Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910496430489600 |
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| author | Sikorski, Alexander Niknejad, Amir Weber, Marcus Donati, Luca |
| author_facet | Sikorski, Alexander Niknejad, Amir Weber, Marcus Donati, Luca |
| contents | Estimating the rate of rare conformational changes in molecular systems is one of the goals of Molecular Dynamics simulations. In the past decades, a lot of progress has been done in data-based approaches towards this problem. In contrast, model-based methods such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the Projected Rate Estimation (PRE), a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09779 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies Sikorski, Alexander Niknejad, Amir Weber, Marcus Donati, Luca Chemical Physics Estimating the rate of rare conformational changes in molecular systems is one of the goals of Molecular Dynamics simulations. In the past decades, a lot of progress has been done in data-based approaches towards this problem. In contrast, model-based methods such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the Projected Rate Estimation (PRE), a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA. |
| title | Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2311.09779 |