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

TL;DR

UFO introduces a novel neural operator framework that enables cross-domain, discretization-decoupled learning, allowing flexible input/output resolutions and robust predictions across diverse benchmarks.

Contribution

It presents UFO, a new operator framework that unifies multiple domains and decouples discretization, improving flexibility and robustness in neural operator learning.

Findings

UFO achieves accurate predictions on four diverse benchmarks.

UFO handles irregular sampling and spectral mismatch effectively.

UFO maintains physical coherence under distribution shifts.

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.