2017

Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations

Raissi, Maziar, Karniadakis, George Em

Understand

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire.

In this paper, we present a new paradigm of learning partial differential equations from {\em small} data.
In particular, we introduce \emph{hidden physics models}, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments.
The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations.

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