[38] Z. Long, Y. Lu, X. Ma, and B. Dong. Pde-net: Learning pdes from data. In J. G. Dy and A. Krause, editors, Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholm, Sweden, July 10-15, 2018, volume 80 of Proceedings of Machine Learning Research, pages 3214-3222. PMLR, 2018.
[39] L. Lu, P. Jin, G. Pang, Z. Zhang, and G. E. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3(3):218-229, 2021.
[40] K. O. Lye, S. Mishra, D. Ray, and P. Chandrashekar. Iterative surrogate model optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks. Computer Methods in Applied Mechanics and Engineering, 374:113575, 2021.
[41] Z. Mao, L. Lu, O. Marxen, T. Zaki, and G. E. Karniadakis. DeepMandMnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. Preprint, available from arXiv:2011.03349v1, 2020.
[42] D. A. Masters, N. J. Taylor, T. Rendall, C. B. Allen, and D. J. Poole. Geometric comparison of aerofoil shape parameterization methods. AIAA Journal, pages 1575-1589, 2017.
[43] A. Molina, P. Schramowski, and K. Kersting. Pad\`e activation units: End-to-end learning of flexible activation functions in deep networks. arXiv preprint arXiv:1907.06732, 2019.
[44] R. Molinaro, y. Yang, E. Engquist, and S. Mishra. Neural inverse operators for solving pde inverse problems. arXiv:2301.11167, 2023.
[45] J. Pathak, S. Subramanian, P. Harrington, S. Raja, A. Chattopadhyay, M. Mardani, T. Kurth, D. Hall, Z. Li, K. Azizzadenesheli, p. Hassanzadeh, K. Kashinath, and A. Anandkumar. Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators. arXiv preprint arXiv:2202.11214, 2022.
[46] P. Petersen and F. Voigtlaender. Equivalence of approximation by convolutional neural networks and fully-connected networks. Proceedings of the American Mathematical Society, 148(4):1567-1581, 2020.
[47] M. Prasthofer, T. De Ryck, and S. Mishra. Variable input deep operator networks. arXiv preprint arXiv:2205.11404, 2022.
[48] A. Quarteroni and A. Valli. Numerical approximation of Partial differential equations, volume 23. Springer, 1994.
[49] M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686-707, 2019.
[50] O. Ronneberger, P. Fischer, and T. Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention-MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pages 234-241. Springer, 2015.
[51] T. Schanze. Sinc interpolation of discrete periodic signals. IEEE Transactions on Signal Processing, 43(6):1502-1503, 1995.
[52] J. H. Seidman, G. Kissas, P. Perdikaris, and G. J. Pappas. NOMAD: Nonlinear manifold decoders for operator learning. arXiv preprint arXiv:2206.03551, 2022.
[53] M. Tancik, P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J. Barron, and R. Ng. Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems, 33:7537-7547, 2020.
[54] M. Telgarsky. Neural networks and rational functions. In International Conference on Machine Learning, pages 3387-3393. PMLR, 2017.