Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912195117318144 |
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| author | Setty, Abhishek Abdusalamov, Rasul Motzoi, Felix |
| author_facet | Setty, Abhishek Abdusalamov, Rasul Motzoi, Felix |
| contents | Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear differential equation, system of differential equations, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network (SAPINN) approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order differential equations. The results indicate a promising approach to the near-term evaluation of differential equations on quantum devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09215 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations Setty, Abhishek Abdusalamov, Rasul Motzoi, Felix Quantum Physics Machine Learning Computational Physics Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear differential equation, system of differential equations, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network (SAPINN) approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order differential equations. The results indicate a promising approach to the near-term evaluation of differential equations on quantum devices. |
| title | Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations |
| topic | Quantum Physics Machine Learning Computational Physics |
| url | https://arxiv.org/abs/2312.09215 |