[en] Modern nuclear reactors utilize core calculations that implement a thermo-hydraulic feedback requiring accurate homogenized few-group cross sections. They describe the interactions of neutrons with matter, and are endowed with the properties of smoothness and regularity, steaming from their underling physical phenomena. This thesis is devoted to the modeling of these functions by industry state-of-the-art and innovative machine learning techniques. Mathematically, the subject can be defined as the analysis of convenient mapping techniques from one multi-dimensional space to another, conceptualize as the aggregated sum of these functions, whose quantity and domain depends on the simulations objectives. Convenient is intended in terms of computational performance, such as the model's size, evaluation speed, accuracy, robustness to numerical noise, complexity, etc; always with respect to the engineering modeling objectives that specify the multidimensional spaces of interest. In this thesis, a standard UO₂ PWR fuel assembly is analyzed for three state-variables, burnup, fuel temperature, and boron concentration. Library storage requirements are optimized meeting the evaluation speed and accuracy targets in view of microscopic, macroscopic cross sections and the infinite multiplication factor. Three approximation techniques are studied: The state-of-the-art spline interpolation using computationally convenient B-spline basis, that generate high order local approximations. A full grid is used as usually done in the industry. Kernel methods, that are a very general machine learning framework able to pose in a normed vector space, a large variety of regression or classification problems. Kernel functions can reproduce different function spaces using an unstructured support, which is optimized with pool active learning techniques. The approximations are found through a convex optimization process simplified by the kernel trick. The intrinsic modular character of the method facilitates segregating the modeling phases: function space selection, application of numerical routines and support optimization through active learning. Artificial neural networks which are 'model free' universal approximators able Artificial neural networks which are 'model free' universal approximators able to approach continuous functions to an arbitrary degree without formulating explicit relations among the variables. With adequate training settings, intrinsically parallelizable multi-output networks minimize storage requirements offering the highest evaluation speed. These strategies are compared to each other and to multi-linear interpolation in a Cartesian grid, the industry standard in core calculations. The data set, the developed tools, and scripts are freely available under a MIT license. (author)