Harish Doddi

Harish Doddi, Saurav Talukdar, Deepjyoti Deka et al.

Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for reconstruction of the topology of a network of cyclostationary processes. To the best of our knowledge, this is the first work to guarantee exact recovery without any assumptions on the underlying structure. The method is based on a lifting technique by which cyclostationary processes are mapped to vector wide sense stationary processes and further on semi-definite properties of matrix Wiener filters for the said processes.We demonstrate the performance of the proposed algorithm on a Resistor-Capacitor network and present the accuracy of reconstruction for varying sample sizes.

Harish Doddi, Deepjyoti Deka, Saurav Talukdar et al.

We consider a networked linear dynamical system with $p$ agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval $T$. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval $T$ consists of $n$ i.i.d. observation windows of length $T/n$ (restart and record), and (b) where $T$ is one continuous observation window (consecutive). Using the theory of $M$-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size $p$. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems \emph{driven by unobserved not-white wide-sense stationary (WSS) inputs}.

Harish Doddi, Deepjyoti Deka, Murti Salapaka

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on dynamical systems excited by temporally uncorrelated processes. In this article, we present a novel algorithm for guaranteed topology learning of networks that are excited by temporally (colored) cyclostationary processes, which encompasses a wide range of temporal correlation including wide-sense stationarity. Furthermore, unlike prior work, the framework applies to linear dynamic system with complex valued dependencies, and leverages group lasso regularization for effective learning of the network structure. In the second part of the article, we analyze conditions for consistent topology learning for bidirected tree networks when a subset of the network is unobserved. Here, the full topology along with unobserved nodes are recovered from observed node's time-series alone. Our theoretical contributions are validated on simulated data as well as on real-world climate data.

Deepjyoti Deka, Harish Doddi, Sidhant Misra et al.

Estimating the structure of physical flow networks such as power grids is critical to secure delivery of energy. This paper discusses statistical structure estimation in power grids in the "under-excited" regime, where a subset of internal nodes do not have external injection. Prior estimation algorithms based on nodal potentials or voltages fail in the under-excited regime. We propose a novel topology learning algorithm for learning underexcited general (non-radial) networks based on physics-informed conservation laws. We prove the asymptotic correctness of our algorithm for grids with non-adjacent under-excited internal nodes. More importantly, we theoretically analyze our algorithm's efficacy under noisy measurements, and determine bounds on maximum noise under which asymptotically correct recovery is guaranteed. Our approach is validated through simulations with non-linear voltage samples generated on test grids with real injection data

Saurav Talukdar, Deepjyoti Deka, Harish Doddi et al.

Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies are considered. An algorithm for the reconstruction of the topology of interaction based on multivariate Wiener filtering is analyzed. It is shown that for a vast and important class of interactions, that respect flow conservation, the topology of the interactions can be exactly recovered. The class of problems where reconstruction is guaranteed to be exact includes power distribution networks, dynamic thermal networks and consensus networks. The efficacy of the approach is illustrated through simulation and experiments on consensus networks, IEEE power distribution networks and thermal dynamics of buildings.

Harish Doddi, Saurav Talukdar, Deepjyoti Deka et al.

System identification of smart buildings is necessary for their optimal control and application in demand response. The thermal response of a building around an operating point can be modeled using a network of interconnected resistors with capacitors at each node/zone called RC network. The development of the RC network involves two phases: obtaining the network topology, and estimating thermal resistances and capacitance's. In this article, we present a provable method to reconstruct the interaction topology of thermal zones of a building solely from temperature measurements. We demonstrate that our learning algorithm accurately reconstructs the interaction topology for a $5$ zone office building in EnergyPlus with real-world conditions. We show that our learning algorithm is able to recover the network structure in scenarios where prior research prove insufficient.