Mainly introduces a simple PINN case, but also in my learning PINN contact with the first model, I would like to share for everyone to learn.
The case can be changed to suit your needs. Time t is not currently considered and further updates will follow, hopefully.
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PDE:
$\frac{\partial^2 u}{\partial x^2}- \frac{\partial^4 u}{\partial y^4}=\left ( 2-x^2 \right ) e^{-y} $ -
BC:
$u_{yy} \left ( x, 0 \right ) = x^2$
$u_{yy} \left ( x, 1 \right ) = \frac{x^2}{e} $
$u \left ( x, 0 \right ) = x^2$
$u \left ( x, 1 \right ) = \frac{x^2}{e} $
$u \left ( 0, y \right ) = 0 $
$u \left ( 1, y \right ) = e^{-y} $
