Lagrangian large eddy simulations via physics-informed machine learning.

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale.

Statistical mechanics of thermostatically controlled multizone buildings.

We study the collective phenomena and constraints associated with the aggregation of individual cooling units from a statistical mechanics perspective. These units are modeled as thermostatically controlled loads (TCLs) and represent zones in a large commercial or residential building. Their energy input is centralized and controlled by a collective unit-the air handling unit (AHU)-delivering cool air to all TCLs, thereby coupling them together.

Prediction and prevention of pandemics via graphical model inference and convex programming.

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g.

Which Neural Network to Choose for Post-Fault Localization, Dynamic State Estimation, and Optimal Measurement Placement in Power Systems?

We consider a power transmission system monitored using phasor measurement units (PMUs) placed at significant, but not all, nodes of the system. Assuming that a sufficient number of distinct single-line faults, specifically the pre-fault state and the (not cleared) post-fault state, are recorded by the PMUs and are available for training, we first design a comprehensive sequence of neural networks (NNs) locating the faulty line. Performance of different NNs in the sequence, including linear regression, feed-forward NNs, AlexNet, graph convolutional NNs, neural linear ordinary differential equations (ODEs) and neural graph-based ODEs, ordered according to the type and amount of the power flow physics involved, are compared for different levels of observability.

Mean-field control for efficient mixing of energy loads.

We pose an engineering challenge of controlling an ensemble of energy devices via coordinated, implementation-light, and randomized on/off switching as a problem in nonequilibrium statistical mechanics. We show that mean-field control with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the demand response regime, i.e.