UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning

2026-05-12

AI Summary

Existing neural operators are typically confined to a single representation domain, limiting their generalization to scenarios where inputs and outputs differ in resolution, sampling locations, or distribution. This work proposes the UFO framework, which introduces the first cross-domain phase-modulated operator that operates without requiring domain alignment. By leveraging joint multi-domain conditional modeling and an adaptive interaction mechanism, UFO enables flexible coupling across physical, spectral, and latent spaces, fully decoupling input and output discretizations during both training and inference. The method achieves highly accurate, robust, and physically consistent predictions across four benchmark tasks exhibiting distribution shifts, significantly enhancing the generalization capability of neural operators.

Abstract

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.

Problem

• neural operators
• cross-domain
• discretization decoupling
• distribution shifts
• function space mappings

Innovation

• cross-domain
• discretization decoupling
• neural operators
• domain-unification-free
• phase-modulated