[1] Bobak Shahriari, Kevin Swersky, Ziyu Wang, Ryan P. Adams, and Nando de Freitas. Taking the Human Out of the Loop: A Review of Bayesian Optimization. Proceedings of the IEEE, 104(1):148-175, January 2016. ISSN 0018-9219, 1558-2256. doi: 10.1109/JPROC.2015.2494218.
[2] Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis. Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. Journal of Computational Physics, 477:111902, 2023. ISSN 0021-9991. doi: https://doi.org/10.1016/j.jcp.2022.111902.
[3] M. Kennedy. Predicting the output from a complex computer code when fast approximations are available. Biometrika, 87(1):1-13, March 2000. ISSN 0006-3444, 1464-3510. doi: 10.1093/biomet/87.1.1.
[4] Matthias Poloczek, Jialei Wang, and Peter Frazier. Multi-Information Source Optimization. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017.
[5] Jialin Song, Yuxin Chen, and Yisong Yue. A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes. In Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, pages 3158–3167. PMLR, April 2019.
[6] L. Parussini, D. Venturi, P. Perdikaris, and G.E. Karniadakis. Multi-fidelity Gaussian process regression for prediction of random fields. Journal of Computational Physics, 336(C):36-50, May 2017. ISSN 0021-9991. doi: 10.1016/j.jcp.2017.01.047.
[7] Zheng Wang, Wei Xing, Robert Kirby, and Shandian Zhe. Multi-Fidelity High-Order Gaussian Processes for Physical Simulation. In International Conference on Artificial Intelligence and Statistics, pages 847–855. PMLR, March 2021.
[8] Shibo Li, Zheng Wang, Robert Kirby, and Shandian Zhe. Infinite-fidelity coregionalization for physical simulation. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 25965-25978. Curran Associates, Inc., 2022.
[9] Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
[10] Loic Le Gratiet. Bayesian analysis of hierarchical multifidelity codes. SIAM/ASA Journal on Uncertainty Quantification, 1(1):244-269, 2013.
[11] Paris Perdikaris, M Raissi, Andreas Damianou, N D. Lawrence, and George Karniadakis. Nonlinear Information Fusion Algorithms for Data-Efficient Multi-Fidelity Modelling, volume 473. Royal Society. doi: 10.1098/rspa.2016.0751.
[12] W. W. Xing, A. A. Shah, P. Wang, S. Zhe, Q. Fu, and R. M. Kirby. Residual gaussian process: A tractable nonparametric bayesian emulator for multi-fidelity simulations. Applied Mathematical Modelling, 97: 36-56, September 2021. ISSN 0307-904X. doi: 10.1016/j.apm.2021.03.041.
[13] Carl Edward Rasmussen and Christopher K. I. Williams. Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning. MIT Press, Cambridge, Mass, 2006. ISBN 978-0-262-18253-9.
[14] Edward N Lorenz. Deterministic nonperiodic flow. Journal of atmospheric sciences, 20(2):130-141, 1963.
[15] William E Boyce, Richard C DiPrima, and Douglas B Meade. Elementary differential equations and boundary value problems. John Wiley & Sons, 2021.
[16] Mauricio A Alvarez, David Luengo, and Neil D Lawrence. Linear latent force models using gaussian processes. IEEE transactions on pattern analysis and machine intelligence, 35(11):2693-2705, 2013.
[17] Andrew G Wilson, Zhiting Hu, Russ R Salakhutdinov, and Eric P Xing. Stochastic variational deep kernel learning. In D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016.
[18] Diederik P. Kingma and Max Welling. Auto-Encoding Variational Bayes. arXiv:1312.6114 [cs, stat], December 2013.