Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Wang, Amy Xiang, Shumaylov, Zakhar, Zaika, Peter, Sherry, Ferdia, Schönlieb, Carola-Bibiane
Institutions: New York University, University of Cambridge
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Nonlocal Methods for Arbitrary Data Sources, Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India, G434337789, Cambridge Mathematics of Information in Healthcare (CMIH), EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems, PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation
OpenAlex ID: W4407123524