Non-Equilibrium Dynamics of Hybrid Continuous-Discrete Ground-State Sampling
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914997662121984 |
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| author | Leleu, Timothée Reifenstein, Samuel |
| author_facet | Leleu, Timothée Reifenstein, Samuel |
| contents | We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings steps to combine search dynamics with and without detailed balance. Our purpose is to study the non-equilibrium dynamics that leads to the ground state of rugged energy landscapes in this general setting. Our results show that MH-driven dynamics reach ``easy'' ground states faster, indicating a stronger bias in the non-equilibrium dynamics of the algorithm with reversible transition probabilities. To validate this, we construct a set of Ising problem instances with a controllable bias in the energy landscape that makes one degenerate solution more accessible than another. The constructed hybrid algorithm demonstrates significant improvements in convergence and ground-state sampling accuracy, achieving a 100x speedup on GPUs compared to simulated annealing, making it well-suited for large-scale applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Equilibrium Dynamics of Hybrid Continuous-Discrete Ground-State Sampling Leleu, Timothée Reifenstein, Samuel Statistical Mechanics Adaptation and Self-Organizing Systems We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings steps to combine search dynamics with and without detailed balance. Our purpose is to study the non-equilibrium dynamics that leads to the ground state of rugged energy landscapes in this general setting. Our results show that MH-driven dynamics reach ``easy'' ground states faster, indicating a stronger bias in the non-equilibrium dynamics of the algorithm with reversible transition probabilities. To validate this, we construct a set of Ising problem instances with a controllable bias in the energy landscape that makes one degenerate solution more accessible than another. The constructed hybrid algorithm demonstrates significant improvements in convergence and ground-state sampling accuracy, achieving a 100x speedup on GPUs compared to simulated annealing, making it well-suited for large-scale applications. |
| title | Non-Equilibrium Dynamics of Hybrid Continuous-Discrete Ground-State Sampling |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2410.22625 |