Results 1 to 10 of about 56,948 (139)
Mathematical analysis of nonlocal PDEs for network generation [PDF]
Mathematical Modelling of Natural Phenomena, 2019 In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses.
Tobias Böhle, Christian Kuehn
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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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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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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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Mathematical Analysis of a PDE System for Biological Network Formation [PDF]
Communications in Partial Differential Equations, 2015 Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate $D ...
Haskovec, Jan +2 more
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Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics [PDF]
Symmetry, 2019 We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a new family of Lie symmetry group and generators of the aforementioned pricing equation are derived.
Bosiu C. Kaibe, John G. O’Hara
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Model Reduction and Neural Networks for Parametric PDEs [PDF]
, 2020 We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model ...
Bhattacharya, Kaushik +3 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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Mathematical analysis of PDE systems which govern fluid-structure interactive phenomena
Boletim da Sociedade Paranaense de Matemática, 2007 In this paper, we review and comment upon recently derived results for time dependent partial differential equation (PDE) models, which have been used to describe the various fluid-structure interactions which occur in nature. For these fluid-structure PDEs, this survey is particularly focused on the authors' results of (i) semigroup wellposedness, (ii)
Avalos, George, Triggiani, Roberto
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Mathematical analysis of a PDE epidemiological model applied to scrapie transmission
Communications on Pure & Applied Analysis, 2008 El objetivo de este trabajo es analizar un modelo dinámico que describe la propagación de la tembladera en un rebaño de ovejas. La tembladera es una encefalopatía espongiforme transmisible, endémica en algunas regiones europeas y sujeta a estrictas medidas de control. El modelo tiene en cuenta varios factores y procesos, incluida la cría estacional, la
Najat Ziyadi +3 more
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