Data-Efficient Time-Dependent PDE Surrogates: Graph Neural Simulators vs. Neural Operators

תקציר מקורי באנגליתarXiv:2509.06154v3 Announce Type: replace Abstract: Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have gained popularity as surrogates for systems driven by partial differential equations (PDEs). However, their reliance on large datasets and limited ability to generalize in low-data regimes hinder their practical utility. We argue that these limitations arise from their global processing of data, which fails to exploit the local, discretized structure of physical systems. To address this, we propose Graph Neural Simulators (GNS) as a principled surrogate modeling paradigm for time-dependent PDEs. GNS leverage