Black and Gray Box Learning of Amplitude Equations: Application to Phase Field Systems. (arXiv:2207.03954v1 [stat.ML])

We present a data-driven approach to learning surrogate models for amplitude
equations, and illustrate its application to interfacial dynamics of phase
field systems. In particular, we demonstrate learning effective partial
differential equations describing the evolution of phase field interfaces from
full phase field data. We illustrate this on a model phase field system, where
analytical approximate equations for the dynamics of the phase field interface
(a higher order eikonal equation and its approximation, the Kardar-Parisi-Zhang
(KPZ) equation) are known. For …

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