Sampling and inference of networked dynamics using Log-Koopman nonlinear graph fourier transform

Monitoring the networked dynamics via the subset of nodes is essential for a variety of scientific and operational purposes. When there is a lack of an explicit model and networked signal space, traditional observability analysis and non-convex methods are insufficient. Current data-driven Koopman linearization, although derives a linear evolution model for selected vector-valued observable of original state-space, may result in a large sampling set due to: (i) the large size of polynomial based observables (O(N2) , N number of nodes in network), and (ii) not factoring in the nonlinear dependency betweenobservables. In this work, to achieve linear scaling (O(N) ) and a small set of sampling nodes, wepropose to combine a novel Log-Koopman operator and nonlinear Graph Fourier Transform (NL-GFT) scheme. First, the Log-Koopman operator is able to reduce the size of observables by transforming multiplicative poly-observable to logarithm summation. Second, anonlinear GFT concept and sampling theory are provided to exploit the nonlinear dependence of observables for observability analysis using Koopman evolution model. The results demonstrate that the proposed Log-Koopman NL-GFT scheme can (i) linearize unknownnonlinear dynamics using O(N) observables, and (ii) achieve lower number of sampling nodes, compared with the state-of-the art polynomial Koopman based observability analysis

Sampling of time-varying network signals from equation-driven to data-driven techniques

Sampling and recovering the time-varying network signals via the subset of network vertices is essential for a wide range of scientific and engineering purposes. Current studies on sampling a single (continuous) time-series or a static network data, are not suitable for time-varying network signals. This will be even more challenging when there is a lack of explicit dynamic models and signal-space that indicate the time-evolution and vertex dependency. The work begins by bridging the time-domain sampling frequency and the network-domain sampling vertices, via the eigenvalues of the graph Fourier transform (GFT) operator composed by the combined dynamic equations and network topology. Then, for signals with hidden governing mechanisms, we propose a data-driven GFT sampling method using a prior signal-space. We characterize the signal dependency (among vertices) into the graph bandlimited frequency domain, and map such bandlimitedness into optimal sampling vertices. Furthermore, to achieve dynamic model and signal-space independent sensor placement, a Koopman based nonlinear GFT sampling is proposed. A novel data-driven Log-Koopman operator is designed to extract a linearized evolution model using small (M = O(N)) and decoupled observables defined on N original vertices. Then, nonlinear GFT is proposed to derive sampling vertices, by exploiting the inherent nonlinear dependence between M observables (defined on N < M vertices), and the time-evolved information presented by Log-Koopman evolution model. The work also informs the planned future work to formulate an easy-to-use and explainable neural network (NN) based sampling framework, for real-world industrial engineering and applications

Neural network approximation of graph Fourier transform for sparse sampling of networked dynamics

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

Graph layer security: encrypting information via common networked physics

The proliferation of low-cost Internet of Things (IoT) devices has led to a race between wireless security and channel attacks. Traditional cryptography requires high computational power and is not suitable for low-power IoT scenarios. Whilst recently developed physical layer security (PLS) can exploit common wireless channel state information (CSI), its sensitivity to channel estimation makes them vulnerable to attacks. In this work, we exploit an alternative common physics shared between IoT transceivers: the monitored channel-irrelevant physical networked dynamics (e.g., water/oil/gas/electrical signal-flows). Leveraging this, we propose, for the first time, graph layer security (GLS), by exploiting the dependency in physical dynamics among network nodes for information encryption and decryption. A graph Fourier transform (GFT) operator is used to characterise such dependency into a graph-bandlimited subspace, which allows the generation of channel-irrelevant cipher keys by maximising the secrecy rate. We evaluate our GLS against designed active and passive attackers, using IEEE 39-Bus system. Results demonstrate that GLS is not reliant on wireless CSI, and can combat attackers that have partial networked dynamic knowledge (realistic access to full dynamic and critical nodes remains challenging). We believe this novel GLS has widespread applicability in secure health monitoring and for digital twins in adversarial radio environments

Analyzing Granger causality in climate data with time series classification methods

Attribution studies in climate science aim for scientifically ascertaining the influence of climatic variations on natural or anthropogenic factors. Many of those studies adopt the concept of Granger causality to infer statistical cause-effect relationships, while utilizing traditional autoregressive models. In this article, we investigate the potential of state-of-the-art time series classification techniques to enhance causal inference in climate science. We conduct a comparative experimental study of different types of algorithms on a large test suite that comprises a unique collection of datasets from the area of climate-vegetation dynamics. The results indicate that specialized time series classification methods are able to improve existing inference procedures. Substantial differences are observed among the methods that were tested

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book