Vol. 40 No. 1 (2026)

Articles

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
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157 48 Pages:1-26
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
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220 63 Pages:27-60
Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank

Tao Tang, Jiang Yang, Yuxiang Zhao, Quanhui Zhu
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399 29 Pages:61-87
A Novel High-Resolution TENO Scheme with Adaptive Artificial Anti-Diffusion

Velmani Murugesan, Manoj T. Nair
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429 51 Pages:88-128
Full-Waveform Inversion with Unbalanced Optimal Transport Metric for Seismic Imaging

Liangrong Wang, Xingpeng Dong, Dinghui Yang
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173 46 Pages:129-152
A Diffusion Model Based Iterative Convolution Thresholding Method for Structural Topological Optimization

Xiaonan Peng, Luyu Cen, Xiaoping Wang
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150 29 Pages:153-175
Network Embedding Using Sparse Approximations of Random Walks

Paula Mercurio, Di Liu
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144 20 Pages:176-198
An Exponential-Free Runge–Kutta Framework for Developing Third-Order Unconditionally Energy Stable Schemes for the Cahn–Hilliard Equation

Haifeng Wang, Jingwei Sun, Hong Zhang, Xu Qian, Songhe Song
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151 34 Pages:199-238
A Locking-Free Weak Galerkin Finite Element Method for Linear Elasticity Problems Based on a Reconstruction Operator

Fuchang Huo, Ruishu Wang, Yanqiu Wang, Ran Zhang
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154 33 Pages:239-262
A Weak Galerkin Finite Element Method Coupled with Mortar Spectral Element Method for Schrödinger Eigenvalue Problem with an Inverse Square Potential

Shusheng Li, Lueling Jia, Qilong Zhai, Zhimin Zhang
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170 54 Pages:263-296