References
- Masri A.R., Partial premixing and stratification in turbulent flames, Proc. Combust. Inst. 35 (2015), pp. 1115–1136. https://doi.org/https://doi.org/10.1016/j.proci.2014.08.032
- Lawn C.J., Lifted flames on fuel jets in co-flowing air, Prog. Energy Combust. Sci. 35 (2009), pp. 1–30. https://doi.org/https://doi.org/10.1016/j.pecs.2008.06.003
- Buckmaster J., Edge-flames, Prog. Energy Combust. Sci. 28 (2002), pp. 435–475.
- Lyons K.M., Toward an understanding of the stabilization mechanisms of lifted turbulent jet flames: experiments, Prog. Energy Combust. Sci. 33 (2007), pp. 211–231.
- van Oijen J.A. and de Goey L.P., A numerical study of confined triple flames using a flamelet-generated manifold, Combust. Theory Model. 8 (2004), pp. 141–163.
- Domingo P., Vervisch L., and Bray K., Partially premixed flamelets in LES of nonpremixed turbulent combustion, Combust. Theory Model. 6 (2002), pp. 529–551.
- Domingo P., Vervisch L., and Réveillon J., Dns analysis of partially premixed combustion in spray and gaseous turbulent flame-bases stabilized in hot air, Combust. Flame 140 (2005), pp. 172–195. http://www.sciencedirect.com/science/article/pii/S0010218004002342
- Knudsen E. and Pitsch H., A general flamelet transformation useful for distinguishing between premixed and non-premixed modes of combustion, Combust. Flame 156 (2009), pp. 678–696. https://doi.org/https://doi.org/10.1016/j.combustflame.2008.10.021
- Knudsen E. and Pitsch H., Capabilities and limitations of multi-regime flamelet combustion models, Combust. Flame 159 (2012), pp. 242–264. https://doi.org/https://doi.org/10.1016/j.combustflame.2011.05.025
- Yamashita H., Shimada M., and Takeno T., A numerical study on flame stability at the transition point of jet diffusion flames, Proc. Combust. Inst. 1996), pp. 27–34.
- Fiorina B., Gicquel O., Vervisch L., Carpentier S., and Darabiha N., Approximating the chemical structure of partially premixed and diffusion counterflow flames using FPI flamelet tabulation, Combust. Flame 140 (2005), pp. 147–160.
- Rosenberg D.A., Allison P.M., and Driscoll J.F., Flame index and its statistical properties measured to understand partially premixed turbulent combustion, Combust. Flame 162 (2015), pp. 2808–2822. https://doi.org/https://doi.org/10.1016/j.combustflame.2015.04.007
- Hartl S., Geyer D., Dreizler A., Magnotti G., Barlow R.S., and Hasse C., Regime identification from Raman / Rayleigh line measurements in partially premixed flames, Combust. Flame 189 (2018), pp. 126–141. https://doi.org/https://doi.org/10.1016/j.combustflame.2017.10.024
- Maas U. and Pope S.B., Simplifying chemical kinetics: Intrinsic low dimensional manifolds in composition space, Combust. Flame 88 (1992), pp. 239–264.
- Lam S., Using CSP to understand complex chemical kinetics, Combust. Sci. Technol. 89 (1993), pp. 375–404.
- Girimaji S.S., Composition-space behavior of diffusion-reaction systems, Theor. Comput. Fluid Dyn. 17 (2004), pp. 171–188.
- Gicquel O., Darabiha N., and Thévenin D., Liminar premixed hydrogen/air counterflow flame simulations using flame prolongation of ILDM with differential diffusion, Proc. Combust. Inst. 28 (2000), pp. 1901–1908. http://www.sciencedirect.com/science/article/pii/S0082078400805-949
- Bongers H., Oijen J.V., and Goey L.D., Intrinsic low-dimensional manifold method extended with diffusion, Proc. Combust. Inst. 29 (2002), pp. 1371–1378. http://www.sciencedirect.com/science/article/pii/S1540748902801687
- Goussis D.A., Valorani M., Creta F., and Najm H.N., Reactive and reactive-diffusive time scales in stiff reaction-diffusion systems, Prog. Comput. Fluid Dyn. Int. J. 5 (2005), pp. 316.
- Najm H.N., Valorani M., Goussis D.A., and Prager J., Analysis of methane-air edge flame structure, Combust. Theory Model. 14 (2010), pp. 257–294. http://www.tandfonline.com/doi/abs/https://doi.org/10.1080/13647830.2010.483021
- Mengers J.D. and Powers J.M., One-dimensional slow invariant manifolds for fully coupled reaction and micro-scale diffusion, SIAM J. Appl. Dyn. Syst. 12 (2013), pp. 560–595.
- Bykov V. and Maas U., The extension of the ildm concept to reaction-diffusion manifolds, Combust. Theory Model. 11 (2007), pp. 839–862. https://doi.org/https://doi.org/10.1080/13647830701242531
- Van Oijen J.A., Lammers F.A., and De Goey L.P., Modeling of complex premixed burner systems by using flamelet-generated manifolds, Combust. Flame 127 (2001), pp. 2124–2134.
