Results 51 to 60 of about 217,226 (371)
ANN-based methods for solving partial differential equations: a survey
Arab Journal of Basic and Applied Sciences, 2022 Traditionally, partial differential equation (PDE) problems are solved numerically through a discretization process. Iterative methods are then used to determine the algebraic system generated by this process. Recently, scientists have emerged artificial
Danang, A. Pratama +3 more
doaj +1 more source
Deep splitting method for parabolic PDEs [PDF]
SIAM Journal on Scientific Computing, 2019 In this paper we introduce a numerical method for parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems.
C. Beck +4 more
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Stochastic switching in infinite dimensions with applications to random parabolic PDEs [PDF]
, 2015 We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution.
Lawley, Sean D. +2 more
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On the geometry of lambda-symmetries, and PDEs reduction
, 2004 We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $\
Cicogna G Gaeta G Morando P +15 more
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Stochastic PDEs with multiscale structure [PDF]
, 2012 We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise.
Hairer, Martin, Kelly, David
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British Journal of Cancer, 2020 Preclinical models that can accurately predict outcomes in the clinic are much sought after in the field of cancer drug discovery and development. Existing models such as organoids and patient-derived xenografts have many advantages, but they suffer from
I. Powley +10 more
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A Theoretical Analysis of Deep Neural Networks and Parametric PDEs [PDF]
Constructive approximation, 2019 We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low dimensionality of the ...
Gitta Kutyniok +3 more
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Applied Numerical Mathematics, 1992 The authors describe a new methodology for solving systems of partial differential equations. They explain the methodology in the case of two- dimensional second-order linear elliptic problems of the form \(L_ i{\mathbf u}_ i = f_ i \text{ for }(x, y) \in D_ i\), \(M_ i{\mathbf u}_ i = g_ i \text{ for }(x, y) \in \partial D_ i\), \(i=1,2,...,m\), where
McFaddin, H. S., Rice, John R.
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Frontiers in Oncology, 2021 Precision medicine approaches that inform clinical management of individuals with cancer are progressively advancing. Patient-derived explants (PDEs) provide a patient-proximal ex vivo platform that can be used to assess sensitivity to standard of care ...
Abby R. Templeton +46 more
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Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs
, 2015 We construct, for any given $ \ell = \frac{1}{2} + {\mathbb N}_0, $ the second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras ...
Aizawa, Naruhiko, Kato, Tadanori
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