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A data-driven approach to PDE-constrained optimization in inverse problems [PDF]
Inverse ProblemsAbstract Many inverse problems are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which the inherent non-linearity of the problem is an important one.
Tristan van Leeuwen, Yunan Yang
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Structured Random Sketching for PDE Inverse Problems [PDF]
SIAM Journal on Matrix Analysis and Applications, 2020 For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable solution $\mathsf{x}$.
Ke Chen +3 more
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Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs [PDF]
, 2019 and Applied Analysis, 2008, pp. 1–19, 2008. http://dx.doi. org/10.1155/2008/192679. [BL76] BERGH, J. AND LÖFSTRÖM, J. Interpolation spaces. An introduction. Springer-Verlag, Berlin-New York, 1976. Grundlehren der Mathematischen Wissenschaften, No.
Frederic Weidling
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Correction to: Remarks on control and inverse problems for PDEs [PDF]
SeMA JournalEnrique Fernández-Carawas
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PDEs in the Inverse Problem of Dynamics [PDF]
, 2003 The basic equations are exposed for the following version of the inverse problem of dynamics: determine the two-dimensional potential compatible with a given family of orbits, traced by a material point. If the potential is known in advance, a nonlinear equation is satisfied by the function representing the family of orbits.
Mira-Cristiana Anisiu
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On the inverse source identification problem in $L^\infty$ for fully nonlinear elliptic PDE [PDF]
Vietnam Journal of Mathematics, 2020 AbstractIn this paper we generalise the results proved in N. Katzourakis (SIAM J. Math. Anal.51, 1349–1370, 2019) by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator.
Birzhan Ayanbayev, Nikos Katzourakis
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Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs [PDF]
SDM, 2021 We propose quadratic residual networks (QRes) as a new type of parameter-efficient neural network architecture, by adding a quadratic residual term to the weighted sum of inputs before applying activation functions.
Jie Bu, A. Karpatne
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Inverse Source Problems for Degenerate Time-Fractional PDE [PDF]
Progress in Fractional Differentiation and Applications, 2022 12 pages, 8 ...
Al-Salti, Nasser, Karimov, Erkinjon
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Mathematics, 2023 Physics-informed neural networks (PINNs) provide a new approach to solving partial differential equations (PDEs), while the properties of coupled physical laws present potential in surrogate modeling.
Meijun Zhou, Gang Mei, Nengxiong Xu
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Gaussian Process Regression for Inverse Problems in Linear PDEs [PDF]
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic
Xin Li +2 more
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