  The computational efficiency of many neural operators, widely used for
learning solutions of PDEs, relies on the fast Fourier transform (FFT) for
performing spectral computations. As the FFT is limited to equispaced
(rectangular) grids, this limits the efficiency of such neural operators when
applied to problems where the input and output functions need to be processed
on general non-equispaced point distributions. Leveraging the observation that
a limited set of Fourier (Spectral) modes suffice to provide the required
expressivity of a neural operator, we propose a simple method, based on the
efficient direct evaluation of the underlying spectral transformation, to
extend neural operators to arbitrary domains. An efficient implementation* of
such direct spectral evaluations is coupled with existing neural operator
models to allow the processing of data on arbitrary non-equispaced
distributions of points. With extensive empirical evaluation, we demonstrate
that the proposed method allows us to extend neural operators to arbitrary
point distributions with significant gains in training speed over baselines
while retaining or improving the accuracy of Fourier neural operators (FNOs)
and related neural operators.
