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We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the…

Analysis of PDEs · Mathematics 2020-07-08 Matteo Santacesaria , Toshiaki Yachimura

This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…

Analysis of PDEs · Mathematics 2012-03-07 Guillaume Bal , Gunther Uhlmann

We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…

Mathematical Physics · Physics 2018-11-15 William Rundell , Masahiro Yamamoto

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Machine Learning · Statistics 2015-03-19 Teng Zhang , Gilad Lerman

This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…

Analysis of PDEs · Mathematics 2025-10-10 Rodrigo Lecaros , Juan López-Ríos , Ariel A. Pérez

This paper studies the data-driven reconstruction of firing rate dynamics of brain activity described by linear-threshold network models. Identifying the system parameters directly leads to a large number of variables and a highly…

Systems and Control · Electrical Eng. & Systems 2023-08-29 Xuan Wang , Jorge Cortes

The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…

Chemical Physics · Physics 2022-02-01 Erik I. Tellgren , Andre Laestadius , Markus Penz

We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements,…

Quantitative Methods · Quantitative Biology 2018-01-22 Joshua C. Chang , Yanli Liu , Tom Chou

We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…

Optimization and Control · Mathematics 2018-01-17 Constantin Christof , Juan Carlos De Los Reyes , Christian Meyer

In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…

Numerical Analysis · Mathematics 2018-06-14 Xiaoyan Song , Guanghui Zheng , Lijian Jiang

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…

Analysis of PDEs · Mathematics 2021-11-08 Rogelio Arancibia , Rodrigo Lecaros , Alberto Mercado , Sebastián Zamorano

In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods…

Numerical Analysis · Mathematics 2022-01-03 Di Yang , Yinnian He

We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…

Optimization and Control · Mathematics 2026-02-17 Claude Le Bris , Frédéric Legoll , Simon Ruget

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…

Analysis of PDEs · Mathematics 2022-09-20 Florian Faucher , Otmar Scherzer

This paper is devoted to the class of paraconvex functions and presents some of its fundamental properties, characterization, and examples that can be used for their recognition and optimization. Next, the convergence analysis of the…

Optimization and Control · Mathematics 2026-03-06 Morteza Rahimi , Susan Ghaderi , Yves Moreau , Masoud Ahookhosh

We revisit the celebrated Kohn-Vogelius penalty method and discuss how to use it for the unique continuation problem where data is given in the bulk of the domain. We then show that the primal-dual mixed finite element methods for the…

Numerical Analysis · Mathematics 2023-04-21 Erik Burman

As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…

Numerical Analysis · Computer Science 2015-08-26 Xiaomao Deng , Xiao-chuan Cai , Jun Zou

We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…

Statistics Theory · Mathematics 2022-02-25 Peijun Sang , Zuofeng Shang , Pang Du

We consider the problem of minimizing a $d$-dimensional Lipschitz convex function using a stochastic gradient oracle. We introduce and motivate a setting where the noise of the stochastic gradient is isotropic in that it is bounded in every…

Optimization and Control · Mathematics 2025-10-24 Annie Marsden , Liam O'Carroll , Aaron Sidford , Chenyi Zhang

We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…

Analysis of PDEs · Mathematics 2026-02-27 Jiho Hong , Bangti Jin , Yavar Kian