PINNs are neat but by my understanding they’re conceptually not too different from traditional numerical solution methods. The solution to your PDE is some comp

PINNs are neat but by my understanding they’re conceptually not too different from traditional numerical solution methods. The solution to your PDE is some complicated function that is not available in closed-form, so you require a numerical approximation of that function. Traditional methods use various kinds of grid discretization systems (possibly with interpolation schemes). PINNs replace the grid with a parametric continuous function. I’m not sure how PINNs handle discontinuities like shocks though.