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Policy evaluation is a crucial step in many reinforcement-learning procedures, which estimates a value function that predicts states' long-term value under a given policy. In this paper, we focus on policy evaluation with linear function…

Machine Learning · Computer Science 2017-06-12 Simon S. Du , Jianshu Chen , Lihong Li , Lin Xiao , Dengyong Zhou

In this paper we derive a new two-dimensional brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small…

Numerical Analysis · Mathematics 2020-04-21 Stefano Almi , Sandro Belz , Stefano Micheletti , Simona Perotto

We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a…

Optimization and Control · Mathematics 2026-04-13 Shabnam Khodakaramzadeh , Soroosh Shafiee , Gabriel de Albuquerque Gleizer , Peyman Mohajerin Esfahani

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret & Raoult. Specific characterizations of the 2D elastic…

Analysis of PDEs · Mathematics 2007-05-23 Jean-Francois Babadjian , Gilles A. Francfort

We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…

Computer Vision and Pattern Recognition · Computer Science 2015-10-16 Konrad Simon , Ronen Basri

The study of entanglement in strongly correlated electron systems typically requires knowledge of the reduced density matrix. Here, we apply the parquet dynamical vertex approximation to study the two-site reduced density matrix at varying…

Strongly Correlated Electrons · Physics 2026-01-28 Frederic Bippus , Anna Kauch , Gergő Roósz , Christian Mayrhofer , Fakher Assaad , Karsten Held

The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…

Analysis of PDEs · Mathematics 2025-07-29 Virginie Ehrlacher , Arthur Lebée , Frédéric Legoll , Adrien Lesage

The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…

Analysis of PDEs · Mathematics 2010-10-05 Elisa Davoli , Maria Giovanna Mora

We discuss how the Reissner-Mindlin plate model can be derived from three-dimensional finite elasticity in terms of $\Gamma$-convergence. The presence of transverse shear effects in the Reissner-Mindlin model requires to scale different…

Analysis of PDEs · Mathematics 2025-08-13 Tamara Fastovska , Janusz Ginster , Barbara Zwicknagl

We study the asymptotic behavior of thin heterogeneous elastoplastic plates in the framework of linearized elastoplasticity, focusing on the regime where the plate thickness vanishes much faster than the characteristic scale of the…

Analysis of PDEs · Mathematics 2026-05-14 Marin Bužančić , Igor Velčić , Josip Žubrinić

We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and…

Classical Physics · Physics 2018-05-16 J. A. Hanna , H. Singh , E. G. Virga

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…

Numerical Analysis · Mathematics 2019-03-06 Wietse M. Boon , Jan M. Nordbotten

A field-theoretic approach is applied to describe behavior of three-dimensional, weakly disordered, elastically isotropic, compressible systems with long-range interactions at various values of a long-range interaction parameter.…

Statistical Mechanics · Physics 2007-05-23 S. V. Belim

This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and…

Optimization and Control · Mathematics 2018-03-13 Elaf J. Ali , David Y. Gao

We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…

Numerical Analysis · Mathematics 2025-06-17 Trong D. Dang , Chanh V. Le , Khoa D. Luu , Loc H Nguyen

One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and…

Optimization and Control · Mathematics 2007-10-09 Christian Léonard

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…

Analysis of PDEs · Mathematics 2021-04-19 Elisa Davoli , Anastasia Molchanova , Ulisse Stefanelli

Compressive mechanical stress exceeding a critical value leads to the formation of periodic surface buckling patterns in film-substrate systems. A comprehensive understanding of this buckling phenomenon is desired in applications where the…

Materials Science · Physics 2025-02-20 Wenqing Zhu

In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…

Analysis of PDEs · Mathematics 2023-04-26 Silvio Fanzon , Mariapia Palombaro , Marcello Ponsiglione

We perform a dimension reduction analysis for a coupled rate-dependent/rate-independent adhesive-contact model in the setting of visco-elastodynamic plates. We work with a weak solvability notion inspired by the theory of (purely)…

Analysis of PDEs · Mathematics 2025-11-14 Giovanna Bonfanti , Elisa Davoli , Riccarda Rossi