In the last decades, the storage capabilities of industrial and academic architectures have been subject to a significant development; the availability of large datasets has motivated the design of methods aimed at extracting the largest amount of information from the collected data, either to make prediction on a phenomenon of interest or to process the acquisitions in an unsupervised and automatic way. A key role in such advances has been played by data processing and machine learning based approaches, that can be either employed alone or in synergy with classical methods, creating new opportunities throughout different disciplines, ranging from inverse problems to dynamical systems and control problems. In this direction, notable examples of hybrid strategies have been developed within the classical framework of variational approaches for inverse problems [1] and for the solution of differential equations as in physics-informed neural networks [2,3]. In this minisymposium, we aim to discuss these two categories of problems where statistical data processing and machine learning are yielding to fast changes and improvements. The speakers in this session will explore the latest trends concerning the extraction of meaningful information from single/multiple one/two-dimensional data; they will highlight the capabilities of pure or hybrid data-driven approaches, while analyzing their limitations and the main challenges for the next future. Key topics will include the integration of artificial intelligence and the application of state-of-the-art algorithms to pressing challenges such as image decomposition, diffusion models, and the management of unstructured data. [1] Arridge, S., Maass, P., Öktem, O., Schönlieb, C.-B. Solving inverse problems using data-driven models. Acta Numerica 28 (2019). [2] Cuomo, S., Di Cola, V.S., Giampaolo, F. et al. Scientific Machine Learning Through Physics–Informed Neural Networks: where we are and what’s next. J Sci Comput 92 (2022). [3] Raissi, M., Perdikaris, P., Karniadakis, G.E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378 (2019).