通过神经网络驱动的重要性采样加速马尔可夫链蒙特卡罗模拟
Accelerated Markov Chain Monte Carlo Simulation via Neural Network-Driven Importance Sampling
AI总结：
该研究提出利用神经网络驱动的重要性采样方法，加速马尔可夫链蒙特卡罗模拟，通过偏置势能和分支随机游走技术提升高维系统的采样效率和准确性。
摘要：
原子级模拟为材料行为的物理过程提供了有价值的见解。然而，其应用从根本上受到暴力模拟可访问的时间尺度的限制。这个瓶颈往往源于复杂的能量景观，其中系统长时间被困在亚稳态中。然而，长期演变由亚稳态之间的过渡控制，这些过渡是罕见事件且难以观察。我们提出了一种重要采样方法，旨在加速马尔可夫链蒙特卡罗（MCMC）模拟的时间尺度。通过使用偏置势能，我们的方法增强了对罕见过渡事件的采样，同时保持不同过渡路径的相对概率。偏置势能由神经网络表示，这为高维系统提供了所需的灵活性。我们提出了一种严谨的公式，以利用从偏置模拟中获得的过渡路径来获得原始亚稳态之间的过渡率。我们进一步使用分支随机游走（BRW）技术来提高效率并减少方差。所提出的方法在二维和14维系统上得到验证，证明了其准确性和可扩展性。
英文摘要：
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This bottleneck often stems from complex energy landscapes where the systems stay trapped in metastable states for long periods of time. Yet, the long-term evolution is controlled by the transitions between the metastable states, which are rare events and difficult to observe. We present an importance sampling method designed to accelerate the time scale of Markov chain Monte Carlo (MCMC) simulations. By employing a bias potential, our approach enhances the sampling of rare transition events while preserving the relative probabilities of distinct transition pathways. The bias potential is represented by a neural network which enables the flexibility needed for high-dimensional systems. We propose a rigorous formulation to obtain the original transition rates between metastable states using transition paths obtained from the biased simulation. We further use a branching random walk (BRW) technique to enhance efficiency and to reduce variance. The proposed methodology is validated on 2-dimensional and 14-dimensional systems, demonstrating its accuracy and scalability.
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