6,185 research outputs found
A reduced basis localized orthogonal decomposition
In this work we combine the framework of the Reduced Basis method (RB) with
the framework of the Localized Orthogonal Decomposition (LOD) in order to solve
parametrized elliptic multiscale problems. The idea of the LOD is to split a
high dimensional Finite Element space into a low dimensional space with
comparably good approximation properties and a remainder space with negligible
information. The low dimensional space is spanned by locally supported basis
functions associated with the node of a coarse mesh obtained by solving
decoupled local problems. However, for parameter dependent multiscale problems,
the local basis has to be computed repeatedly for each choice of the parameter.
To overcome this issue, we propose an RB approach to compute in an "offline"
stage LOD for suitable representative parameters. The online solution of the
multiscale problems can then be obtained in a coarse space (thanks to the LOD
decomposition) and for an arbitrary value of the parameters (thanks to a
suitable "interpolation" of the selected RB). The online RB-LOD has a basis
with local support and leads to sparse systems. Applications of the strategy to
both linear and nonlinear problems are given
Monte Carlo Approaches to Parameterized Poker Squares
The paper summarized a variety of Monte Carlo approaches employed in the top three performing entries to the Parameterized Poker Squares NSG Challenge competition. In all cases AI players benefited from real-time machine learning and various Monte Carlo game-tree search techniques
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