Ilge Akkaya, Marcin Andrychowicz, Maciek Chociej, Mateusz Litwin, Bob McGrew, and others. Solving rubik's cube with a robot hand. arXiv:1910.07113, 2019.


Li-Wei Chen, Berkay A Cakal, Xiangyu Hu, and Nils Thuerey. Numerical investigation of minimum drag profiles in laminar flow using deep learning surrogates. Journal of Fluid Mechanics, 2021. URL:


Li-Wei Chen and Nils Thuerey. Towards high-accuracy deep learning inference of compressible turbulent flows over aerofoils. In arXiv. 2021. URL:


Mengyu Chu, Nils Thuerey, Hans-Peter Seidel, Christian Theobalt, and Rhaleb Zayer. Learning Meaningful Controls for Fluids. ACM Trans. Graph., 2021. URL:


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Philipp Holl, Vladlen Koltun, and Nils Thuerey. Learning to control pdes with differentiable physics. In International Conference on Learning Representations. 2019. URL:


Philipp Holl, Vladlen Koltun, and Nils Thuerey. Physical gradients and scale-invariant physics for deep learning. In arXiv:2109.15048. 2021. URL:


Byungsoo Kim, Vinicius C Azevedo, Nils Thuerey, Theodore Kim, Markus Gross, and Barbara Solenthaler. Deep Fluids: A Generative Network for Parameterized Fluid Simulations. Comp. Grap. Forum, 38(2):12, 2019. URL:


Diederik P Kingma and Jimmy Ba. Adam: a method for stochastic optimization. arXiv:1412.6980, 2014.


Dmitrii Kochkov, Jamie A Smith, Ayya Alieva, Qing Wang, Michael P Brenner, and Stephan Hoyer. Machine learning–accelerated computational fluid dynamics. Proceedings of the National Academy of Sciences, 2021.


Georg Kohl, Kiwon Um, and Nils Thuerey. Learning similarity metrics for numerical simulations. International Conference on Machine Learning, 2020. URL:


Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems. 2012.


Bjoern List, Liwei Chen, and Nils Thuerey. Learned turbulence modelling with differentiable fluid solvers. In arXiv:2202.06988. 2022. URL:


Rajesh Maingi, Arnold Lumsdaine, Jean Paul Allain, Luis Chacon, SA Gourlay, and others. Summary of the fesac transformative enabling capabilities panel report. Fusion Science and Technology, 75(3):167–177, 2019.


Peter JJ O’Malley, Ryan Babbush, Ian D Kivlichan, Jonathan Romero, Jarrod R McClean, Rami Barends, Julian Kelly, Pedram Roushan, Andrew Tranter, Nan Ding, and others. Scalable quantum simulation of molecular energies. Physical Review X, 6(3):031007, 2016.


Mohammed Al Quraishi. Alphafold at casp13. Bioinformatics, 35(22):4862–4865, 2019.


Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.


Maziar Raissi, Paris Perdikaris, and George 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.


Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia. Learning to simulate complex physics with graph networks. In International Conference on Machine Learning, 8459–8468. 2020.


Patrick Schnell, Philipp Holl, and Nils Thuerey. Half-inverse gradients for physical deep learning. In ICLR. 2022. URL:


John Schulman, Philipp Moritz, Sergey Levine, Michael Jordan, and Pieter Abbeel. High-dimensional continuous control using generalized advantage estimation. arXiv:1506.02438, 2015.


John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv:1707.06347, 2017.


David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, and others. Mastering the game of Go without human knowledge. Nature, 2017.


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Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction. MIT press, 2018.


Nils Thuerey, Konstantin Weissenow, Lukas Prantl, and Xiangyu Hu. Deep learning methods for reynolds-averaged navier–stokes simulations of airfoil flows. AIAA Journal, 58(1):25–36, 2020. URL:


Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, and Ken Perlin. Accelerating eulerian fluid simulation with convolutional networks. In Proceedings of Machine Learning Research, 3424–3433. 2017.


Kiwon Um, Robert Brand, Philipp Holl, Raymond Fei, and Nils Thuerey. Solver-in-the-loop: learning from differentiable physics to interact with iterative pde-solvers. Advances in Neural Information Processing Systems, 2020. URL:


Benjamin Ummenhofer, Lukas Prantl, Nils Thuerey, and Vladlen Koltun. Lagrangian fluid simulation with continuous convolutions. In International Conference on Learning Representations. 2019. URL:


Steffen Wiewel, Moritz Becher, and Nils Thuerey. Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow. Comp. Grap. Forum, 38(2):12, 2019. URL:


Steffen Wiewel, Byungsoo Kim, Vinicius C Azevedo, Barbara Solenthaler, and Nils Thuerey. Latent space subdivision: stable and controllable time predictions for fluid flow. Symposium on Computer Animation, 2020. URL:


You Xie, Erik Franz, Mengyu Chu, and Nils Thuerey. tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow. ACM Trans. Graph., 2018. URL: