Abstract

This paper introduces Multi-Objective Physics-Informed Neural Networks (MOPINNs). MOPINNs use an EMO algorithm to find the set of trade-offs between the data and physical losses of PINNs and therefore allow practitioners to correctly identify which of these trade-offs better represent the solution they want to reach. We discuss how MOPINNs overcome the complexity of weighting the different loss functions and to the best of our knowledge this is the first work relating multi-objective optimization problems (MOPs) and PINNs via evolutionary algorithms. We provide an exploratory analysis of this technique in order to determine its feasibility by applying MOPINNs on PDEs of particular interest: the heat, waves, and Burgers equations.