In numerous scientific and engineering applications, it is crucial to numerically study the interaction between multiple immiscible fluids, phases, or materials. Classical methods often fail to accurately simulate such phenomena because of the sharp interface between the different elements. One of the most commonly used methods in this context is the Volume Of Fluid (VOF) method. The central idea of the VOF method is to consider the percentage of each fluid, named volume fraction, in every cell of an underlying mesh, and to let it evolve according to suitable closed formulas as in a Finite Volume scheme. The flux associated with each volume fraction is computed locally, using the information of the cells in a small stencil, and the specific formula characterizes the specific class of VOF method. The most commonly used are the YOUNGS, LVIRA, ELVIRA, and PLIC. In this talk, we describe the VOF-ML method, which is a specific VOF method relying on a neural network to compute the local flux. This way, it is possible to exploit the superior expressivity of neural networks to more accurately capture the effects of nonlinear and (possibly) non-regular sharp interfaces. The method has been initially presented in [1] and [2]. In particular, we focus on the extension to three-dimensional advection problems and on the implementation details of such an extension. Indeed, due to the increased geometrical dimension, it is essential to generalize the generation of the synthetic training dataset, the physical and geometrical constraints, and the neural network structure. Numerical results are proposed to show the superior performance with respect to more classical alternatives. [1] B. Després and H. Jourdren, Machine learning design of volume of fluid schemes for compressible flows. Journal of Computational Physics, 408:109275, 2020. [2] M. Ancellin, B. Després, S. Jaouen. Extension of generic two-component VOF interface advection schemes to an arbitrary number of components, Journal of Computational Physics, 473, 2023.