Yadav, S (2023) QPDE: Quantum Neural Network Based Stabilization Parameter Prediction for Numerical Solvers for Partial Differential Equations. In: AppliedMath, 3 . pp. 552-562.
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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. © 2023 by the author.
| Item Type: | Journal Article |
|---|---|
| Publication: | AppliedMath |
| Publisher: | Multidisciplinary Digital Publishing Institute (MDPI) |
| Additional Information: | The copyright for this article belongs to author. |
| Department/Centre: | Division of Interdisciplinary Sciences > Computational and Data Sciences |
| Date Deposited: | 19 Sep 2024 07:16 |
| Last Modified: | 19 Sep 2024 07:16 |
| URI: | http://eprints.iisc.ac.in/id/eprint/86101 |
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