  A novel comparison is presented of the effect of optimiser choice on the
accuracy of physics-informed neural networks (PINNs). To give insight into why
some optimisers are better, a new approach is proposed that tracks the training
trajectory curvature and can be evaluated on the fly at a low computational
cost. The linear advection equation is studied for several advective
velocities, and we show that the optimiser choice substantially impacts PINNs
model performance and accuracy. Furthermore, using the curvature measure, we
found a negative correlation between the convergence error and the curvature in
the optimiser local reference frame. It is concluded that, in this case, larger
local curvature values result in better solutions. Consequently, optimisation
of PINNs is made more difficult as minima are in highly curved regions.
