A physics-informed neural network approach to simulating wave packets at different speeds: an educational demonstration

Abstract

We present a physics-informed neural network (PINN) based numerical experiment for undergraduate wave physics, using one-dimensional Gaussian wave packet propagation to illustrate a complementary pedagogical perspective that is less readily accessible with conventional numerical methods. Unlike finite difference schemes where physical laws are implicit in discrete stencils, PINNs embed the wave equation directly into the loss function, rendering the governing physics transparent and trainable. Students can explicitly observe how the differential operator, initial conditions, and boundary constraints compete and balance during network optimization—a process that mirrors variational reasoning in analytical mechanics. We train PINN models for two distinct propagation regimes, validate them against finite difference solutions, and superpose the results to demonstrate linearity. This architecture further enables seamless exploration of parametric variations in wave speed without re-meshing, offering flexibility that exposes students to modern machine learning workflows while reinforcing core physics concepts. The experiment addresses the common misconception that wave superposition always produces interference fringes, distinguishing broadband packet superposition from monochromatic interference. Step-by-step classroom activities are provided as a ready-to-use, inquiry-based computational lab.