Machine Learning Model Selection of PDE for Targeted Crystalline Patterns

20.03.2019 14:45 – 15:45

Partial differential equations (PDE) have been widely used to reproduce patterns in nature, and to give an insight on the mechanism underlying pattern formation. Although enormous number of PDE models have been proposed, they rely on pre-request knowledge of physical laws and symmetries, and one has difficulties to develop a model to reproduce a given desired pattern. Here we show the order parameters extracting symmetries of a pattern together with Bayesian model selection successfully estimate parameters in a model as well as the best model to make the target pattern. We apply our method two-dimensional and three-dimensional nontrivial patterns, namely quasi-crystal with twelve-fold symmetry and double gyroid structure reproduced by using a family of generalised Swift-Hohenberg equations. Our method not only estimates the parameters to reproduce these patterns, but gives an insight on the appropriate number of length scales hidden in the patterns.

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Bâtiment: Ecole de Physique

Salle 234, 24 quai Ernest-Ansermet

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