论文标题
在存在嘈杂数据的情况下，由机器学习驱动的分层模型减少
Hierarchical model reduction driven by machine learning for parametric advection-diffusion-reaction problems in the presence of noisy data
论文作者
论文摘要
我们提出了一种新方法，以在存在嘈杂数据的情况下为参数椭圆问题生成可靠的还原模型。根据离线/在线范式，参考模型还原过程是定向HIPOD方法，它结合了层次模型的降低与标准正交分解。在本文中，我们表明，当问题数据受噪声影响时，方向性HIPOD会在准确性方面失去。这是由于插值推动了在线阶段，因为根据定义，它重复了噪声趋势。为了克服此限制，我们用机器学习拟合模型代替了插值，这些模型可以更好地区分数据中无关的非组织噪声中的相关物理特征。数值评估虽然初步，但仍证实了新方法的潜力。
We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.
