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fixed Burgers eq, thanks to YuSha

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@@ -137,7 +137,7 @@ Due to the lack of explicit spatial sampling points, an MLP, i.e., fully-connect
To pick a simple example, Burgers equation in 1D, To pick a simple example, Burgers equation in 1D,
$\frac{\partial u}{\partial{t}} + u \nabla u = \nu \nabla \cdot \nabla u $ , we can directly $\frac{\partial u}{\partial{t}} + u \nabla u = \nu \nabla \cdot \nabla u $ , we can directly
formulate a loss term $R = \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2} u$ that should be minimized as much as possible at training time. For each of the terms, e.g. $\frac{\partial u}{\partial x}$, formulate a loss term $R = \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2}$ that should be minimized as much as possible at training time. For each of the terms, e.g. $\frac{\partial u}{\partial x}$,
we can simply query the DL framework that realizes $u$ to obtain the corresponding derivative. we can simply query the DL framework that realizes $u$ to obtain the corresponding derivative.
For higher order derivatives, such as $\frac{\partial^2 u}{\partial x^2}$, we can simply query the derivative function of the framework multiple times. In the following section, we'll give a specific example of how that works in tensorflow. For higher order derivatives, such as $\frac{\partial^2 u}{\partial x^2}$, we can simply query the derivative function of the framework multiple times. In the following section, we'll give a specific example of how that works in tensorflow.