Probing optimisation in physics-informed neural networks
This work addresses the challenge of optimising PINNs for computational physics applications, though it is incremental as it focuses on a specific equation and optimiser analysis.
The study investigated how optimiser choice affects the accuracy of physics-informed neural networks (PINNs) for solving the linear advection equation, finding that optimiser selection significantly impacts performance and that larger local curvature correlates with better solutions.
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.