[10] Loic Le Gratiet. Bayesian analysis of hierarchical multifidelity codes. SIAM/ASA Journal on Uncertainty Quantification, 1(1):244-269, 2013.
[41] Steven C Chapra, Raymond P Canale, et al. Numerical methods for engineers. Boston: McGraw-Hill Higher Education..
[42] TJ Chung. Computational fluid dynamics. Cambridge university press.
[43] Krzysztof Burdzy, Zhen-Qing Chen, John Sylvester, et al. The heat equation and reflected brownian motion in time-dependent domains. The Annals of Probability, 32(1B):775-804.
[28] Wei W. Xing, Robert M. Kirby, and Shandian Zhe. Deep coregionalization for the emulation of simulation-based spatial-temporal fields. Journal of Computational Physics, 428:109984, March 2021. ISSN 00219991. doi: 10.1016/j.jcp.2020.109984.
[37] Rui Tuo, C. F. Jeff Wu, and Dan Yu. Surrogate Modeling of Computer Experiments With Different Mesh Densities. Technometrics, 56(3):372-380, July 2014. ISSN 0040-1706, 1537-2723. doi: 10.1080/00401706.2013.842935.
[38] Mehmet Onder Efe and Hitay Ozbay. Proper orthogonal decomposition for reduced order modeling: 2d heat flow. In Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003., volume 2, pages 1273-1277. IEEE.
[39] Maziar Raissi and George Em Karniadakis. Machine Learning of Linear Differential Equations using Gaussian Processes. Journal of Computational Physics, 348:683-693, November 2017. ISSN 00219991. doi: 10/gbzfrgr.
[48] N Sugimoto. Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves. Journal of fluid mechanics, 225:631-653.
[49] Kai Nagel. Particle hopping models and traffic flow theory. Physical review E, 53(5):4655.
[50] S Kutluay, AR Bahadir, and A Ozdecs. Numerical solution of one-dimensional burgers equation: explicit and exact-explicit finite difference methods. Journal of Computational and Applied Mathematics, 103(2): 251-261.
[51] A. A. Shah, W. W. Xing, and V. Triantafyllidis. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2200):20160809, April 2017. ISSN 1364-5021, 1471-2946. doi: 10.1098/rspa.2016.0809.
[52] Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:1711.10561.
[53] S Persides. The laplace and poisson equations in Schwarzschild's space-time. Journal of Mathematical Analysis and Applications, 43(3):571-578.
[54] I.E. Lagaris, A. Likas, and D.I. Fotiadis. Artificial neural networks for solving ordinary and partial differential equations. IEEE Transactions on Neural Networks, 9(5):987-1000, Sept./1998. ISSN 10459227. doi: 10.1109/72.712178.
[55] Frank Spitzer. Electrostatic capacity, heat flow, and brownian motion. Probability theory and related fields, 3(2):110-121.
[56] Fischer Black and Myron Scholes. The pricing of options and corporate liabilities. Journal of political economy, 81(3):637-654.
[57] Wei Xing, Shireen Y. Elhabian, Vahid Keshavarzzadeh, and Robert M. Kirby. Shared-Gaussian Process: Learning Interpretable Shared Hidden Structure Across Data Spaces for Design Space Analysis and Exploration. Journal of Mechanical Design, 142(8), August 2020. ISSN 1050-0472, 1528-9001. doi: 10.1115/1.4046074.
[58] Erik Andreassen, Anders Clausen, Mattias Schevenels, Boyan S. Lazarov, and Ole Sigmund. Efficient topology optimization in matlab using 88 lines of code. Structural and Multidisciplinary Optimization, 43(1):1-16, Jan 2011. ISSN 1615-1488.
[59] Martin Philip Bendsoe and Ole Sigmund. Topology optimization: Theory, methods and applications. Springer, 2004.