Neural operators learn resolution independent map-
pings between functional spaces, and are a pop-
ular way to generate solutions for an entire class
of partial differential equations (PDE) as opposed
to just one instance, leading to significant compu-
tational gains. However, these methods rely on a
continuous-discrete equivalence between the func-
tional form and the samples, which may be vio-
lated if the samples are not captured faithfully. We
propose the multi-kernel neural operator (MKNO)
which can capture different frequency components
at varying levels of resolutions. MKNO accom-
plishes this by using the Fourier kernels to capture
lower frequency global information and graph ker-
nels to capture more local and high frequency fea-
ture information. MKNO is discretization invariant,
and learns a general solution operator that can be
applied to varying discretizations. To validate our
architecture we apply MKNO to a number of differ-
ent two dimensional PDEs.
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