Alessandro Trenta

Tai Hoang, Alessandro Trenta, Alessio Gravina et al.

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data, yet often struggle to capture long-range interactions and suffer from error accumulation under autoregressive rollouts. To address these challenges, we propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics. This structure guarantees preservation of information across the graph, while extending to port-Hamiltonian systems allows the model to capture a broader class of dynamics, including non-conservative effects. IGNS further incorporates a warmup phase to initialize global context, geometric encoding to handle irregular meshes, and a multi-step training objective to reduce rollout error. To evaluate these properties systematically, we introduce new benchmarks that target long-range dependencies and challenging external forcing scenarios. Across all tasks, IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems.

Alessandro Trenta, Andrea Cossu, Davide Bacciu

We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that effectively transfers knowledge from a pre-trained model to a student one. We provide theoretical guarantees that DERL can learn the true physical system, being consistent with the underlying physical laws, even when using empirical derivatives. DERL outperforms state-of-the-art methods in generalizing an ODE to unseen initial conditions and a parametric PDE to unseen parameters. We also design a method based on DERL to transfer physical knowledge across models by extending them to new portions of the physical domain and a new range of PDE parameters. We believe this is the first attempt at building physical models incrementally in multiple stages.

Alessandro Trenta, Davide Bacciu, Andrea Cossu et al.

We develop MultiSTOP, a Reinforcement Learning framework for solving functional equations in physics. This new methodology produces actual numerical solutions instead of bounds on them. We extend the original BootSTOP algorithm by adding multiple constraints derived from domain-specific knowledge, even in integral form, to improve the accuracy of the solution. We investigate a particular equation in a one-dimensional Conformal Field Theory.