受光传输启发,提出可解释的神经算子架构,提升物理建模效率。
Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

- 用反射、折射、散射模拟潜空间演化,实现局部调制与全局通信分离
- 散射模块将复杂度从二次降至线性,大幅降低计算开销
- 结构清晰可解释,适合需要物理一致性的科学计算场景
神经算子通过学习无限维函数空间间的映射,为参数化偏微分方程提供数据驱动的代理建模范式。现有架构通常通过预设变换域中的积分核参数化或对离散空间点施加类似注意力的交互来获得表达能力。尽管取得显著进展,但常面临物理可解释性、非局部空间通信、网格可扩展性与计算成本之间的权衡。本文提出受光启发的神经算子(LiNO),其潜空间演化分解为三个源于基础光传输机制的组件:反射与折射作为潜空间中的自适应逐点变换,实现局部特征重定向与各向异性调制;散射则在物理域上执行输入相关的非局部传播。我们首先将散射形式化为带有相对位置偏置的归一化成对核,随后设计一种高效变体,以正特征全局传播和局部扩散分支替代显式成对交互,将主导空间复杂度从二次降至线性。该结构实现了局部特征调制与全局空间通信的解耦,同时保持模块化与可解释性。
原文摘要 · Abstract (English)
Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs). Existing architectures typically obtain expressivity by parameterizing integral kernels in prescribed transform domains or by applying attention-like interactions over discretized spatial points. While these approaches have achieved substantial progress, they often face a persistent trade-off among physical interpretability, nonlocal spatial communication, mesh scalability, and computational cost. We propose a Light-inspired neural operator(LiNO), an operator-learning architecture whose latent evolution is decomposed into three mechanisms motivated by elementary light transport: reflection, refraction, and scattering. Reflection and refraction act as adaptive pointwise transformations in latent feature space, enabling local feature reorientation and anisotropic modulation, whereas scattering performs input-dependent nonlocal propagation over the physical domain. We first formulate scattering as a normalized pairwise kernel with relative positional bias, and then develop an efficient scattering variant that replaces explicit pairwise interactions with positive-feature global propagation and a local diffusion branch, reducing the dominant spatial complexity from quadratic to linear. This yields a structured neural operator that separates local feature modulation from global spatial communication while retaining a modular and interpretable latent evolution.
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