Cellular Probabilistic Automata-A Novel Method for Uncertainty Propagation

被引：6
作者：
Kohler, Dominic [1 ,2 ]
Mueller, Johannes [1 ,3 ]
Wever, Utz [2 ]
机构：
[1] Tech Univ Munich, Ctr Math Sci, D-85748 Garching, Germany
[2] Siemens AG, Corp Technol, D-81730 Munich, Germany
[3] Helmholtz Zentrum Munchen, Inst Computat Biol, D-85764 Neuherberg, Germany
来源：
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION | 2014年 / 2卷 / 01期
关键词：
uncertainty propagation for partial differential equations; set oriented numerics; cellular automata; APPROXIMATION; ADSORPTION;
D O I：
10.1137/120897183
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We propose a novel density based numerical method for uncertainty propagation under distinct partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method using the example of initial value uncertainties under deterministic dynamics and show that it is consistent. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations.
引用
收藏
页码：29 / 54
页数：26
相关论文
共 49 条
[1]  
[Anonymous], 1998, Markov Chain Monte Carlo in Practice
[2]  
[Anonymous], 1974, Solving least squares problems
[3]   Stochastic Galerkin techniques for random ordinary differential equations [J].
Augustin, F. ;
Rentrop, P. .
NUMERISCHE MATHEMATIK, 2012, 122 (03) :399-419
[4]   Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients [J].
Barth, Andrea ;
Schwab, Christoph ;
Zollinger, Nathaniel .
NUMERISCHE MATHEMATIK, 2011, 119 (01) :123-161
[5]   The transition from differential equations to Boolean networks: A case study in simplifying a regulatory network model [J].
Davidich, Maria ;
Bornholdt, Stefan .
JOURNAL OF THEORETICAL BIOLOGY, 2008, 255 (03) :269-277
[6]   On the approximation of complicated dynamical behavior [J].
Dellnitz, M ;
Junge, O .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (02) :491-515
[7]  
Dellnitz M., 2002, Handbook of Dynamical Systems, P221, DOI [DOI 10.1016/S1874-575X(02)80026-1, 10.1016/s1874-575x(02)80026-1]
[8]  
Deutsch A., 2005, CELLULAR AUTOMATON M
[9]  
Fox B., 1999, Strategies for Quasi-Monte Carlo
[10]  
Ghanem R., 1991, STOCHASTIC FINITE EL, VVolume 1, P1, DOI [10.1007/978-1-4612-3094-6, DOI 10.1007/978-1-4612-3094-6]
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