  Numerically solving partial differential equations typically requires fine
discretization to resolve necessary spatiotemporal scales, which can be
computationally expensive. Recent advances in deep learning have provided a new
approach to solving partial differential equations that involves the use of
neural operators. Neural operators are neural network architectures that learn
mappings between function spaces and have the capability to solve partial
differential equations based on data. This study utilizes a novel neural
operator called Hyena, which employs a long convolutional filter that is
parameterized by a multilayer perceptron. The Hyena operator is an operation
that enjoys sub-quadratic complexity and state space model to parameterize long
convolution that enjoys a global receptive field. This mechanism enhances the
model's comprehension of the input's context and enables data-dependent weight
for different partial differential equations instances. To measure how
effective the layers are in solving partial differential equations, we conduct
experiments on Diffusion-Reaction equation and Navier Stokes equation. Our
findings indicate Hyena Neural operator can serve as an efficient and accurate
model for learning partial differential equations solution operator. The data
and code used can be found at:
https://github.com/Saupatil07/Hyena-Neural-Operator
