2025/02/01 by Zakhar Shumaylov, Wang, Amy Xiang, Shumaylov, Zakhar +6 · 1 citation
Chemistry · Physics and Astronomy · Earth and Planetary Sciences · #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2502.00373
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 generators compared to standard symmetries, leading to a more informative training signal. We demonstrate that leveraging evolutionary representatives enhances the performance of neural operators, resulting in improved data efficiency and accuracy during training.