论文标题
图形傅立叶变换的神经网络近似,用于网络流动动力学的稀疏采样
Neural Network Approximation of Graph Fourier Transforms for Sparse Sampling of Networked Flow Dynamics
论文作者
论文摘要
基础设施监控对于安全运营和可持续性至关重要。水分配网络(WDN)是具有复杂级联动力学的大规模网络关键系统,难以预测。无处不在的监视是昂贵的,关键的挑战是从部分稀疏监测数据中推断污染物动力学。现有方法使用多目标优化来找到最小的基本监视点集,但缺乏性能保证和理论框架。 在这里,我们首先开发图形傅立叶变换(GFT)运算符,以压缩网络污染扩展动态,以识别具有推理性能保证的基本原理数据收集点。然后,我们构建了自动编码器(AE)启发的神经网络(NN),以概括GFT采样过程,并从初始采样集中进一步样本,从而允许一小部分数据点,以在很大程度上重建污染动力学而不是真实和人工WDN。测试了污染的各种来源,我们使用大约5-10%的样品集获得了高精度重建。这种通过神经网络的压缩和采样不足的恢复的通用方法可以应用于广泛的网络基础架构以实现数字双胞胎。
Infrastructure monitoring is critical for safe operations and sustainability. Water distribution networks (WDNs) are large-scale networked critical systems with complex cascade dynamics which are difficult to predict. Ubiquitous monitoring is expensive and a key challenge is to infer the contaminant dynamics from partial sparse monitoring data. Existing approaches use multi-objective optimisation to find the minimum set of essential monitoring points, but lack performance guarantees and a theoretical framework. Here, we first develop Graph Fourier Transform (GFT) operators to compress networked contamination spreading dynamics to identify the essential principle data collection points with inference performance guarantees. We then build autoencoder (AE) inspired 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 sample set. This general approach of compression and under-sampled recovery via neural networks can be applied to a wide range of networked infrastructures to enable digital twins.