2.3k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Shuguang Cui5 profiles29 · h 63
- Arnulf Jentzen22 · h 49
- Z. Luo18 · h 89
- Guangxu Zhu5 profiles17 · h 33
- Xiaoguang Han2 profiles15 · h 42
- Hang Li2 profiles13 · h 18
- Tsung-Hui Chang11 · h 45
- Qingjiang Shi3 profiles9 · h 36
- H. Poor2 profiles7 · h 141
- Rui Zhang3 profiles7 · h 137
- Shiyin Li7 · h 21
- Xiaoyang Li2 profiles7 · h 9
- Chinese University of Hong Kong, ShenzhenCN158 papers
- University of MünsterDE21 papers
- Chinese University of Hong KongHK16 papers
- University of Hong KongHK15 papers
- ETH ZurichCH14 papers
- Sun Yat-sen UniversityCN13 papers
- National University of SingaporeSG12 papers
- Peng Cheng LaboratoryCN10 papers
- Princeton UniversityUS10 papers
- Tongji UniversityCN10 papers
- Beijing University of Posts and TelecommunicationsCN9 papers
- Chinese Academy of SciencesCN9 papers
17 papers · 1 filter
Adaptive feature capture method for solving partial differential equations with near singular solutions
Yangtao Deng, Qiaolin He, Xiaoping Wang
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh gene…
A Relaxed Lagrange Multiplier Approach for Phase Field Models
Jinpeng Zhang, Chaoyu Quan, Xiaoping Wang
This paper introduces a novel relaxed Lagrange multiplier (RLM) method for designing efficient and energy-stable numerical schemes for phase-field models. The proposed approach ref…
An efficient Monte Carlo scheme for Zakai equations
Christian Beck, Sebastian Becker, Patrick Cheridito +2
In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE i…
Fast operator splitting methods for obstacle problems
Hao Liu, Dong Wang
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this pape…
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
Sebastian Becker, Arnulf Jentzen, Marvin S. Müller +1
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many fina…
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions
Arnulf Jentzen, Adrian Riekert
In this article we study the stochastic gradient descent (SGD) optimization method in the training of fully-connected feedforward artificial neural networks with ReLU activation. T…
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
Patrick Cheridito, Arnulf Jentzen, Adrian Riekert +1
Gradient descent optimization algorithms are the standard ingredients that are used to train artificial neural networks (ANNs). Even though a huge number of numerical simulations i…
An overview on deep learning-based approximation methods for partial differential equations
Christian Beck, Martin Hutzenthaler, Arnulf Jentzen +1
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-b…
Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
Weinan E, Jiequn Han, Arnulf Jentzen
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonli…
Neural Parametric Fokker-Planck Equations
Shu Liu, Wuchen Li, Hongyuan Zha +1
In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a for…
Jacobi-type algorithm for low rank orthogonal approximation of symmetric tensors and its convergence analysis
Jianze Li, Konstantin Usevich, Pierre Comon
In this paper, we propose a Jacobi-type algorithm to solve the low rank orthogonal approximation problem of symmetric tensors. This algorithm includes as a special case the well-kn…
Full error analysis for the training of deep neural networks
Christan Beck, Arnulf Jentzen, Benno Kuckuck
Deep learning algorithms have been applied very successfully in recent years to a range of problems out of reach for classical solution paradigms. Nevertheless, there is no complet…
Deep neural network approximations for Monte Carlo algorithms
Philipp Grohs, Arnulf Jentzen, Diyora Salimova
Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are…
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients
Arnulf Jentzen, Diyora Salimova, Timo Welti
In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, ob…
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Philipp Grohs, Fabian Hornung, Arnulf Jentzen +1
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recogniti…
Approximate Newton Methods
Haishan Ye, Luo Luo, Zhihua Zhang
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsam…
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Weinan E, Martin Hutzenthaler, Arnulf Jentzen +1
We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time p…