UPINN for Burger's equation

Universal Physics Informed Neural Network (UPINN) applied on Burger's Equation:

$$ \frac{\partial u}{\partial t} = -u \frac{\partial u}{\partial x} + \nu \frac{\partial^2 u}{\partial x^2}, \quad \nu=\frac{1}{100 \pi}, \quad u(x,0)=-\sin(\pi x) $$

where the differential operator $-u \frac{\partial u}{\partial x}$ is assumed to be unknown and is approximated by a Neural Network $F(\vec{u};\theta_F)$.