  Physics-informed neural networks (PINN) is a extremely powerful paradigm used
to solve equations encountered in scientific computing applications. An
important part of the procedure is the minimization of the equation residual
which includes, when the equation is time-dependent, a time sampling. It was
argued in the literature that the sampling need not be uniform but should
overweight initial time instants, but no rigorous explanation was provided for
these choice. In this paper we take some prototypical examples and, under
standard hypothesis concerning the neural network convergence, we show that the
optimal time sampling follows a truncated exponential distribution. In
particular we explain when the time sampling is best to be uniform and when it
should not be. The findings are illustrated with numerical examples on linear
equation, Burgers' equation and the Lorenz system.
