QPDE: Quantum Neural Network Based Stabilization Parameter Prediction for Numerical Solvers for Partial Differential Equations-Reference-Cited by-同舟云学术

QPDE: Quantum Neural Network Based Stabilization Parameter Prediction for Numerical Solvers for Partial Differential Equations

Published:2023-07-13 Issue:3 Volume:3 Page:552-562
ISSN:2673-9909
Container-title:AppliedMath
language:en
Short-container-title:AppliedMath

Author:

Yadav Sangeeta¹

Affiliation:

1. Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru 560012, Karnataka, India

Abstract

We propose a Quantum Neural Network (QNN) for predicting stabilization parameter for solving Singularly Perturbed Partial Differential Equations (SPDE) using the Streamline Upwind Petrov Galerkin (SUPG) stabilization technique. SPDE-Q-Net, a QNN, is proposed for approximating an optimal value of the stabilization parameter for SUPG for 2-dimensional convection-diffusion problems. Our motivation for this work stems from the recent progress made in quantum computing and the striking similarities observed between neural networks and quantum circuits. Just like how weight parameters are adjusted in traditional neural networks, the parameters of the quantum circuit, specifically the qubits’ degrees of freedom, can be fine-tuned to learn a nonlinear function. The performance of SPDE-Q-Net is found to be at par with SPDE-Net, a traditional neural network-based technique for stabilization parameter prediction in terms of the numerical error in the solution. Also, SPDE-Q-Net is found to be faster than SPDE-Net, which projects the future benefits which can be earned from the speed-up capabilities of quantum computing.

Publisher

MDPI AG

Link

https://www.mdpi.com/2673-9909/3/3/29/pdf

Reference20 articles.

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