Title: LFNO: Bridging Laplace and Fourier for Effective Operator Learning
Primary area: other topics in machine learning (i.e., none of the above)
Keywords: Operator Learning, Neural Operators, Laplace transform, Fourier integral operator, transient response, steady-state response

Abstract: We introduce Laplace–Fourier Neural Operator (LFNO), a novel operator learning model that bridges the strengths of Laplace Neural Operators (LNO) and Fourier Neural Operators (FNO).
By combining the transient response of LNO with the steady-state response of FNO through the Fourier integral operator, our model enables capturing transient behavior more effectively than both LNO and FNO while remaining comparable on linear and nonlinear PDEs. We demonstrate LFNO's effectiveness on solving three ODEs (Duffing, Lorenz, Pendulum) and five PDEs (Euler-Bernoulli beam, diffusion, reaction-diffusion, Brusselator, Gray-Scott) in comparison to FNO and LNO. 
These results highlight LFNO’s ability to unify transient and steady-state modeling, delivering superior accuracy and stability across various dynamical systems.

TL;DR: We Unify LNO and FNO for effective operator learning