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This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.

CO2 Sequestration is one of the strategies currently used to decrease the amount of CO2 in the atmosphere. In this work, the modelling of CO2 sequestration involves the simulation of CO2 capture from flue gases and the CO2 storage in the subsurface considering a sustainability approach. The main focus of the CO2 sequestration is to reduce the greenhouse emission but in many cases, the models do not consider the carbon footprint associated with the process. We present an integrated approach where the CO2 sequestration model involves the power plant simulation of the CO2 capture, the numerical simulation of CO2 storage, economics and the life cycle assessment for the minimisation of the carbon footprint. This study provides an insight for future development of integrated approaches considering oxycombustion carbon capture focussed on the air separation unit and the simulation and monitoring of the subsurface storage sites. Our work considers the CO2 capture process using Cryogenic and Membrane Air Separation Units for Oxi-Combustion because it is associated with a reduced carbon footprint when compared to other processes as post-combustion and pre-combustion. Our CO2 storage approach includes the compositional simulation of fluid flow in porous media and the characterisation of the sealing rock above realistic heterogeneous storage models by using an Ensemble Kalman Filter approach on a long term simulation of 100 years. Initial realisations of the subsurface model were generated using stochastic modelling and considering the uncertainty on the petrophysical properties of the rock, in particular permeability and porosity. In this work, one of the main purposes of the CO2storage simulation is to avoid the vertical leakage of the CO2 and for this, the fluid saturation in every cell is monitored during the simulation approach. From the results associated with the oxy-combustion application, the Cryogenic model and membrane model reduce the carbon footprint by 78.34% and 66.84% respectively compared to the power plant model without carbon capture. It is also observed that electricity consumption produces the biggest carbon footprint portion for both models, hence future improvement should be focused in reducing process energy requirement. In terms of energy production, carbon footprint, and economic, oxy-combustion power plant with cryogenic air separation demonstrates better performance. However, the results of this study indicate that the membrane O2/N2 needs produce lower net power production and oxygen purity compared to the cryogenic model. Hence, further development of membrane material is still needed before it can be considered as a competitive option for air separation unit. An economic evaluation is also performed and the results show that cryogenic air separation is still a more economical option compared to membrane. The design of the well locations is dependent of the heterogeneity of the model and the correct characterisation of the sealing rock. The performance, environmental, and economic considerations are taken into account, resulting in an integrated and broader understanding of CO2 sequestration.

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