This mini-symposium is dedicated to methodological and theoretical aspects of hybrid approaches combining Machine Learning techniques with traditional numerical methods or modeling for the resolution of partial differential equations (PDEs). Recent years have seen the emergence of models that intertwine data-driven components—neural networks, kernel methods, or learned operators—with well-established discretization schemes (finite differences, finite elements, spectral methods, etc.), which offer new ways to accelerate simulations, increase accuracy and adaptivity of the solvers in complex regimes, and automate parameter selection. They also open up promising avenues for tackling high-dimensional problems, multiscale dynamics, model uncertainties or inverse problems. However, their integration raises important theoretical questions regarding stability, convergence, expressivity, and generalization. We invite contributions that shed light on: - the proposal of novel, efficient, and principled hybridization strategies combining machine learning and traditional PDE solvers; - the mathematical foundations and analysis of hybrid ML–PDE methods; - theoretical properties of learned components when embedded in numerical schemes; - the impact of training dynamics and data sampling on the numerical solvers Our objective is to foster rigorous dialogue around the design principles and theoretical guarantees that underpin successful hybrid application of machine learning to PDEs.