UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning
This work addresses the need for discretization-decoupled neural operators that can handle distribution shifts, benefiting scientific computing and engineering applications where input and output resolutions vary.
UFO introduces a cross-domain neural operator framework that learns mappings between function spaces through adaptive interactions among representations in different domains, achieving discretization decoupling. It delivers accurate and robust predictions across four benchmarks covering discontinuous inputs, irregular sampling, nonlinear dynamics, and stochastic high-frequency fields.
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.