[69] X. Jin, S. Cai, H. Li, and George Em Karniadakis. Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations. J. Comput. Phys., 426:109951, 2021.
[70] J. Kaczmarzyk, P. McClure, W. Zulfikar, A. Rana, H. Rajaei, A. Ritchie-Halford, S. Bansal, D. Jarecka, J. Lee, and S. Ghosh. neuronets/nobrainer: 0.4.0, October 2022.
[71] T. Karras, T. Aila, S. Laine, and J. Lehtinen. Progressive growing of GANs for improved quality, stability, and variation. In International Conference on Learning Representations, 2018.
[72] D. P. Kingma and J. Ba. Adam: a method for stochastic optimization. arXiv:1412.6980, 2017.
[73] N. Kovachki, Z. Li, B. Liu, K. Azizzadnesheli, K. Bhattacharya, A. Stuart, and A. Anandkumar. Neural operator: Learning maps between function spaces with applications to PDEs. J. Mach. Learn. Res., 24:1-97, 2023.
[74] F. Krahmer and R. Ward. Stable and robust sampling strategies for compressive imaging. IEEE Trans. Image Process., 23(2):612-622, 2013.
[75] G. Kutyniok, P. Petersen, M. Raslan, and R. Schneider. A theoretical analysis of deep neural networks and parametric PDEs. Constr. Approx., 55:73-125, 2022.
[76] D. J. Larkman and R. G. Nunes. Parallel Magnetic Resonance Imaging. Phys. Med. Biol., 52(7):R15, 2007.
[77] J. B. Lasserre and E. Pauwels. The empirical Christoffel function with applications in data analysis. Adv. Comput. Math., 45:1439-1468, 2019.
[78] Y. Li, M. Anitescu, O. Roderick, and F. Hickernell. Orthogonal bases for polynomial regression with derivative information in uncertainty quantification. Int. J. Uncertain. Quantif., 1(4):297-320, 2011.
[79] D. Liang, J. Cheng, Z. Ke, and L. Ying. Deep Magnetic Resonance image reconstruction: inverse problems meet neural networks. IEEE Signal Process. Mag., 37(1):141-151, 2020.
[80] Z. Liang and P. C. Lauterbur. Principles of Magnetic Resonance Imaging: A Signal Processing Perspective. IEEE Press Series on Biomedical Engineering. Wiley-IEEE Press, New York, 2000.
[81] J. Liu and Z. Liu. Non-iterative recovery from nonlinear observations using generative models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 233–243, 2022.
[82] B. Lockwood and D. Mavriplis. Gradient-based methods for uncertainty quantification in hypersonic flows. Comput. & Fluids, 85:27-38, 2013.
[83] L. Lu, P. Jin, Z. Pang, G. Zhang, and G. E. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell., 3:218-229, 2021.
[84] A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos. Using deep neural networks for inverse problems in imaging: beyond analytical methods. IEEE Signal Process. Mag., 35(1):20-36, 2018.
[85] P. Ma, M. W. Mahoney, and B. Yu. A statistical perspective on algorithmic leveraging. J. Mach. Learn. Res., 16:861-911, 2015.
[86] Z. Mao and X. Meng. Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions. Applied Mathematics and Mechanics, 44(7):1069-1084, 2023.
[87] M. Mardani, E. Gong, J. Y. Cheng, S. S. Vasanawala, G. Zaharchuk, L. Xing, and J. M. Pauly. Deep generative adversarial neural networks for compressive sensing MRI. IEEE transactions on medical imaging, 38(1):167-179, 2018.