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  • Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks

    Jingrun Chen, Rui Du, Panchi Li, Liyao Lyu
    2021-01-26
    DOI:10.4208/nmtma.OA-2020-0062
    46504 2785 pp. 377-404
  • Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations

    Fengjiang Fu, Xiaoqun Wang
    2023-08-29
    DOI:10.4208/nmtma.OA-2022-0166
    28533 2542 pp. 668-700
  • Error Analysis of the Mixed Residual Method for Elliptic Equations

    Kai Gu, Peng Fang, Zhiwei Sun, Rui Du
    2024-05-11
    DOI:10.4208/nmtma.OA-2023-0136
    21191 1750 pp. 534-554
  • Analysis of Deep Ritz Methods for Semilinear Elliptic Equations

    Mo Chen, Yuling Jiao, Xiliang Lu, Pengcheng Song, Fengru Wang, Jerry Zhijian Yang
    2024-02-26
    DOI:10.4208/nmtma.OA-2023-0058
    23900 2469 pp. 181-209
  • Error Analysis of the Deep Mixed Residual Method for High-Order Elliptic Equations

    Mengjia Bai, Jingrun Chen, Rui Du, Zhiwei Sun
    2025-05-16
    DOI:10.4208/nmtma.OA-2024-0134
    7578 593 pp. 395-436
  • HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network

    Muzhou Hou, Yinghao Chen, Shen Cao, Yuntian Chen, Jinyong Ying
    2023-11-07
    DOI:10.4208/nmtma.OA-2023-0097
    29995 2587 pp. 883-913
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