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• Asymptotic Expansion Regularization for Inverse Source Problems in Two-Dimensional Singularly Perturbed Nonlinear Parabolic PDEs

  Dmitrii Chaikovskii, Aleksei Liubavin, Ye Zhang

  2023-10-26

  27069 2446 Pages:721-757

• A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements

  Xiaodong Liu, Shixu Meng

  2023-10-26

  29396 2606 Pages:653-671

• Determination of Source Terms in Diffusion and Wave Equations by Observations After Incidents: Uniqueness and Stability

  Jin Cheng, Shuai Lu, Masahiro Yamamoto

  2023-02-14

  31702 2993 Pages:381-418

• Failure-Informed Adaptive Sampling for PINNs, Part III: Applications to Inverse Problems

  Wenbin Liu, Liang Yan, Tao Zhou, Yuancheng Zhou

  2024-08-02

  22989 1653 Pages:636-670

• Solving the Inverse Potential Problem in the Parabolic Equation by the Deep Neural Networks Method

  Mengmeng Zhang, Zhidong Zhang

  2024-11-29

  12978 1199 Pages:852-883

• Convergence Analysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions

  Yubin Zhao, Peter Mathé, Shuai Lu

  2020-12-31

  40507 3739 Pages:693-714