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math.NA2025
Numerical Analysis of Unsupervised Learning Approaches for Parameter Identification in PDEs
Siyu Cen, Bangti Jin, Qimeng Quan +1
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches…
math.NA2025
Numerical Approximation and Analysis of the Inverse Robin Problem Using the Kohn-Vogelius Method
Erik Burman, Siyu Cen, Bangti Jin +1
In this work, we numerically investigate the inverse Robin problem of recovering a piecewise constant Robin coefficient in an elliptic or parabolic problem from the Cauchy data on…
math.NA2025
Finite element approximation for quantitative photoacoustic tomography in a diffusive regime
Giovanni S. Alberti, Siyu Cen, Zhi Zhou
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption…