Neural Network Approximation of Graph Fourier Transforms for Sparse Sampling of Networked Flow Dynamics

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.

Graph Input Representations for Machine Learning Applications in Urban Network Analysis

Understanding and learning the characteristics of network paths has been of particular interest for decades and has led to several successful applications. Such analysis becomes challenging for urban networks as their size and complexity are significantly higher compared to other networks. The state-of-the-art machine learning (ML) techniques allow us to detect hidden patterns and, thus, infer the features associated with them. However, very little is known about the impact on the performance of such predictive models by the use of different input representations. In this paper, we design and evaluate six different graph input representations (i.e., representations of the network paths), by considering the network's topological and temporal characteristics, for being used as inputs for machine learning models to learn the behavior of urban networks paths. The representations are validated and then tested with a real-world taxi journeys dataset predicting the tips using a road network of New York. Our results demonstrate that the input representations that use temporal information help the model to achieve the highest accuracy (RMSE of 1.42$).