Hyena Neural Operator for Partial Differential Equations

Understand

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.