Title: Uncertainty in AI-driven Monte Carlo simulations Show Chinese title

Title: 人工智能驱动的蒙特卡洛模拟中的不确定性

Abstract: In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can become computationally expensive. To accelerate these simulations, deep learning models are increasingly employed as surrogate functions to approximate the energy landscape or force fields. However, such models introduce epistemic uncertainty in their predictions, which may propagate through the sampling process and affect the system's macroscopic behavior. In our work, we present the Penalty Ensemble Method (PEM) to quantify epistemic uncertainty and mitigate its impact on Monte Carlo sampling. Our approach introduces an uncertainty-aware modification of the Metropolis acceptance rule, which increases the rejection probability in regions of high uncertainty, thereby enhancing the reliability of the simulation outcomes. Show Chinese abstract

Abstract: 在复杂系统的研究中，评估物理可观测量通常需要通过蒙特卡洛技术采样代表性构型。 这些方法依赖于对系统能量和力场的重复评估，这可能会变得计算昂贵。 为了加速这些模拟，深度学习模型被越来越多地用作代理函数，以近似能量景观或力场。 然而，这样的模型在其预测中引入了认识性不确定性，这可能在采样过程中传播，并影响系统的宏观行为。 在我们的工作中，我们提出了惩罚集合方法（PEM）来量化认识性不确定性并减轻其对蒙特卡洛采样的影响。 我们的方法引入了一种考虑不确定性的马尔可夫链蒙特卡洛接受规则的修改，在高不确定性区域增加了拒绝概率，从而提高了模拟结果的可靠性。