Implicit Bias in Understanding Deep Learning for Solving PDEs Beyond Ritz-Galerkin Method
CSIAM Transactions on Applied Mathematics, 2022 Summary: This paper aims at studying the difference between Ritz-Galerkin (R-G) method and deep neural network (DNN) method in solving partial differential equations (PDEs) to better understand deep learning. To this end, we consider solving a particular Poisson problem, where the information of the right-hand side of the equation \(f\) is only ...
Wang, Jihong +3 more
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Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems [PDF]
, 2015 The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed.
Kuzemsky, A. L.
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An investigation of the basement complex aquifer system in Lofa county, Liberia, for the purpose of siting boreholes [PDF]
, 2014 Liberia is recovering from a 14 year civil war and only 51% of the rural population has access to safe drinking water. Little hydrogeological knowledge survives in Liberia, increasing the difficulty in successfully siting new boreholes.
Elster, D. +3 more
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The Deep Ritz Method for Parametric $p$-Dirichlet Problems
, 2022 30 pages, 11 ...
Kaltenbach, Alex, Zeinhofer, Marius
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Communications in Mathematical Research, 2020 Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical methods, such as finite difference method and finite element method, the enforcement of boundary conditions in deep neural networks is highly nontrivial.
Chen, Jingrun, Du, Rui, Wu, Keke
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Linear Stochastic Models of Nonlinear Dynamical Systems
, 1998 We investigate in this work the validity of linear stochastic models for nonlinear dynamical systems. We exploit as our basic tool a previously proposed Rayleigh-Ritz approximation for the effective action of nonlinear dynamical systems started from ...
B. A. Finlayson +17 more
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The Gamma-ray Albedo of the Moon [PDF]
, 2007 We use the GEANT4 Monte Carlo framework to calculate the gamma-ray albedo of the Moon due to interactions of cosmic ray (CR) nuclei with moon rock. Our calculation of the albedo spectrum agrees with the EGRET data. We show that the spectrum of gamma rays
/Stanford U., HEPL +3 more
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At-sea abundance and distribution of skuas and jaegers (Charadriiformes: Stercorariidae) at coastal waters off central Chile [PDF]
, 2014 Indexación: Web of Science; Scielo.BACKGROUND: Skuas and jaegers (Charadriiformes: Stercorariidae) are seabirds breeding at moderate to high latitudes and some perform extensive post-breeding transequatorial migrations.
Anguita, Cristóbal +2 more
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Stability of Few-Charge Systems in Quantum Mechanics [PDF]
, 2004 We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions.
Armour, E. A. G. +2 more
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Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
, 2021 arXiv admin note: substantial text overlap with arXiv:2103.13330; text overlap with arXiv:2109 ...
Duan, Chenguang +5 more
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