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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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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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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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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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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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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A mixed $\ell_1$ regularization approach for sparse simultaneous approximation of parameterized PDEs
, 2018 We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs.
Dexter, Nick +2 more
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Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise [PDF]
Mathematics of Computation, 2017 The stochastic time-fractional equation $\partial_t \psi -\Delta\partial_t^{1-\alpha} \psi = f + \dot W$ with space-time white noise $\dot W$ is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate ...
M. Gunzburger, Buyang Li, Jilu Wang
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On two aspects of the Painleve analysis
, 2013 We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic ...
Sakovich, Sergei
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