References

AAB+15

Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dandelion Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: large-scale machine learning on heterogeneous systems. 2015. Software available from tensorflow.org. URL: https://www.tensorflow.org/.

BJ89

Timothy Barth and Dennis Jespersen. The design and application of upwind schemes on unstructured meshes. In 27th Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, 1989. doi:10.2514/6.1989-366.

CBA17

Kevin Carlberg, Matthew Barone, and Habir Antil. Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction. Journal of Computational Physics, 330:693–734, 2017. doi:10.1016/j.jcp.2016.10.033.

C+15

François Chollet and others. Keras. 2015. URL: https://keras.io.

DXSM04

Li Ding, Guoping Xia, Venkateswaran Sankaran, and Charles L. Merkle. Computational framework for complex fluid physics applications. Third International Conference on Computational Fluid Dynamics, pages 619–624, 2004. doi:10.1007/3-540-31801-1_89.

GY08

Irvin Glassman and Richard A Yetter. Combustion. Academic Press, 2008.

Har12

Matthew E. Harvazinski. Modeling self-excited combustion instabilities using a combination of two- and three-dimensional simulations. PhD thesis, Purdue University, 2012.

HWDM20

Cheng Huang, Christopher R. Wentland, Karthik Duraisamy, and Charles Merkle. Model reduction for multi-scale transport problems using structure-preserving least-squares projections with variable transformation. arXiv:2011.02072v3, 2020.

LC20

Kookjin Lee and Kevin T. Carlberg. Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders. Journal of Computational Physics, 2020. doi:10.1016/j.jcp.2019.108973.

Pin85

Allan Pinkus. n-Widths in Approximation Theory. Springer, 1985.

Roe81

Philip L. Roe. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43(2):357–372, 1981. doi:10.1016/0021-9991(81)90128-5.

RCM04

Clarence W. Rowley, Tim Colonius, and Richard M. Murray. Model reduction for compressible flows using pod and galerkin projection. Physica D, 189:115–129, 2004. doi:10.1016/j.physd.2003.03.001.

Ven93

V. Venkatakrishnan. On the accuracy of limiters and convergence to steady state solutions. In 31st Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, 1993. doi:10.2514/6.1993-880.

VM95

Sankaran Venkateswaran and Charles L. Merkle. Dual time-stepping and preconditioning for unsteady computations. 33rd Aerospace Sciences Meeting and Exhibit, 1995. doi:10.2514/6.1995-78.