Predicting the unobserved: A statistical mechanics framework for non-equilibrium material response with quantified uncertainty
Predicting the unobserved: A statistical mechanics framework for non-equilibrium material response with quantified uncertainty
复制标题
预测未观察到的情况：具有量化不确定性的非平衡材料响应的统计力学框架
DOI：
10.1016/j.jmps.2022.104779
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发表时间：
2022
影响因子：
5.3
通讯作者：
Reina, Celia
中科院分区：
文献类型：
--
作者：
Huang, Shenglin;Graham, Ian R.;Riggleman, Robert A.;Arratia, Paulo E.;Fitzgerald, Steve;Reina, Celia
在任意载荷作用下，远离平衡的材料响应是否可以从平衡数据中推断出来，反之亦然？元素嬗变对力学行为的影响可以预测吗？值得注意的是，由于从路径积分形式主义导出的轨迹的概率密度之间的一组精确关系，这种外推在原则上对于由随机微分方程控制的系统是可能的（Chen和Horing，2007; Nummela和Andricioaei，2007; Kieninger和Keller，2021）。在这篇文章中，我们系统地研究推断（在整体平均值的形式）系统/过程S的基础上系统/过程S的随机轨迹数据，量化的不确定性，直接解决上述问题。有趣的是，这样的推论及其相关的不确定性并不需要S的任何模拟或实验。通过数值模拟的方法，在两个说明性的例子的结果举例说明：一个一维系统作为原型的聚合物和生物大分子，和一个二维的玻璃态系统。原则上，该方法可以被推到极端情况，其中S是简单地由布朗轨迹组成，即平衡非相互作用粒子，而S是远离平衡的复杂相互作用系统。然而，在实践中，对于系统S的固定数量的实现，距离S“越远“S，预测的不确定性就越大。
Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible in principle for systems governed by stochastic differential equations, thanks to a set of exact relations between probability densities for trajectories derived from the path integral formalism (Chen and Horing, 2007; Nummela and Andricioaei, 2007; Kieninger and Keller, 2021). In this article, we systematically investigate inferences (in the form of ensemble-averages) drawn on system/process S based on stochastic trajectory data of system/process S ̃, with quantified uncertainty, to directly address the aforementioned questions. Interestingly, such inferences and their associated uncertainty do not require any simulations or experiments of S. The results are exemplified over two illustrative examples by means of numerical simulations: a one-dimensional system as a prototype for polymers and biological macromolecules, and a two-dimensional glassy system. In principle, the approach can be pushed to the extreme case where S ̃ is simply comprised of Brownian trajectories, ie, equilibrium non-interacting particles, and S is a complex interacting system driven far from equilibrium. In practice, however, the “further” S ̃ is from S, the greater the uncertainty in the predictions, for a fixed number of realizations of system S ̃.