Physics-Informed Neural Networks (PINNs) combine the power of neural networks with the physical laws governing a system, allowing for the incorporation of domain knowledge and enforcing physical constraints during training, making them suitable for solving partial differential equations and related problems.
Fitting
- Govern function:
$\frac{dy}{dx}=y, x\in[0, 1]$ - Data:
$y(0)=1$
Fitting 2D Burgers' Equation with:
- Govern function:
$z_x + zz_y - \frac{0.01}{\pi}z_{yy}=0, x\in [0, 1], y\in [-1, 1]$ - Data:
$z(0, y) = -\sin(\pi y)$ $z(x, -1) = z(x, 1) = 0$
