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2021-03-09 16:39:54 +08:00
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@@ -24,7 +24,7 @@ $
\mathbf{u}_t = \mathcal F ( \mathbf{u}_{x}, \mathbf{u}_{xx}, ... \mathbf{u}_{xx...x} ) ,
$
where the $_{\mathbf{x}}$ subscripts denote spatial derivatives with respect to one of the spatial dimensions
of higher and higher order (this can of course also include derivatives with repsect to different axes).
of higher and higher order (this can of course also include derivatives with respect to different axes).
In this context we can employ DL by approximating the unknown $\mathbf{u}$ itself
with a NN, denoted by $\tilde{\mathbf{u}}$. If the approximation is accurate, the PDE