highlight
• 提出了一种基于机器学习方法的参数化非侵入式ROM。
• P-NIROM为城市空气污染预测和控制提供了快速工具。
• P-NIROM强大而有效地表示任何参数化的PDE。
• 应用于不同排放强度污染物的模拟。
• CPU成本降低了几个数量级，同时精度仍然存在。
抽象
首次开发了基于正交分解（POD）和机器学习方法的参数化非侵入式降阶模型（P-NIROM），用于污染物运移方程的模型简化。我们的动机是提供快速响应的城市空气污染预测和控制。P-NIROM中的变化参数是污染源。训练数据集是从参考空间上所选参数（此处为污染源）的高保真度建模解决方案（称为快照）获得的[RP。从这些训练数据集中，机器学习方法用于生成减少的解决方案和输入（污染源）之间的关系[RP。此外，构造与每个POD基函数相关联的一组超表面函数，用于表示在减小的空间上的流体动力学。P-NIROM的准确性高度依赖于训练集的质量，这里从高保真模型中获得。在现有的机器学习方法中，这里提出的P-NIROM算法具有以下优点：（1）它与NIROM相结合，从而提供快速，合理准确的解决方案; （2）当模型参数/输入变化时，它是用于表示任何参数化偏微分方程的稳健且有效的方法。在这项研究中，我们展示了如何为污染物运输方程实施P-NIROM的方式（但不限于其稳健性）。它的预测能力在中国大区域的电厂羽流的三维（3-D）模拟中得到了说明，其中变化的参数是三个位置的发射强度。结果表明，与高保真度模型相比，CPU成本降低了五个数量级，同时保持了合理的精度。
关键词
机器学习有限元正确的正交分解减少订单建模空气污染
@article{XIAO2018,
title = "Machine learning-based rapid response tools for regional air pollution modelling",
journal = "Atmospheric Environment",
year = "2018",
issn = "1352-2310",
doi = "https://doi.org/10.1016/j.atmosenv.2018.11.051",
url = "http://www.sciencedirect.com/science/article/pii/S1352231018308318",
author = "D. Xiao and F. Fang and J. Zheng and C.C. Pain and I.M. Navon",
keywords = "Machine learning, Finite element, Proper orthogonal decomposition, Reduced order modelling, Air pollution",
abstract = "A parameterised non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) and machine learning methods has been firstly developed for model reduction of pollutant transport equations. Our motivation is to provide rapid response urban air pollution predictions and controls. The varying parameters in the P-NIROM are pollutant sources. The training data sets are obtained from the high fidelity modelling solutions (called snapshots) for selected parameters (pollutant sources, here) over the parameter space RP. From these training data sets, the machine learning method is used to generate the relationship between the reduced solutions and inputs (pollutant sources) over RP. Furthermore a set of hyper-surface functions associated with each POD basis function is constructed for representing the fluid dynamics over the reduced space. The accuracy of the P-NIROM is highly dependent on the quality of the training set, here obtained from the high fidelity model. Over existing machine learning methods, the P-NIROM algorithm proposed here has the advantages that (1) it is combined with NIROM, thus providing rapid and reasonably accurate solutions; and (2) it is a robust and efficient approach for representation of any parametrised partial differential equations as the model parameters/inputs vary. In this study, we demonstrate the way how to implement the P-NIROM for the pollutant transport equation (but not limited to due to its robustness). Its predictive capability is illustrated in a three-dimensional (3-D) simulation of power plant plumes over a large region in China, where the varying parameters are the emission intensity at three locations. Results indicate that in comparison to the high fidelity model, the CPU cost is reduced by factor up to five orders of magnitude while reasonable accuracy remains."
}
