Search Results

• Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations

  Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler, Arnulf Jentzen, Philippe von Wurstemberger

  2020-11-18

  64386 3357 Pages:2109-2138

• A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

  Yaqin Zhang, Ke Li, Zhipeng Chang, Xuejiao Liu, Yunqing Huang, Xueshuang Xiang

  2025-07-11

  5235 749 Pages:181-222

• Application of High Dimensional B-Spline Interpolation in Solving the Gyro-Kinetic Vlasov Equation Based on Semi-Lagrangian Method

  Xiaotao Xiao, Lei Ye, Yingfeng Xu & Shaojie Wang

  2017-09-02

  41217 3267 Pages:789-802

• An Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient

  Zhiwen Zhang, Xin Hu, Thomas Y. Hou, Guang Lin & Mike Yan

  2014-12-08

  39606 3927 Pages:571-598

• An Efficient Reduced-Order Model Based on Dynamic Mode Decomposition for Parameterized Spatial High-Dimensional PDEs

  Yifan Lin, Xiang Sun, Jie Nie, Yuanhong Chen, Zhen Gao

  2025-09-02

  11746 904 Pages:575-602

• High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method

  Bangde Liu, Guang Lin

  2020-11-18

  62546 3360 Pages:1937-1969

• Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units

  Bo Li, Shanshan Tang, Haijun Yu

  2019-12-07

  51826 3403 Pages:379-411

• Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

  Zhen Gao & Jan S. Hesthaven

  2011-10-01

  38124 3983 Pages:253-278

• Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations

  F. Chinesta, E. Abisset-Chavanne, A. Ammar & E. Cueto

  2018-04-02

  38759 2982 Pages:975-1006

• VAE-KRnet and Its Applications to Variational Bayes

  Xiaoliang Wan, Shuangqing Wei

  2022-03-30

  52262 3243 Pages:1049-1082

• Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm

  Mingwei Dai, Shuyang Dai, Junjun Huang, Lican Kang, Xiliang Lu

  2021-04-30

  50008 4654 Pages:190-209

• Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature

  Gregery T. Buzzard & Dongbin Xiu

  2011-03-05

  39245 3847 Pages:542-567

• Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport

  Sihong Shao, Tiao Lu & Wei Cai

  2011-03-05

  39530 3945 Pages:711-739

• A Generalized Stationary Algorithm for Resonant Tunneling: Multi-Mode Approximation and High Dimension

  Naoufel Ben Abdallah & Hao Wu

  2011-10-01

  40233 4126 Pages:882-898

• Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

  Xiaoda Pan, Hengliang Zhu, Fan Yang & Xuan Zeng

  2013-09-05

  39255 3919 Pages:639-663

• On the Choice of Design Points for Least Square Polynomial Approximations with Application to Uncertainty Quantification

  Zhen Gao & Tao Zhou

  2014-08-03

  42425 4122 Pages:365-381

• Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics

  Lukas Felsberger & Phaedon-Stelios Koutsourelakis

  2019-01-10

  48659 5379 Pages:1259-1301

• Optimal Error Estimates of a Linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki Equations

  Dongfang Li, Waixiang Cao, Chengjian Zhang & Zhimin Zhang

  2019-04-28

  48598 3339 Pages:838-854

• Upwind Biased Local RBF Scheme with PDE Centres for the Steady Convection Diffusion Equations with Continuous and Discontinuous Boundary Conditions

  K. Monysekar, Y. V. S. S. Sanyasiraju

  2019-12-07

  45099 3142 Pages:460-479

• A Distributed Optimal Control Problem with Averaged Stochastic Gradient Descent

  Qi Sun, Qiang Du

  2020-07-30

  46613 3720 Pages:753-774

• Preface

  2020-11-18

  245 60 Pages:i-i

• Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

  Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma

  2020-11-18

  86027 4254 Pages:1746-1767

• A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales

  Xi-An Li, Zhi-Qin John Xu, Lei Zhang

  2020-11-18

  67253 3664 Pages:1886-1906

• An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems

  Liang Yan, Tao Zhou

  2020-11-18

  67252 3430 Pages:2180-2205

• High Performance Algorithms Based on a New Wavelet Expansion for Time Dependent Acoustic Obstacle Scattering

  L. Fatone, G. Rao, M. C. Recchioni & F. Zirilli

  2007-02-01

  37864 4066 Pages:1139-1173

• Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem

  Jiajie Chen, Xiaofeng Cai, Jianxian Qiu, Jing-Mei Qiu

  2021-04-30

  48557 4329 Pages:67-96

• Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

  Zhen Gao, Qi Liu, Jan S. Hesthaven, Bao-Shan Wang, Wai Sun Don, Xiao Wen

  2021-04-30

  49968 4514 Pages:97-123