arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2103.07405stat.MLcs.LGstat.ME
收藏

基于概率数字孪生模型的最优序贯决策

Optimal sequential decision making with probabilistic digital twins

DNV;University of Oslo(奥斯陆大学)

Christian Agrell, Kristina Rognlien Dahl, Andreas Hafver

摘要:

数字孪生模型正在许多行业中出现,通常由与特定物理系统相关的仿真模型和数据组成。开发数字孪生模型的主要原因之一是能够模拟给定行为的可能后果,而不需要干扰物理系统本身。感兴趣的物理系统及其运行环境并不总是确定性的。此外,关于系统及其环境的信息通常是不完整或不完善的。因此,可能需要系统和环境的概率表示,特别是为了支持行动可能产生严重后果的应用领域的决策。在本文中,我们介绍了概率数字孪生(PDT)。我们将开始讨论如何认识的不确定性可以使用测量理论,通过建模认识信息通过$σ$ -代数。在此基础上,我们给出了一个形式化的定义,如何认知不确定性可以更新的PDT。然后,我们研究了最优序贯决策问题。也就是说,我们考虑的情况下,每一个决定的结果可能会通知下一个。在PDT框架内,我们制定这个优化问题。我们讨论如何解决这个问题(至少在理论上)通过最大值原理方法或动态规划原理。然而,由于维数灾难,这些方法在实践中往往不容易处理。为了弥补这一点,我们提出了一个通用的近似解决方案,使用深度强化学习和定义在集合上的神经网络。我们在一个实际问题上说明了该方法,考虑了用于估计故障概率的最佳信息收集。

英文摘要:

Digital twins are emerging in many industries, typically consisting of simulation models and data associated with a specific physical system. One of the main reasons for developing a digital twin, is to enable the simulation of possible consequences of a given action, without the need to interfere with the physical system itself. Physical systems of interest, and the environments they operate in, do not always behave deterministically. Moreover, information about the system and its environment is typically incomplete or imperfect. Probabilistic representations of systems and environments may therefore be called for, especially to support decisions in application areas where actions may have severe consequences. In this paper we introduce the probabilistic digital twin (PDT). We will start by discussing how epistemic uncertainty can be treated using measure theory, by modelling epistemic information via $σ$-algebras. Based on this, we give a formal definition of how epistemic uncertainty can be updated in a PDT. We then study the problem of optimal sequential decision making. That is, we consider the case where the outcome of each decision may inform the next. Within the PDT framework, we formulate this optimization problem. We discuss how this problem may be solved (at least in theory) via the maximum principle method or the dynamic programming principle. However, due to the curse of dimensionality, these methods are often not tractable in practice. To mend this, we propose a generic approximate solution using deep reinforcement learning together with neural networks defined on sets. We illustrate the method on a practical problem, considering optimal information gathering for the estimation of a failure probability.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