Classical numerical solvers are reliable for modeling physical systems, but their computational cost rapidly increases with geometric complexity, multiscale effects, and coupled dynamics, limiting their use in fast or real-time applications such as digital twins. Data-driven surrogate models address this challenge by learning efficient approximations of high-fidelity simulations, enabling rapid and scalable predictions. Graph-based neural operators have shown strong potential due to their ability to operate on unstructured domains [1]. However, most existing approaches rely on message-passing schemes, which suffer from intrinsic limitations in information propagation, expressiveness, and scalability, including the under-reaching phenomenon and related effects [2]. These limitations motivate the exploration of representations beyond pairwise graph interactions for complex systems. In this work, we explore learning frameworks enriched with topological inductive biases, leveraging higher-order structures to better capture the interactions present in discretized physical systems. Building on recent advances in Topological Deep Learning [3], the proposed approach overcomes key shortcomings of standard message-passing models and enables more accurate and scalable surrogates for complex PDE-driven dynamics, particularly in the presence of strong nonlinearities, heterogeneity, and coupled physics.