Multiple Nonlinear Waves by (Quantum) Neural Networks: Checking the AI supremacy

Abstract

To test the potential of so-called quantum physics-informed neural network (QPINN) technology for solving evolutionary partial differential equations, we consider the problem of multiple wave propagation in a weakly nonlinear medium described by the Korteweg-de Vries equation with periodic boundary conditions. Although this problem is solvable analytically, high-genus solutions could represent a rather challenging testbed for numerical methods. Therefore, our idea is to test whether a QPINN is sufficiently mature for application in this context by providing a set of indicators of merit and performing several numerical experiments.