Abstract

Physics-informed neural networks allow the neural network to be trained by both the training data and prior domain knowledge about the physical system that models the data. In particular, it has a loss function for the data and the physics, where the latter is the deviation from a partial differential equation describing the system. Conventionally, both loss functions are combined by a weighted sum, but this leaves the optimal weight unknown. Additionally, it is necessary to find the optimal architecture of the neural network. In our work, we propose a multi-objective optimization approach to find the optimal value for the loss function weighting, as well as the optimal activation function, number of layers, and number of neurons for each layer. We validate our results on the Burgers and wave equations and show that we are able to find accurate approximations of the solution using optimal hyperparameters.