Explore the process of learning discrete Lagrangians for variational partial differential equations (PDEs) from data and discover techniques for detecting travelling waves in this insightful 20-minute conference talk presented at GSI. Delve into the intersection of machine learning and mathematical physics, examining how data-driven approaches can be applied to understand and model complex physical systems. Gain valuable insights into the challenges and opportunities of using computational methods to analyze PDEs and identify important wave phenomena.