Training Gives Me PINNS and Needles - On the Complexity of Training Physics-Informed Neural Networks
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Physics-informed neural networks (PINNs) have become increasingly popular in various disciplines such as engineering or biomedicine, and are capable of solving differential equations given only information about the initial and boundary conditions. However, previous attempts have shown that training PINNs in this context is a difficult endeavour, often leading to incorrectly predicted system dynamics. In our own work, we have investigated the underlying reasons for training difficulties in PINNs with a particular focus on the mathematics of physical and dynamical systems, such as for fluid flow or pendulum dynamics. We have shown that several “nonphysical” solutions are represented by minima in the optimization landscape of the PINN training, and slow down or even prevent convergence to the correct system dynamics. Our insights contribute to understanding training difficulties in PINNs, and help in choosing the right remedies.