A technique for characterising feature size and quality of manifolds
A technique for characterising feature size and quality of manifolds
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DOI：
10.1080/13647830.2021.1931715
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发表时间：
2021-06-03
影响因子：
1.3
通讯作者：
Sutherland, James C.
中科院分区：
文献类型：
--
作者：
Armstrong, Elizabeth;Sutherland, James C.
有效的降维是促进高维动力系统大规模模拟的关键因素。低维代理模型的行为往往依赖于精确的重建量，可以是原始参数的非线性函数。例如，在低维燃烧模型中，代表复杂化学动力学的源项必须在降维空间中准确建模，以便产生准确的预测。诸如感兴趣的量（QoI）中的尖锐梯度或非唯一性的特征可以通过参数化引入并且对重建技术造成困难。许多现有的流形质量评估不考虑这些功能，并限制检查的原始参数和低维嵌入。我们已经开发了一种技术，用于定量评估歧管质量，通过监测方差的变化，在一个不断增加的过滤器宽度的特征尺寸的生活质量。通过在小尺度上的方差的识别，该技术检测不期望的尖锐梯度和非唯一性的QoS。我们的技术不限于特定的还原方法，可以用于比较或评估任意维度的流形参数化。我们证明了我们的技术从模拟和实验的燃烧数据。
Effective dimension reduction is a key factor in facilitating large-scale simulation of high-dimensional dynamical systems. The behaviour of low-dimensional surrogate models often relies on accurate reconstruction of quantities that can be nonlinear functions of the original parameters. For instance, in low-dimensional combustion models, source terms representative of complex chemical kinetics must be modelled accurately in the reduced dimensional space in order to yield accurate predictions. Features such as sharp gradients or non-uniqueness in a quantity of interest (QoI) may be introduced through parameterisation and pose difficulties for reconstruction techniques. Many existing manifold quality assessments do not consider these features and limit examination to the original parameters and low-dimensional embedding. We have developed a technique for quantitatively assessing manifold quality through characterising the feature size of QoIs by monitoring the change in variance over an increasing filter width. Through the identification of variance at small scales, this technique detects undesirable sharp gradients and non-uniqueness of QoIs. Our technique is not limited to a specific reduction method and can be used to compare or assess manifold parameterisations in arbitrary dimensions. We demonstrate our technique on combustion data from both simulation and experiment.