Nonlinear PDEs approach to statistical mechanics of dense associative memories [PDF]
Journal of Mathematics and Physics, 2022 Dense associative memories (DAMs) are widely used models in artificial intelligence for pattern recognition tasks; computationally, they have been proven to be robust against adversarial inputs and, theoretically, leveraging their analogy with spin-glass
E. Agliari, A. Fachechi, Chiara Marullo
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Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton–Jacobi PDEs [PDF]
MCSS. Mathematics of Control, Signals and Systems, 2021 Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are, respectively, used to ...
J. Darbon, P. Dower, Tingwei Meng
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Near-optimal approximation methods for elliptic PDEs with lognormal coefficients [PDF]
Mathematics of Computation, 2021 This paper studies numerical methods for the approximation of elliptic PDEs with lognormal coefficients of the form $-{\rm div}(a\nabla u)=f$ where $a=\exp(b)$ and $b$ is a Gaussian random field.
A. Cohen, G. Migliorati
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Mathematics, 2022 Heat and mass transfer study of hybrid nanomaterial Casson fluid with time-dependent flow over a vertical Riga sheet was deliberated under the stagnation region.
Taqi A. M. Shatnawi +2 more
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Arabian Journal of Mathematics, 2022 Here the assessment of entropy generation with Soret and Dufour impact in flow of MHD Prandtl fluid along an unsteady stretching surface has been measured.
S. Asad, Shehnila Riaz
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A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science [PDF]
, 2019 In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows.
Dong, Guozhi +2 more
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Decay Estimates for 1-D Parabolic PDEs with Boundary Disturbances [PDF]
, 2017 In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the L2 and H1 norms of the solution and discontinuous disturbances
Karafyllis, Iasson, Krstic, Miroslav
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Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps [PDF]
, 2013 Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities ...
AV Knyazev +24 more
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Weak Continuity and Compactness for Nonlinear Partial Differential Equations [PDF]
, 2015 We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role.
Chen, Gui-Qiang G.
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Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization: The many-subdomain case [PDF]
Mathematics of Computation, 2016 Schwarz methods are attractive parallel solution techniques for solving large-scale linear systems obtained from discretizations of partial differential equations (PDEs).
M. Gander, Soheil Hajian
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