POD-Galerkin
Canuto, C., Tonn, T., & Urban, K. (2009). A posteriori error analysis of the reduced basis method for nonaffine parametrized nonlinear PDEs. SIAM Journal on Numerical Analysis, 47(3), 2001-2022
Couplet, M., Basdevant, C., & Sagaut, P. (2005). Calibrated reduced-order POD-Galerkin system for fluid flow modelling. Journal of Computational Physics, 207(1), 192-220
Hijazi, S., Stabile, G., Mola, A., & Rozza, G. (2020). Data-driven POD-Galerkin reduced order model for turbulent flows. Journal of Computational Physics, 416, 109513
PODI
P. G. Constantine. (2015). Active subspaces: Emerging ideas for dimension reduction in parameter studies. Society for Industrial and Applied Mathematics.
N. Demo, M. Tezzele, and G. Rozza. (2019). A non-intrusive approach for the reconstruction of pod modal coefficients through active subspaces. Comptes Rendus Mécanique, 347(11):873– 881. Data-Based Engineering Science and Technology.
D. Rajaram, T. G. Puranik, C. Perron, and D. N. Mavris. (2020). Non-intrusive parametric reduced order modeling using randomized algorithms. In AIAA Scitech 2020 Forum, page p. 23, 01
Berzins, A., Helmig, J., Key, F., & Elgeti, S. (2020). Standardized non-intrusive reduced order modeling using different regression models with application to complex flow problems. CoRR.
EIM
EIM simultaneous RB - SER version (nethodology) - Daversin, C., & Prud’Homme, C. (2015). Simultaneous empirical interpolation and reduced basis method for non-linear problems. Comptes Rendus Mathematique, 353(12), 1105-1109
NIRB 2-grid
Chakir, R., Maday, Y., Parnaudeau, P. (2019). A non-intrusive reduced basis approach for parametrized heat transfer problems. Journal of Computational Physics, 376, 617-633.
Grosjean, E., & Maday, Y. (2021). Error estimate of the non-intrusive reduced basis method with finite volume schemes. ESAIM: Mathematical Modelling and Numerical Analysis, 55(5), 1941-1961
PBDW
Gong, H., Maday, Y., Mula, O., & Taddei, T. (2019). PBDW method for state estimation: error analysis for noisy data and nonlinear formulation. arXiv preprint arXiv:1906.00810.
Maday, Y., Patera, A. T., Penn, J. D., & Yano, M. (2015). A parameterized‐background data‐weak approach to variational data assimilation: formulation, analysis, and application to acoustics. International Journal for Numerical Methods in Engineering, 102(5), 933-965.
Hammond, J. K., Chakir, R., Bourquin, F., & Maday, Y. (2019). PBDW: A non-intrusive Reduced Basis Data Assimilation method and its application to an urban dispersion modeling framework. Applied Mathematical Modelling, 76, 1-25.
General RBM
Quarteroni, A., Manzoni, A., & Negri, F. (2015). Reduced basis methods for partial differential equations: an introduction (Vol. 92). Springer.