A Comparative Study of Supervised Learning Techniques for the Radiative Transfer Equation Inversion

Estimation of the constituents of a gas (e.g. temperature, concentration) from high resolution spectroscopic measurements is a fundamental step to control and improve the efficiency of combustion processes governed by the Radiative Transfer Equation (RTE). Typically such estimation is performed using thermocouples; however, these sensors are intrusive and must undergo the harsh furnace environment. In this paper, we follow a machine learning approach to learn the relation between the spectroscopic measurements and gas constituents such as temperature, concentration and length. This is a challenging problem due to the non-linear behavior of the RTE and the high dimensional data obtained from sensor measurements. We perform a comparative study of linear and neural network regression models, using canonical correlation analysis (CCA), principal component analysis (PCA), reduced rank regression(RRR), and kernel canonical correlation (KCCA) to reduce the dimensionality.