Search for optimal architecture of physically informed neural networks using differential evolution algorithm

The accuracy of solving partial differential equations using Physics-Informed Neural Networks (PINNs) significantly depends on their architecture and the choice of hyperparameters. However, manually searching for the optimal configuration can be difficult due to the high computational complexity. In this paper, we propose an approach for optimizing the PINN architecture using a differential evolution algorithm. We focus on optimizing over a small number of training epochs, which allows us to consider a wider range of configurations while reducing the computational cost. The number of epochs is chosen such that the accuracy of the model at the initial stage correlates with its accuracy after full training, which significantly speeds up the optimization process. To improve efficiency, we also apply a surrogate model based on a Gaussian process, which reduces the number of required PINN trainings. The paper presents the results of optimizing PINN architectures for solving various partial differential equations and offers recommendations for improving their performance.