Generalized Lie Symmetries in Physics-informed Neural Operator
Amy Xiang Wang*, Zakhar Shumaylov*, Peter Zaika, Ferdia Sherry, and Carola-Bibiane Schönlieb
Scientific Computing and Machine Learning, Oral Presentation , 2025
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can significantly enhance the training efficiency of PINOs, primarily through techniques like data, architecture, and loss augmentation. In this work we focus on the latter, highlighting that point symmetries oftentimes result in no training signal, limiting their effectiveness in many problems. To address this, we propose a novel loss augmentation strategy that leverages evolutionary representatives of point symmetries, a specific class of generalized symmetries of the underlying PDE. These generalized symmetries provide a richer set of constraints than standard symmetries, leading to a more informative training signal. We demonstrate that this approach significantly enhances performance of neural operators across a variety of PDEs, achieving improved data efficiency.