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• Connections Between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation

  Hao Liu, Xue-Cheng Tai, Raymond Chan

  2023-11-06

  24741 2731 Pages:406-428 Open-access

• Deep Neural Network Approaches for Computing the Defocusing Action Ground State of Nonlinear Schrödinger Equation

  Zhipeng Chang, Zhenye Wen, Xiaofei Zhao

  2025-04-15

  6120 819 Pages:42-76

• Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

  Yuling Jiao, Xiliang Lu, Jerry Zhijian Yang, Cheng Yuan, Pingwen Zhang

  2023-09-15

  30240 2822 Pages:239-263

• On Residual Minimization for PDEs: Failure of PINN, Modified Equation, and Implicit Bias

  Tao Luo, Qixuan Zhou

  2026-01-21

  135 54 Pages:313-376