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2018

Machine Learning of Space-Fractional Differential Equations

Gulian, Mamikon, Raissi, Maziar, Perdikaris, Paris et al.

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Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial data, treating and discovering unknown equation parameters as hyperparameters of a modified "physics informed" Gaussian Process kernel.

This kernel includes the parametrized differential operators applied to a prior covariance kernel.
We extend this framework to linear space-fractional differential equations.
The methodology is compatible with a wide variety of fractional operators in $\mathbb{R}^d$ and stationary covariance kernels, including the Matern class, and can optimize the Matern parameter during training.

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