HOMO-PINN: Hyperparameter Optimization of a Multi-output Physics-Informed Neural Network

Operations Research Forum, vol. 6

Abstract

Abstract The good choice of hyperparameters is crucial for the successful application of Deep Learning (DL) networks in order to find accurate solutions or the best parameter in solving Partial Differential Equations (PDEs), that are sensitive to errors in coefficient estimation. For this purpose, Hyperparameter Optimization of Multi-Output Physics-Informed Neural Networks (HOMO-PINNs) is based on the optimal search of PINN hyperparameters for solving PDEs with uncertain coefficients in the Uncertainty Quantification (UQ) field. By testing this novel methodology on different PDEs, the relationship between activation functions, the number of output neurons, and the degree of coefficient uncertainty can be observed. The experimental results show that adding output neurons to the Neural Network (NN) even if a theoretically incorrect activation function is chosen, keeps the predicted solution accurate.

Authors 4

1. Mariapia De Rosa

   Institute of Biostructure and Bioimaging · National Research Council

   Affiliation as printed

   Istitute of Biostructures and Bioimaging (IBB) of the National Research Council (CNR), Via Tommaso De Amicis, 95, 80145, Naples, Italy

2. Laura Pompameo

   University of Naples Federico II

   Affiliation as printed

   University of Naples Federico II, Via Cintia, 26, 80126, Naples, Italy

3. Alexander Litvinenko Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Pontdriesch, 14-16, 52062, Aachen, Germany

4. Salvatore Cuomo corresponding

   University of Naples Federico II

   Affiliation as printed

   University of Naples Federico II, Via Cintia, 26, 80126, Naples, Italy