标题： 无限系统中模拟算法的精度评估标准：一种基于网络模型的方法 显示英文标题

标题： Precision Evaluation Criteria for Simulation Algorithms in Infinite Systems: A Network Model-Based Approach

摘要： 随着粒子数量的增加，各种模拟算法的计算需求显著上升，同时精度也明显提高。 问题是，这种提高的精度是否会渐近地趋于零，还是在某个有限常数处趋于平稳。 为了解决这个问题，本文提出了一种将无限系统转化为有限节点网络架构的方法，为评估这一问题提供了严格的框架。 通过将蒙特卡洛算法应用于伊辛模型作为案例研究，本文证明了即使模拟扩展到无限晶格尺寸，仍然存在一个基本的误差界限。 本文明确推导了这一误差下限，提供了对算法在无限尺度极限下局限性的定量理解。 此外，我将这种方法扩展到了分子动力学模拟，通过其在电池系统中的应用进行了举例。 这种转换策略不仅突显了该方法的普遍性，还强调了其在指导模拟算法优化方面的实际意义。 此外，它还提供了从宏观数据中估计微观信息的见解。 分子模拟的关键信息，即势能，已被快速估算。 显示英文摘要

摘要： As the particle count escalates, the computational demands of diverse simulation algorithms surge, paralleled by a marked enhancement in accuracy. The question arises whether this heightened precision asymptotically dwindles towards zero or plateaus at a finite constant. To address this, this work introduces an approach that translates infinite systems into finite-node network architectures, providing a rigorous framework for assessing this question. Employing the Monte Carlo algorithm's application to the Ising model as a case study, this paper demonstrate that despite the simulation's extension to an infinite lattice size, a fundamental error bound persists. This work explicitly derive this lower bound on the error, offering a quantitative understanding of the algorithm's limitations in the limit of infinite scale. Furthermore, I extend this methodology to Molecular Dynamics simulations, exemplified through its application to battery systems. This conversion strategy not only underscores the generality of this approach but also highlights its practical significance in guiding the optimization of simulation algorithms. Moreover, it offers insights into estimating micro-level information from macro-level data. The crucial information of Molecular Simulation, namely the potential energy, has been quickly estimated.