SINO: Scale-Invariant Neural Operator

תקציר מקורי באנגליתarXiv:2609.36890v1 Announce Type: new Abstract: In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solving equations on coarse grids, missing information leads to the closure problem: modeling unresolved physics to recover lost dynamics. Although closure terms depend on grid resolution, they represent scale-invariant physical laws. A model truly learning physics should capture these mechanisms with low-rank parameterization rather than memorizing grid-specific patterns. Inspired by this, we propose the Scale-Invariant Neural Operator (SINO), which learns on normalized physical scales via a dual-branch architecture operating in spectral and spatial domains. SINO uses bottleneck MLPs to generate con