Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics
Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics
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DOI：
10.1145/3461838
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发表时间：
2021-09
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影响因子：
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通讯作者：
Alessio Pagani;Zhuangkun Wei;Ricardo Silva;Weisi Guo
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作者：
Alessio Pagani;Zhuangkun Wei;Ricardo Silva;Weisi Guo
基础设施监控对于安全运营和可持续性至关重要。与许多网络化系统一样，给水管网既具有图形拓扑结构，又具有复杂的嵌入流动动力学。在没有大量传感器数据的情况下，很难预测由此产生的网络级联动力学。然而，无处不在的传感器监测在地下环境中是昂贵的，而一个关键的挑战是从部分稀疏的监测数据中推断污染物的动态。现有的方法使用多目标优化来寻找最小的基本监测点集合，但缺乏性能保证和理论框架。在这里，我们首先开发了一种新的图形傅立叶变换(GFT)算子来压缩网络污染动力学，在保证推理性能的情况下识别关键的主要数据采集点。因此，GFT方法提供了理论抽样范围。然后，我们通过构建自动编码器(AE)神经网络(NN)来概括GFT采样过程，并从初始采样集进一步进行欠采样，从而实现欠采样性能，允许非常小的数据点集合在很大程度上重建真实和人工WDN上的污染动态。对各种污染源进行了测试，对于已知污染源，我们使用了大约5%-10%的网络节点进行了高精度重建，对于未知源情况，我们使用了50%-75%的网络节点，虽然比污染物检测和来源识别方案的重建精度要大，但比目前的污染物数据恢复采样方案要小。这种通过神经网络进行压缩和欠采样恢复的通用方法可以应用于广泛的网络基础设施，以实现数字双胞胎的有效数据采样。
Infrastructure monitoring is critical for safe operations and sustainability. Like many networked systems, water distribution networks (WDNs) exhibit both graph topological structure and complex embedded flow dynamics. The resulting networked cascade dynamics are difficult to predict without extensive sensor data. However, ubiquitous sensor monitoring in underground situations is expensive, and a key challenge is to infer the contaminant dynamics from partial sparse monitoring data. Existing approaches use multi-objective optimization to find the minimum set of essential monitoring points but lack performance guarantees and a theoretical framework. Here, we first develop a novel Graph Fourier Transform (GFT) operator to compress networked contamination dynamics to identify the essential principal data collection points with inference performance guarantees. As such, the GFT approach provides the theoretical sampling bound. We then achieve under-sampling performance by building auto-encoder (AE) neural networks (NN) to generalize the GFT sampling process and under-sample further from the initial sampling set, allowing a very small set of data points to largely reconstruct the contamination dynamics over real and artificial WDNs. Various sources of the contamination are tested, and we obtain high accuracy reconstruction using around 5%–10% of the network nodes for known contaminant sources, and 50%–75% for unknown source cases, which although larger than that of the schemes for contaminant detection and source identifications, is smaller than the current sampling schemes for contaminant data recovery. This general approach of compression and under-sampled recovery via NN can be applied to a wide range of networked infrastructures to enable efficient data sampling for digital twins.