Annealing-based approach to solving partial differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918488687247360 |
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| author | Kudo, Kazue |
| author_facet | Kudo, Kazue |
| contents | Solving partial differential equations (PDEs) using an annealing-based approach involves solving generalized eigenvalue problems. Discretizing a PDE yields a system of linear equations (SLE). Solving an SLE can be formulated as a general eigenvalue problem, which can be transformed into an optimization problem with an objective function given by a generalized Rayleigh quotient. The proposed algorithm requires iterative computations. However, it enables efficient annealing-based computation of eigenvectors to arbitrary precision without increasing the number of variables. Investigations using simulated annealing demonstrate how the number of iterations scales with system size and annealing time. Computational performance depends on system size, annealing time, and problem characteristics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_17364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Annealing-based approach to solving partial differential equations Kudo, Kazue Numerical Analysis Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics Solving partial differential equations (PDEs) using an annealing-based approach involves solving generalized eigenvalue problems. Discretizing a PDE yields a system of linear equations (SLE). Solving an SLE can be formulated as a general eigenvalue problem, which can be transformed into an optimization problem with an objective function given by a generalized Rayleigh quotient. The proposed algorithm requires iterative computations. However, it enables efficient annealing-based computation of eigenvectors to arbitrary precision without increasing the number of variables. Investigations using simulated annealing demonstrate how the number of iterations scales with system size and annealing time. Computational performance depends on system size, annealing time, and problem characteristics. |
| title | Annealing-based approach to solving partial differential equations |
| topic | Numerical Analysis Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2406.17364 |