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• Full-Waveform Inversion with Unbalanced Optimal Transport Metric for Seismic Imaging

  Liangrong Wang, Xingpeng Dong, Dinghui Yang

  2026-04-10

  104 16 Pages:129-152

• A Complete Error Analysis of PINNs for Elliptic Equations Using Projected Stochastic Gradient Descent

  Yuling Jiao, Ruoxuan Li, Defeng Sun, Peiying Wu, Jerry Zhijian Yang

  2026-04-10

  111 25 Pages:27-60

• 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

  103 22 Pages:1-26

• The First- and Second-Order Energy Stable, Mass Conservative and Bounds-Preserving Schemes for Two-Phase Incompressible Flow with Rock Compressibility

  Yujing Yan, Huangxin Chen, Xiaoli Li

  2026-01-18

  817 173 Pages:1332-1362

• Local Discontinuous Galerkin Method for Nonlinear BSPDEs of Neumann Boundary Conditions with Deep Backward Dynamic Programming Time-Marching

  Yixiang Dai, Yunzhang Li, Jing Zhang

  2026-01-18

  779 121 Pages:1299-1331

• A Highly Efficient CN-Like Scheme for the Transient Wigner Equation

  Yidan Wang, Haiyan Jiang, Tiao Lu, Wenqi Yao

  2026-01-03

  1915 101 Pages:775-798

• Solving Multi-Group Neutron Diffusion Eigenvalue Problem with Decoupling Residual Loss Function

  Shupei Yu, Qiaolin He, Shiquan Zhang, Qihong Yang, Yu Yang, Helin Gong

  2026-01-18

  768 108 Pages:1231-1266

• A Locally Mass-Conservative Enriched Petrov-Galerkin Method Without Penalty for the Darcy Flow in Porous Media

  Huangxin Chen, Piaopiao Dong, Shuyu Sun, Zixuan Wang

  2026-01-18

  743 109 Pages:1199-1230

• Maximum-Principle-Preserving and Positivity-Preserving Central WENO Schemes on Overlapping Meshes

  Zhanjing Tao, Zhengfu Xu, Jianxian Qiu

  2026-01-18

  743 116 Pages:1164-1198

• Long-Time Integration of Nonlinear Wave Equations with Neural Operators

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  784 143 Pages:1137-1163

• Steady-State Simulation of Euler Equations by the Discontinuous Galerkin Method with the Jump Filter

  Lei Wei, Yinhua Xia

  2026-01-18

  784 153 Pages:1103-1136

• High-Order Structure-Preserving Spectral Difference Methods for Hyperbolic Conservation Laws

  Yupeng Ren, Zhimin Zhang

  2026-01-18

  826 181 Pages:1059-1102

• Do We Need Decay-Preserving Error Estimate for Solving Parabolic Equations with Initial Singularity?

  Jiwei Zhang, Zhimin Zhang, Chengchao Zhao

  2026-01-18

  788 157 Pages:1027-1058

• Least-Squares Recovery of Dual Variables in ROMs for Saddle-Point Problems

  M. Azaïez, T. Chacόn Rebollo, M. Oulghelou, I. Sánchez Muñoz

  2026-01-18

  759 151 Pages:1002-1026

• Quantum Simulation of the Fokker-Planck Equation via Schrödingerization

  Shi Jin, Nana Liu, Yue Yu

  2026-01-18

  1051 296 Pages:969-1001

• Reconstruction of Dynamical Systems Without Time Label

  Zhijun Zeng, Chenglong Bao, Pipi Hu, Yi Zhu, Zuoqiang Shi

  2026-01-03

  1936 110 Pages:941-968

• Derivation of Asymptotic Limiting Equations for Multigroup Anisotropic-Scattering Transport Processes in Optically Thick Regimes

  Weiming Li, Chang Liu, Peng Song

  2026-01-03

  1917 94 Pages:919-940

• Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations II: A CNNs-Based Automatic Implementation

  Jingfeng Wang, Guanghui Hu

  2026-01-03

  1926 80 Pages:884-918

• Neural-Network-Augmented Empirical Interpolation Method for Field Reconstruction with Noise and Vibration Tolerance

  Han Li, Helin Gong, Chuanju Xu

  2026-01-03

  1919 80 Pages:855-883

• Scale-Decomposed Physics-Informed Neural Networks for Singular Perturbation Problems

  Lei Zhang, Guowei He

  2026-01-18

  1014 227 Pages:1267-1298

• Efficient Dual Algorithms for Image Segmentation Using TV-Allen-Cahn Type Models

  Li-Lian Wang, Ying Cu

  2011-09-01

  38955 4051 Pages:859-877

• Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge

  Huadong Gao

  2019-10-31

  42904 4908 Pages:182-201

• A Mixed Finite Element Scheme for Biharmonic Equation with Variable Coefficient and von Kármán Equations

  Huangxin Chen, Amiya K. Pani, Weifeng Qiu

  2022-05-06

  44701 3342 Pages:1434-1466

• Nonconforming Finite Elements for the −curl∆curl and Brinkman Problems on Cubical Meshes

  Qian Zhang, Min Zhang, Zhimin Zhang

  2023-12-11

  34215 2660 Pages:1332-1360