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Spatiotemporal sensitivity of systems modeled by cellular automata
Author(s) -
Fujarewicz Krzysztof,
Łakomiec Krzysztof
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5358
Subject(s) - cellular automaton , sensitivity (control systems) , mathematics , continuous spatial automaton , stochastic cellular automaton , scalar (mathematics) , function (biology) , automaton , mathematical optimization , algorithm , quantum finite automata , computer science , theoretical computer science , automata theory , geometry , engineering , biology , electronic engineering , evolutionary biology
Cellular automata are frequently used to model dynamics of spatial systems. This work shows how a so‐called structural adjoint sensitivity analysis may be applied to such systems. It is assumed that the cellular automaton has a continuous state, a spatiotemporal input, and is characterized by one scalar objective function specified, for example, in a given optimization or parameter optimization problem. With this analysis, it is possible to calculate efficiently a gradient of the objective function in a space of the spatiotemporal input of the automata. As an example, a model of tumor growth with an introduced spatiotemporal irradiation signal is analysed.