Neural Network Approximation of Graph Fourier Transforms for Sparse Sampling of Networked Flow Dynamics
This addresses the challenge of expensive ubiquitous monitoring in networked infrastructures like water systems, enabling more efficient digital twins, though it is incremental as it builds on existing compression and neural network methods.
The paper tackled the problem of inferring contamination dynamics in water distribution networks from sparse monitoring data by developing Graph Fourier Transform operators to identify essential sampling points and using neural networks to further undersample, achieving high accuracy reconstruction with only 5-10% of the sample set.
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.