Title: Illuminating Neural Operators: A Framework Based on Reflection, Refraction, and Scattering

Abstract

Neural operators facilitate data-driven surrogate modeling for parametric partial differential equations (PDEs) by learning mappings between infinite-dimensional function spaces. Current architectural designs generally enhance expressivity through either the parameterization of integral kernels within specific transform domains or by employing attention-like mechanisms across discretized spatial nodes. Although these methods have yielded significant advancements, they frequently encounter a difficult trade-off involving physical interpretability, nonlocal spatial communication, scalability across different meshes, and computational efficiency.

To address these challenges, we introduce Light-inspired Neural Operator (LiNO), an architecture that decomposes latent evolution into three distinct mechanisms inspired by fundamental light transport phenomena: reflection, refraction, and scattering. In this framework, reflection and refraction function as adaptive pointwise transformations within the latent feature space, facilitating local feature reorientation and anisotropic modulation. Conversely, scattering enables input-dependent nonlocal propagation throughout the physical domain.

We initially define scattering as a normalized pairwise kernel incorporating relative positional bias. Subsequently, we present an optimized scattering variant that substitutes explicit pairwise interactions with a combination of global propagation driven by positive features and a local diffusion branch. This innovation reduces the dominant spatial complexity from quadratic to linear. The resulting structured neural operator effectively decouples local feature modulation from global spatial communication, maintaining a modular and interpretable latent evolution process.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC