[21] G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang. Physics informed machine learning. Nature Reviews Physics, pages 1-19, may 2021.
[22] T. Karras, M. Aittala, S. Laine, E. Härkönen, J. Hellsten, J. Lehtinen, and T. Aila. Alias-free generative adversarial networks. Advances in Neural Information Processing Systems, 34:852-863, 2021.
[23] G. Kissas, J. H. Seidman, L. F. Guilhoto, V. M. Preciado, G. J. Pappas, and P. Perdikaris. Learning operators with coupled attention. Journal of Machine Learning Research, 23(215):1-63, 2022.
[24] N. Kovachki, S. Lanthaler, and S. Mishra. On universal approximation and error bounds for fourier neural operators. Journal of Machine Learning Research, 22:Art-No, 2021.
[25] N. Kovachki, Z. Li, B. Liu, K. Azizzadensheli, K. Bhattacharya, A. Stuart, and A. Anandkumar. Neural operator: Learning maps between function spaces. arXiv preprint arXiv:2108.08481v3, 2021.
[26] S. Lanthaler, S. Mishra, and G. E. Karniadakis. Error estimates for DeepONets: A deep learning framework in infinite dimensions. Transactions of Mathematics and Its Applications, 6(1):tnac001, 2022.
[27] S. Lanthaler, S. Mishra, and C. Parés-Pulido. Statistical solutions of the incompressible Euler equations. Mathematical Models and Methods in Applied Sciences, 31(02):223-292, Feb 2021.
[28] S. Lanthaler, R. Molinaro, P. Hadorn, and S. Mishra. Nonlinear reconstruction for operator learning of pdes with discontinuities. In International Conference on Learning Representations, 2023.
[29] Y. LeCun, Y. Bengio, and G. Hinton. Deep learning. Nature, 521(7553):436-444, 2015.
[30] Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278-2324, 1998.
[31] M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural networks, 6(6):861-867, 1993.
[32] Z. Li, D. Z. Huang, B. Liu, and A. Anandkumar. Fourier neural operator with learned deformations for pdes on general geometries, 2022.
[33] Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar. Fourier neural operator for parametric partial differential equations. In International Conference on Learning Representations, 2021.
[34] Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. M. Stuart, and A. Anandkumar. Neural operator: Graph kernel network for partial differential equations. CoRR, abs/2003.03485, 2020.
[35] Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, A. M. Stuart, K. Bhattacharya, and A. Anandkumar. Multipole graph neural operator for parametric partial differential equations. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems (NeurIPS), volume 33, pages 6755-6766. Curran Associates, Inc., 2020.
[36] Z. Li, H. Zheng, N. Kovachki, D. Jin, H. Chen, B. Liu, K. Azizzadenesheli, and A. Anandkumar. Physics-informed neural operator for learning partial differential equations. arXiv preprint arXiv:2111.03794, 2021.
[37] Z. Liu, H. Mao, C. Wu, C. Feichtenhofer, T. Darrell, and S. Xie. A convnet for the 2020s. In Proceedings - 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2022, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 11966-11976. IEEE Computer Society, 2022.