提出无需统一域的神经算子框架，实现跨域自适应推理。
UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning
- 通过不同域表示间的自适应联合条件交互实现算子
- 支持输入输出分辨率解耦，跨分布变化仍保持高精度
- 适合处理不连续、非规则采样等复杂物理场景
神经算子已成为学习函数空间映射的有效框架，但现有架构大多仅在单一表示域（如物理域、谱域或隐空间）内实现。本文提出UFO（Domain-Unification-Free Operator），一种跨域神经算子框架，通过在不同域上定义的表示间进行自适应、联合条件交互来实现算子。UFO实现了离散化解耦：输入函数可在与训练时不同分辨率或位置观测，而解可以在任意输出分辨率查询。在涵盖不连续输入、非规则采样与谱失配、非线性动力学及随机高频场的四个互补基准上，UFO在分布漂移下仍能提供准确、鲁棒且物理一致的预测。这些结果确立了跨域、相位调制实现是实现离散化解耦神经算子学习的强大框架。
原文摘要 · Abstract (English)
Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In this work, we introduce UFO (Domain-Unification-Free Operator), a cross-domain neural operator framework that realizes operators through adaptive, jointly conditioned interactions among representations defined on distinct domains. UFO enables discretization decoupling: the input function can be observed at resolutions or locations different from those used during training, while the solution can be queried at arbitrary output resolutions. Across four complementary benchmarks covering discontinuous inputs, irregular sampling with spectral mismatch, nonlinear dynamics, and stochastic high-frequency fields, UFO delivers accurate, robust, and physically coherent predictions under distribution shifts. These results establish cross-domain, phase-modulated realization as a powerful framework for discretization-decoupled neural operator learning.
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