<ul data-eligibleForWebStory="true"><li>Physics-informed neural operators (PINOs) are effective for learning solution operators of PDEs.</li><li>Recent research has shown that incorporating Lie point symmetry information can boost the training efficiency of PINOs.</li><li>Techniques like data, architecture, and loss augmentation are used to integrate Lie point symmetries.</li><li>However, traditional point symmetries can sometimes offer no training signal, limiting their effectiveness in certain problems.</li><li>To overcome this limitation, a novel loss augmentation strategy is proposed in this work.</li><li>The strategy leverages evolutionary representatives of point symmetries, a type of generalized symmetries of the underlying PDE.</li><li>Generalized symmetries provide a more extensive set of generators than standard symmetries, offering a more informative training signal.</li><li>By using evolutionary representatives, the performance of neural operators is enhanced, leading to better data efficiency and accuracy in training.</li></ul>

Generalized Lie Symmetries in Physics-Informed Neural Operators

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