Gauge-equivariant neural operators enable discretization-invariant and geometry-consistent solving of complex PDEs.
March 17, 2026
Original Paper
Gauge-Equivariant Intrinsic Neural Operators for Geometry-Consistent Learning of Elliptic PDE Maps
arXiv · 2603.14734
The Takeaway
By decoupling geometry from learnable functional dependence, this method allows scientific surrogate models to remain robust under metric perturbations and resolution changes. This is a significant advance for applying deep learning to high-fidelity physics simulations like fluid dynamics.
From the abstract
Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform under changes of local frame (gauge), many existing operator-learning architectures remain representation-dependent, brittle under metric perturbations, and sensitive to discretization changes. We propose Gauge-Equivariant Intrinsic Neural Operators (GINO), a cla