Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

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• 作者：Patrick Gel&szlig ; ; ^{p.gelss@fu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; Sebastian Matera ^{matera@math.fu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; Christof Schü ; tte ^{schuette@mi.fu-berlin.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Heterogeneous catalysis ; Master equation ; Kinetic Monte Carlo ; Tensor decompositions ; Tensor train format ; Alternating linear scheme
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：314
• 期：Complete
• 页码：489-502
• 全文大小：662 K

文摘

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO₂(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.