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Model Structural Inference Using Local Dynamic Operators
International Journal for Uncertainty Quantification ( IF 1.5 ) Pub Date : 2019-01-01 , DOI: 10.1615/int.j.uncertaintyquantification.2019025828
Anthony M. DeGennaro , Nathan M. Urban , Balasubramanya T. Nadiga , Terry Haut

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification (UQ), in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity-of-interest (QOI) from some empirical dataset. Specifically, we: (1) define a discrete, local representation of the structure of a partial differential equation, which we refer to as the "local dynamical operator" (LDO); (2) identify model structure non-intrusively from numerical code output; (3) non-intrusively construct a reduced order model (ROM) of the numerical model through POD-DEIM-Galerkin projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water (RSW) equations as an example system.

中文翻译:

使用局部动态算子的模型结构推理

本文重点讨论在时间演化动力系统的背景下量化模型结构不确定性影响的问题。这是由计算机物理模拟中的多模型不确定性引起的:开发人员经常在数值近似和过程简化中做出不同的建模选择,导致表面上代表相同潜在动力学的不同数值代码。我们认为模型结构推理是一种两步法:第一步是对可以观察到完整状态的数字代码进行系统识别;第二步是结构不确定性量化 (UQ),其目标是搜索“接近”数字代码代理的候选模型,以寻找与某些经验数据集中的感兴趣数量 (QOI) 最匹配的模型。具体来说,我们: (1) 定义偏微分方程结构的离散局部表示,我们将其称为“局部动力学算子”(LDO);(2) 从数字代码输出中非侵入式地识别模型结构;(3)通过POD-DEIM-Galerkin投影非侵入式构建数值模型的降阶模型(ROM);(4) 扰动 ROM 动力学以近似替代模型结构的行为;(5) 应用贝叶斯推理和能量守恒定律来将 LDO 校准到给定的 QOI。我们使用二维旋转浅水 (RSW) 方程作为示例系统来演示这些技术。(2) 从数字代码输出中非侵入式地识别模型结构;(3)通过POD-DEIM-Galerkin投影非侵入式构建数值模型的降阶模型(ROM);(4) 扰动 ROM 动力学以近似替代模型结构的行为;(5) 应用贝叶斯推理和能量守恒定律来将 LDO 校准到给定的 QOI。我们使用二维旋转浅水 (RSW) 方程作为示例系统来演示这些技术。(2) 从数字代码输出中非侵入式地识别模型结构;(3)通过POD-DEIM-Galerkin投影非侵入式构建数值模型的降阶模型(ROM);(4) 扰动 ROM 动力学以近似替代模型结构的行为;(5) 应用贝叶斯推理和能量守恒定律来将 LDO 校准到给定的 QOI。我们使用二维旋转浅水 (RSW) 方程作为示例系统来演示这些技术。(5) 应用贝叶斯推理和能量守恒定律来将 LDO 校准到给定的 QOI。我们使用二维旋转浅水 (RSW) 方程作为示例系统来演示这些技术。(5) 应用贝叶斯推理和能量守恒定律来将 LDO 校准到给定的 QOI。我们使用二维旋转浅水 (RSW) 方程作为示例系统来演示这些技术。
更新日期:2019-01-01
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