Tensor-SqRA：基于势能建模相互作用分子系统的跃迁速率
Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies
AI总结：
针对分子系统罕见构象变化速率估计问题，提出融合SqRA与耦合系统张量结构的tSqRA方法，还开发了混合式PRE算法，并探究了低秩近似的整合可能。
摘要：
估计分子系统中罕见构象变化的速率是分子动力学模拟的目标之一。在过去几十年中，针对这一问题的基于数据的方法取得了诸多进展。与之不同，诸如平方根近似（Square Root Approximation, SqRA）等基于模型的方法可直接从势能函数推导这些物理量。本文论证了SqRA形式体系如何与多系统耦合得到的张量结构自然融合，由此产生基于张量的平方根近似（tSqRA）。该方法可利用SqRA高效处理高维系统，并给出分子子系统间耦合能影响的代数表达式。基于tSqRA，我们还开发了投影速率估计（Projected Rate Estimation, PRE）——一种混合数据与模型的算法，可高效估计耦合系统的最慢速率。此外，我们探究了在该框架内整合低秩近似的可能性，以最大化发挥tSqRA的潜力。
英文摘要：
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.
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