{"ID":3005037,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-05T07:16:01.131756733Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.03262","arxiv_id":"2606.03262","title":"Let There Be Light: Reflection, Refraction and Scattering for Neural Operators","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2606.03262","url_pdf":"https://arxiv.org/pdf/2606.03262v1","authors":"[\"Keke Wu\",\"Yixuan Zhang\",\"Jingrun Chen\"]","published":"2026-06-02T07:25:49Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.NA\"]","methods":"[\"Diffusion Model\"]","has_code":false}