Search Results

• Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Lévy Equations

  Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi

  2026-04-10

  16 9 Pages:1-26

• 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

  11908 963 Pages:575-602

• 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

  39705 3967 Pages:571-598

• 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

  41316 3295 Pages:789-802

• 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

  64566 3385 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

  5368 890 Pages:181-222

• 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

  38829 3011 Pages:975-1006

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

  Zhen Gao, Jan S. Hesthaven

  2011-10-01

  38207 4009 Pages:253-278

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

  Bo Li, Shanshan Tang, Haijun Yu

  2019-12-07

  52007 3443 Pages:379-411

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

  Bangde Liu, Guang Lin

  2020-11-18

  62690 3393 Pages:1937-1969

• VAE-KRnet and Its Applications to Variational Bayes

  Xiaoliang Wan, Shuangqing Wei

  2022-03-30

  52385 3283 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

  50095 4778 Pages:190-209

• 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

  50085 4589 Pages:97-123

• 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

  48674 4392 Pages:67-96

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

  Lorella Fatone, Giuseppe Rao, Maria Cristina Recchioni, Francesco Zirilli

  2007-02-01

  37948 4102 Pages:1139-1173

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

  Liang Yan, Tao Zhou

  2020-11-18

  67461 3467 Pages:2180-2205

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

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

  2020-11-18

  67411 3702 Pages:1886-1906

• 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

  86730 4362 Pages:1746-1767

• Preface

  2020-11-18

  364 102 Pages:i-i

• A Mixed Wavelet-Learning Method of Predicting Macroscopic Effective Heat Transfer Conductivities of Braided Composite Materials

  Hao Dong, Wenbo Kou, Junyan Han, Jiale Linghu, Minqiang Zou, Junzhi Cui

  2022-01-27

  43169 3276 Pages:593-625

• 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

  45191 3171 Pages:460-479

• 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

  48709 3389 Pages:838-854

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

  Lukas Felsberger, Phaedon-Stelios Koutsourelakis

  2019-01-10

  48761 5411 Pages:1259-1301

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

  Zhen Gao, Tao Zhou

  2014-08-03

  42513 4174 Pages:365-381

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

  Xiaoda Pan, Hengliang Zhu, Fan Yang, Xuan Zeng

  2013-09-05

  39330 3946 Pages:639-663

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

  Naoufel Ben Abdallah, Hao Wu

  2011-10-01

  40313 4158 Pages:882-898

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

  Sihong Shao, Tiao Lu, Wei Cai

  2011-03-05

  39602 3982 Pages:711-739