This repository provides the official source code for the paper:
Hermite Neural Operator for Solving Partial Differential Equations on Unbounded Domains
Ruijie Bai, Ziyuan Liu, Xiangyao Wu, Yuhang Wu, and Xu Qian
(Link to published paper will be added upon acceptance)
The Hermite Neural Operator (HNO) is a novel framework that solves PDEs on unbounded domains by integrating the classical Hermite spectral method into a neural operator architecture. By using Hermite functions as the basis, HNO inherently enforces the correct far-field decay conditions required for unbounded problems.
As demonstrated in the paper, HNO achieves significantly high accuracy and robust off-grid extrapolation on challenging benchmarks, including the Nonlinear Schrödinger (NLS) and Heat equations.