The minisymposium proposes recent results of Applied Mathematics based on physical models and Machine Learning approaches, including hybrid techniques, to obtain relevant contributions in the industrial sector. Special attention is given to problems considering fluid percolation in a porous medium. Such a problem finds application in the extraction of espresso coffee, which is widespread throughout the world. Coffee is a multi-purpose beverage with functional, social and health benefits, and from a scientific point of view, its extraction is a complex physical-chemical process. The study of the percolation problem, through a proper approximation and calibration of the initial-boundary value model, allows for obtaining the resulting chemistry composition in the cup. A particularly intriguing challenge is the inverse problem: determining the optimal brewing conditions starting from a desired composition in the cup. This task, which is central to digital coffee personalisation, is highly nonlinear and ill-posed. Physics-Informed Neural Networks (PINNs) offer a promising solution by embedding physical constraints into data-driven models. This minisymposium aims to present the results of the ongoing project “Digital twin per la personalizzazione del caffè espresso INSILICOFFEE”, funded by the cascade call Spoke 9 (Università degli Studi di Napoli Federico II) - ‘Digital Society & Smart City’ - National Centre ICSC. Moreover, the minisymposium would like to be an opportunity to exchange ideas on similar research interests, especially among young researchers, and pave the way for future collaborations. The topics of interest are percolation problems in porous media or similar fluid-dynamics problems and Machine Learning techniques for complex inverse problems.