Hyena Neural Operator for Partial Differential Equations

arXiv2306.16524MaRDI QIDQ6441901

Amir Barati Farimani, Saurabh Patil, Zijie Li

Publication date: 28 June 2023

Abstract: Numerically solving partial differential equations (PDEs) 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 PDEs 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 global receptive field. This mechanism enhances the model's comprehension of the input's context and enables data-dependent weight for different PDE instances. To measure how effective the layers are in solving PDEs, we conduct experiments on Burger's equation and Navier Stokes equation. Our findings indicate Hyena Neural operator can serve as an efficient and accurate model for learning PDEs' solution operator. The data and code used can be found at: https://github.com/Saupatil07/Hyena-Neural-Operator

Has companion code repository: https://github.com/saupatil07/hyena-neural-operator

This page was built for publication: Hyena Neural Operator for Partial Differential Equations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6441901)