@misc{dl3-c02-1, title = {Fourier Neural Operator for Parametric Partial Differential Equations}, author = {Zongyi Li and Nikola Kovachki and Kamyar Azizzadenesheli and Burigede Liu and Kaushik Bhattacharya and Andrew Stuart and Anima Anandkumar}, year = {2020}, url = {https://arxiv.org/abs/2010.08895}, howpublished = {arXiv author manuscript}, archivePrefix = {arXiv}, eprint = {2010.08895}, note = {Cited author-manuscript edition; peer review is not inferred from arXiv} } @misc{dl3-c02-2, title = {Neural Operator: Learning Maps Between Function Spaces}, author = {Nikola Kovachki and Zongyi Li and Burigede Liu and Kamyar Azizzadenesheli and Kaushik Bhattacharya and Andrew Stuart and Anima Anandkumar}, year = {2021}, url = {https://arxiv.org/abs/2108.08481}, howpublished = {arXiv author manuscript}, archivePrefix = {arXiv}, eprint = {2108.08481}, note = {Cited author-manuscript edition; peer review is not inferred from arXiv} } @misc{dl3-c02-3, title = {DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators}, author = {Lu Lu and Pengzhan Jin and George Em Karniadakis}, year = {2019}, url = {https://arxiv.org/abs/1910.03193}, howpublished = {arXiv author manuscript}, archivePrefix = {arXiv}, eprint = {1910.03193}, note = {Cited author-manuscript edition; peer review is not inferred from arXiv} } @misc{dl3-c02-4, title = {Error estimates for DeepOnets: A deep learning framework in infinite dimensions}, author = {Samuel Lanthaler and Siddhartha Mishra and George Em Karniadakis}, year = {2021}, url = {https://arxiv.org/abs/2102.09618}, howpublished = {arXiv author manuscript}, archivePrefix = {arXiv}, eprint = {2102.09618}, note = {Cited author-manuscript edition; peer review is not inferred from arXiv} } @misc{dl3-c02-5, title = {Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning}, author = {Francesca Bartolucci and Emmanuel de Bézenac and Bogdan Raonić and Roberto Molinaro and Siddhartha Mishra and Rima Alaifari}, year = {2023}, url = {https://arxiv.org/abs/2305.19913}, howpublished = {arXiv author manuscript}, archivePrefix = {arXiv}, eprint = {2305.19913}, note = {Cited author-manuscript edition; peer review is not inferred from arXiv} } @misc{dl3-c02-6, title = {Convolutional Neural Operators for robust and accurate learning of PDEs}, author = {Bogdan Raonić and Roberto Molinaro and Tim De Ryck and Tobias Rohner and Francesca Bartolucci and Rima Alaifari and Siddhartha Mishra and Emmanuel de Bézenac}, year = {2023}, url = {https://arxiv.org/abs/2302.01178}, howpublished = {arXiv author manuscript}, archivePrefix = {arXiv}, eprint = {2302.01178}, note = {Cited author-manuscript edition; peer review is not inferred from arXiv} }