- Nguyen P.D., Vervisch L., Subramanian V., and Domingo P., Multidimensional flamelet-generated manifolds for partially premixed combustion, Combust. Flame 157 (2010), pp. 43–61. https://doi.org/https://doi.org/10.1016/j.combustflame.2009.07.008
- Sutherland J.C. and Parente A., Combustion modeling using principal component analysis, Proc. Combust. Inst. 32 I (2009), pp. 1563–1570. https://doi.org/https://doi.org/10.1016/j.proci.2008.06.147
- Echekki T. and Mirgolbabaei H., Principal component transport in turbulent combustion: A posteriori analysis, Combust. Flame 162 (2015), pp. 1919–1933. https://doi.org/https://doi.org/10.1016/j.com-bustflame.2014.12.011
- Wu H. and Ihme M., Compliance of combustion models for turbulent reacting flow simulations, Fuel 186 (2016), pp. 853–863. http://www.sciencedirect.com/science/article/pii/S001623611-6306779
- Zirwes T., Zhang F., Habisreuther P., Hansinger M., Bockhorn H., Pfitzner M., and Trimis D., Identification of flame regimes in partially premixed combustion from a quasi-DNS datasets, Flow Turbul. Combust. (2020).
- Brunton S.L. and Kutz J.N., Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge University Press, Cambridge, 2019.
- Grogan K.P. and Ihme M., Identification of governing physical processes of irregular combustion through machine learning, Shock Waves 28 (2018), pp. 941–954. https://doi.org/https://doi.org/10.1007/s00193-018-0852-y
- D'Alessio G., Parente A., Stagni A., and Cuoci A., Adaptive chemistry via pre-partitioning of composition space and mechanism reduction, Combust. Flame 211 (2020), pp. 68–82. https://doi.org/https://doi.org/10.1016/j.combustflame.2019.09.010
- Goodfellow I., Bengio Y., and Courville A., Deep Learning, The MIT Press, Cambridge, Massachusetts, 2016.
- Baum E.B. and Wilczek F., Supervised learning of probability distributions by neural networks, in Neural Information Processing Systems, D.Z. Anderson, ed., American Institute of Physics, 1988, pp. 52–61. Available at http://papers.nips.cc/paper/3-supervised-learning-of-probability-distributions-by-neural-networks.pdf.
- Duin R.P.W. and Tax D.M.J., Classifier conditional posterior probabilities, in Advances in Pattern Recognition, A. Amin, D. Dori, P. Pudil, and H. Freeman, eds., Springer, Berlin Heidelberg, 1998, pp. 611–619.
- Richard M.D. and Lippmann R.P., Neural network classifiers estimate bayesian a posteriori probabilities, Neural Comput. 3 (1991), pp. 461–483. https://doi.org/https://doi.org/10.1162/neco.1991.3.4.461, pMID: 31167331
- Lippmann R.P., Neural networks, bayesian a posteriori probabilities, and pattern classification, in From Statistics to Neural Networks, V. Cherkassky, J.H. Friedman, and H. Wechsler, eds., Springer, Berlin Heidelberg, 1994, pp. 83–104.
- Rojas R., A short proof of the posterior probability property of classifier neural networks, Neural Comput. 8 (1996), pp. 41–43. https://doi.org/https://doi.org/10.1162/neco.1996.8.1.41
- Gish H., A probabilistic approach to the understanding and training of neural network classifiers, Int. Conf. Acoust. Speech Signal Process. 3 (1990), pp. 1361–1364.
- Wan E.A., Neural network classification: A bayesian interpretation, IEEE Trans. Neural Netw. 1 (1990), pp. 303–305.
- Ruck D.W., Rogers S.K., Kabrisky M., Oxley M.E., and Suter B.W., The multilayer perceptron as an approximation to a bayes optimal discriminant function, IEEE Trans. Neural Netw. 1 (1990), pp. 296–298.
- Hung M.S., Hu M.Y., Patuwo B.E., and Shanker M., Estimating Posterior Probabilities in Classification Problems With Neural Networks. International Journal of Computational Intelligence and Organizations 1(1) (1996), pp. 49–60.
- Cuoci A., Frassoldati A., Faravelli T., and Ranzi E., A computational tool for the detailed kinetic modeling of laminar flames: Application to c2h4/ch4 coflow flames, Combust. Flame 160 (2013), pp. 870–886.
- Cuoci A., Frassoldati A., Faravelli T., and Ranzi E., Numerical modeling of laminar flames with detailed kinetics based on the operator-splitting method, Energy Fuels 27 (2013), pp. 7730–7753.
- Cuoci A., Frassoldati A., Faravelli T., and Ranzi E., Opensmoke++: An object-oriented framework for the numerical modeling of reactive systems with detailed kinetic mechanisms, Comput. Phys. Commun. 192 (2015), pp. 237–264.
- Ranzi E., Frassoldati A., Grana R., Cuoci A., Faravelli T., Kelley A., and Law C., Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon and oxygenated fuels, Prog. Energy Combust. Sci. 38 (2012), pp. 468–501. http://www.sciencedirect.com/science/article/pii/S0360128512000196
- Klambauer G., Unterthiner T., Mayr A., and Hochreiter S., Self-normalizing neural networks, in Proceedings of the 31st International Conference on Neural Information Processing Systems, Curran Associates Inc., NIPS'17, Red Hook, NY, 2017, pp. 972–981.
- Kingma D.P. and Ba J., Adam: A method for stochastic optimization, 2014. Available at http://arxiv.org/abs/1412.6980, arxiv:1412.6980Comment: Published as a conference paper at the 3rd International Conference for Learning Representations, San Diego, 2015.