and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 7910-7921. Curran Associates, Inc., 2020.
[72] Han Gao, Matthew J Zahr, and Jian-Xun Wang. Physics-informed graph neural galerkin networks: A unified framework for solving pde-governed forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 390:114502, 2022.
[73] Masanobu Horie and NAOTO MITSUME. Physics-embedded neural networks: Graph neural pde solvers with mixed boundary conditions. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 23218–23229. Curran Associates, Inc., 2022.
[74] Jan Bohn and Michael Feischl. Recurrent neural networks as optimal mesh refinement strategies. Computers & Mathematics with Applications, 97:61-76, 2021.
[75] Roland Becker and Rolf Rannacher. Weighted a posteriori error control in FE methods. IWR, 1996.
[76] Roland Becker and Rolf Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta numerica, 10:1-102, 2001.
[77] Krzysztof J Fidkowski and Guodong Chen. Metric-based, goal-oriented mesh adaptation using machine learning. Journal of Computational Physics, 426:109957, 2021.
[78] Guodong Chen and Krzysztof J Fidkowski. Output-based adaptive aerodynamic simulations using convolutional neural networks. Computers & Fluids, 223:104947, 2021.
[79] Julian Roth, Max Schröder, and Thomas Wick. Neural network guided adjoint computations in dual weighted residual error estimation. SN Applied Sciences, 4(2):62, 2022.
[80] Filipe De Avila Belbute-Peres, Thomas Economon, and Zico Kolter. Combining differentiable pde solvers and graph neural networks for fluid flow prediction. In international conference on machine learning, pages 2402–2411. PMLR, 2020.
[81] Andrew Gillette, Brendan Keith, and Socratis Petrides. Learning robust marking policies for adaptive mesh refinement. arXiv preprint arXiv:2207.06339, 2022.
[82] Jie Pan, Jingwei Huang, Gengdong Cheng, and Yong Zeng. Reinforcement learning for automatic quadrilateral mesh generation: A soft actor-critic approach. Neural Networks, 157:288-304, 2023.
[83] Peter Sunehag, Guy Lever, Audrunas Gruslys, Wojciech Marian Czarnecki, Vinicius Zambaldi, Max Jaderberg, Marc Lanctot, Nicolas Sonnerat, Joel Z Leibo, Karl Tuyls, et al. Value-decomposition networks for cooperative multi-agent learning. arXiv preprint arXiv:1706.05296, 2017.
[84] Andrew Cohen, Ervin Teng, Vincent-Pierre Berges, Ruo-Ping Dong, Hunter Henry, Marwan Mattar, Alexander Zook, and Sujoy Ganguly. On the use and misuse of absorbing states in multi-agent reinforcement learning. arXiv preprint arXiv:2111.05992, 2021.
[85] Jon Louis Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9):509-517, 1975.
[86] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, and Martin Riedmiller. Playing atari with deep reinforcement learning. arXiv preprint arXiv:1312.5602, 2013.
[87] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Bellemare, Alex Graves, Martin Riedmiller, Andreas K Fidjeland, Georg Ostrovski, et al. Human-level control through deep reinforcement learning. nature, 518(7540):529-533, 2015.
[88] John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.
[89] Tom Gustafsson and Georgie Drummond Mcbain. scikit-fem: A python package for finite element assembly. Journal of Open Source Software, 5(52):2369, 2020.
[90] Peter Binev, Wolfgang Dahmen, and Ron DeVore. Adaptive finite element methods with convergence rates. Numerische Mathematik, 97:219-268, 2004.
[91] Wolfgang Bangerth, Carsten Burstedde, Timo Heister, and Martin Kronbichler. Algorithms and data structures for massively parallel generic adaptive finite element codes. ACM Transactions on Mathematical Software (TOMS), 38(2):1-28, 2012.