تقرير
Quantum-Inspired Tensor Neural Networks for Partial Differential Equations
| العنوان: | Quantum-Inspired Tensor Neural Networks for Partial Differential Equations |
|---|---|
| المؤلفون: | Patel, Raj, Hsing, Chia-Wei, Sahin, Serkan, Jahromi, Saeed S., Palmer, Samuel, Sharma, Shivam, Michel, Christophe, Porte, Vincent, Abid, Mustafa, Aubert, Stephane, Castellani, Pierre, Lee, Chi-Guhn, Mugel, Samuel, Orus, Roman |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Condensed Matter Physics (Other) Quantum Physics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Condensed Matter - Strongly Correlated Electrons, Computer Science - Artificial Intelligence, Physics - Computational Physics, Quantum Physics |
| الوصف: | Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of dimensionality in new ways. However, deep learning methods are constrained by training time and memory. To tackle these shortcomings, we implement Tensor Neural Networks (TNN), a quantum-inspired neural network architecture that leverages Tensor Network ideas to improve upon deep learning approaches. We demonstrate that TNN provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. We benchmark TNN by applying them to solve parabolic PDEs, specifically the Black-Scholes-Barenblatt equation, widely used in financial pricing theory, empirically showing the advantages of TNN over DNN. Further examples, such as the Hamilton-Jacobi-Bellman equation, are also discussed. Comment: 14 pages, 11 figures, minimal changes |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.02235 |
| رقم الأكسشن: | edsarx.2208.02235 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |