker-Planck equations
    2024/04/08 by Taorui Wang, Wang, Taorui, Zheyuan Hu +7 · 2 citations
    Physics and Astronomy · Computer Science · Mathematics · #Model Reduction and Neural Networks #Gaussian Processes and Bayesian Inference #Tensor decomposition and applications
12. On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients
    2025/02/07 by Jiamin Jian, Qingshuo Song, Jian, Jiamin +7 · 4 citations
    Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Gas Dynamics and Kinetic Theory
13. Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients II: finite moments and higher-order schemes
    2024/06/20 by Yuying Zhao, Xiaojie Wang, Zhao, Yuying +3 · 1 citation
    Economics, Econometrics and Finance · Mathematics · Computer Science · #Stochastic processes and financial applications #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering