Learning Quantities of Interest from dynamical systems for observation-consistent inversion
Learning Quantities of Interest from dynamical systems for observation-consistent inversion
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DOI：
10.1016/j.cma.2021.114230
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发表时间：
2021-11-12
影响因子：
7.2
通讯作者：
Estep, D.
中科院分区：
文献类型：
--
作者：
Mattis, S. A.;Steffen, K. R.;Estep, D.
动力系统出现在物理、工程、生命和社会科学的各种数学模型中。一个常见的挑战是量化模型输入（即参数）上的不确定性，这些不确定性对应于可观察的兴趣量（QoI）上的不确定性的定量表征。为此，我们考虑一个随机逆问题（SIP），其解由回拉概率测度描述。这被称为观察一致的解决方案，因为它通过qi映射的后续推进与模型输出上观察到的概率分布相匹配。在用于解决SIP和任意模型输出数据的qi之间进行了区分。在动力系统中，模型输出数据通常是在特定时间窗口内记录的一系列状态变量响应。因此，由于观察的频率，输出数据的维度很容易超过0 （1E4）或更多，并且从该数据中正确选择或构建qi并不是不言而喻的。我们提出了一个新的框架，学习不确定量（LUQ），促进了动态系统sip的可处理解。给定预测（模拟）时间序列和（噪声）观测数据的集合，LUQ提供了过滤数据、以无监督的方式学习底层动态、对观测值进行分类以及执行特征提取以学习qos映射的例程。随后，时间序列数据被转换为来自与qi相关的底层预测和观察分布的样本，以便SIP的解决方案是可计算的。在LUQ的介绍和演示之后，给出了生命科学和物理科学中出现的各种动力系统的几个sip的数值结果。为了科学的可重复性，我们提供了LUQ的Python实现的链接，以及复制本文中结果所需的所有数据和脚本。(C) 2021 Elsevier B.V.版权所有
Dynamical systems arise in a wide variety of mathematical models from the physical, engineering, life, and social sciences. A common challenge is to quantify uncertainties on model inputs (i.e., parameters) that correspond to a quantitative characterization of uncertainties on observable Quantities of Interest (QoI). To this end, we consider a stochastic inverse problem (SIP) with a solution described by a pullback probability measure. This is referred to as an observation-consistent solution since its subsequent push-forward through the QoI map matches the observed probability distribution on model outputs. A distinction is made between QoI useful for solving the SIP and arbitrary model output data. In dynamical systems, model output data are often given as a series of state variable responses recorded over a particular time window. Consequently, the dimension of output data can easily exceed O(1E4) or more due to the frequency of observations, and the correct choice or construction of a QoI from this data is not self-evident. We present a new framework, Learning Uncertain Quantities (LUQ), that facilitates the tractable solution of SIPs for dynamical systems. Given ensembles of predicted (simulated) time series and (noisy) observed data, LUQ provides routines for filtering data, learning the underlying dynamics in an unsupervised manner, classifying the observations, and performing feature extraction to learn the QoI map. Subsequently, time series data are transformed into samples coming from the underlying predicted and observed distributions associated with the QoI so that solutions to the SIP are computable. Following the introduction and demonstration of LUQ, numerical results from several SIPs are presented for a variety of dynamical systems arising in the life and physical sciences. In the interest of scientific reproducibility, we provide links to our Python implementation of LUQ, as well as all data and scripts required to reproduce the results in this manuscript. (C) 2021 Elsevier B.V. All rights reserved.