In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on ...

Abstract: Fourier neural operator (FNO) is a recently proposed data-driven scheme to approximate the implicit operators characterized by partial differential equations (PDEs) between functional spaces ...

In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on ...

Abstract: Long-term time series forecasting presents a critical challenge across numerous application domains. Recently, various transformer-based models have been employed for this task; however, ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

The essential spectra of Fourier integral operators (and related operators) on L²(R), determined by piecewise continuous symbol functions, are derived from a ...