[35] E. Musharbash, F. Nobile, and T. Zhou. Error analysis of the dynamically orthogonal approximation of time dependent random PDEs. SIAM Journal on Scientific Computing, 37(2):A776-A810, 2015.
[36] K. Otness, A. Gjoka, J. Bruna, D. Panozzo, B. Peherstorfer, T. Schneider, and D. Zorin. An extensible benchmark suite for learning to simulate physical systems. In NeurIPS 2021 Track Datasets and Benchmarks, 2021.
[37] Samet Oymak, Zalan Fabian, Mingchen Li, and Mahdi Soltanolkotabi. Generalization, adaptation and low-rank representation in neural networks. In 2019 53rd Asilomar Conference on Signals, Systems, and Computers, pages 581-585, 2019.
[38] B. Peherstorfer. Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling. SIAM Journal on Scientific Computing, 42:A2803-A2836, 2020.
[39] B. Peherstorfer and K. Willcox. Online adaptive model reduction for nonlinear systems via low-rank updates. SIAM Journal on Scientific Computing, 37(4):A2123-A2150, 2015.
[40] Benjamin Peherstorfer. Breaking the Kolmogorov barrier with nonlinear model reduction. Notices of the American Mathematical Society, 69(5):725-733, May 2022.
[41] 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.
[42] R. Rico-Martinez, K. Krischer, I. G. Kevrekidis, M. C. Kube, and J. L. Hudson. Discrete- vs. continuous-time nonlinear signal processing of cu electrodissolution data. Chemical Engineering Communications, 118(1):25-48, 1992.
[43] Grant M. Rotskoff, Andrew R. Mitchell, and Eric Vanden-Eijnden. Active importance sampling for variational objectives dominated by rare events: Consequences for optimization and generalization. arXiv, 2008.06334, 2021.
[44] Samuel H. Rudy, J. Nathan Kutz, and Steven L. Brunton. Deep learning of dynamics and signal-noise decomposition with time-stepping constraints. Journal of Computational Physics, 396:483-506, 2019.
[45] Themistoklis P. Sapsis and Pierre F.J. Lermusiaux. Dynamically orthogonal field equations for continuous stochastic dynamical systems. Physica D: Nonlinear Phenomena, 238(23):2347-2360, 2009.
[46] Justin Sirignano and Konstantinos Spiliopoulos. DGM: A deep learning algorithm for solving partial differential equations. Journal of Computational Physics, 375:1339-1364, dec 2018.
[47] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15(56):1929-1958, 2014.
[48] N. Sukumar and Ankit Srivastava. Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Computer Methods in Applied Mechanics and Engineering, 389:114333, 2022.
[49] Yi-Lin Sung, Varun Nair, and Colin Raffel. Training neural networks with fixed sparse masks. arXiv, 2111.09839, 2021.
[50] Qian Wang, Nicolò Ripamonti, and Jan S. Hesthaven. Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism. J. Comput. Phys., 410:109402, 2020.
[51] Sifan Wang, Shyam Sankaran, and Paris Perdikaris. Respecting causality is all you need for training physics-informed neural networks. arXiv, 2203.07404, 2022.
[52] Elad Ben Zaken, Shauli Ravfogel, and Yoav Goldberg. BitFit: Simple parameter-efficient fine-tuning for transformer-based masked language-models. arXiv, 2106.10199, 2022.