Michael Chertkov

University of Arizona

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Scott Backhaus

National Institute of Standards and Technology

Deepjyoti Deka

Los Alamos National Laboratory

Vladimir Chernyak

Wayne State University

I. V. Kolokolov

Landau Institute for Theoretical Physics

Sidhant Misra

Los Alamos National Laboratory

Marc Vuffray

Los Alamos National Laboratory

ВВ

В. В. Лебедев

National Technical University "Kharkiv Polytechnic Institute"

Mikhail Stepanov

University of Arizona

Konstantin Turitsyn

D. E. Shaw Research

Daniel Livescu

Los Alamos National Laboratory

Cooperative Institutions

Los Alamos National Laboratory

University of Arizona

Los Alamos National Security (United States)

Centre National de la Recherche Scientifique

Landau Institute for Theoretical Physics

Skolkovo Institute of Science and Technology

Russian Academy of Sciences

Applied Mathematics (United States)

Computational Physics (United States)

Massachusetts Institute of Technology

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Topology Learning in Radial Distribution Grids

Elsevier eBooks (2017)

Deepjyoti Deka Michael Chertkov

10.1016/b978-0-12-811968-6.00012-7

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Citations (3)

Learning from power system data stream

Mauro Escobar Daniel Bienstock Michael Chertkov

Assuming access to synchronized stream of Phasor Measurement Unit (PMU) data over a significant portion of a power system interconnect, say controlled by an Independent System Operator (ISO), what can you extract about past, current and future state of the system? We have focused on answering this practical questions pragmatically - empowered with nothing but standard tools of data analysis, such as PCA, filtering and cross-correlation analysis. Quite surprisingly we have found that even during the quiet "no significant events" period this standard set of statistical tools allows the "phasor-detective" to extract from the data important hidden anomalies, such as problematic control loops at loads and wind farms, and mildly malfunctioning assets, such as transformers and generators. We also discuss and sketch future challenges a mature phasor-detective can possibly tackle by adding machine learning and physics modeling sophistication to the basic approach.

Phasor measurement unit

Units of measurement

Sketch

10.1109/ptc.2019.8810950

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Citations (3)

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

Journal of Physics A Mathematical and Theoretical (2013)

Vladimir Chernyak Michael Chertkov Joris Bierkens Hilbert J. Kappen

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi–Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

Stochastic control

Statistical Mechanics

Langevin dynamics

10.1088/1751-8113/47/2/022001

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Citations (16)

Data-Driven Mori-Zwanzig: Approaching a Reduced Order Model for Hypersonic Boundary Layer Transition

arXiv (Cornell University) (2023)

Mark Woodward Yifeng Tian Arvind Mohan Yen Ting Lin Christoph Hader

In this work, we apply, for the first time to spatially inhomogeneous flows, a recently developed data-driven learning algorithm of Mori-Zwanzig (MZ) operators, which is based on a generalized Koopman's description of dynamical systems. The MZ formalism provides a mathematically exact procedure for constructing non-Markovian reduced-order models of resolved variables from high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. The algorithm developed in this work applies Mori's linear projection operator and an SVD based compression to the selection of the resolved variables (equivalently, a low rank approximation of the two time covariance matrices). We show that this MZ decomposition not only identifies the same spatio-temporal structures found by DMD, but it can also be used to extract spatio-temporal structures of the hysteresis effects present in the memory kernels. We perform an analysis of these structures in the context of a laminar-turbulent boundary-layer transition flow over a flared cone at Mach 6, and show the dynamical relevance of the memory kernels. Additionally, by including these memory terms learned in our data-driven MZ approach, we show improvement in prediction accuracy over DMD at the same level of truncation and at a similar computational cost. Furthermore, an analysis of the spatio-temporal structures of the MZ operators shows identifiable structures associated with the nonlinear generation of the so-called "hot" streaks on the surface of the flared code, which have previously been observed in experiments and direct numerical simulations.

Dynamic Mode Decomposition

Operator (biology)

Kernel (algebra)

10.48550/arxiv.2301.07203

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PMD-Induced Fluctuations of Bit-Error Rate in Optical Fiber Systems

Journal of Lightwave Technology (2004)

Vladimir Chernyak Michael Chertkov Ildar R. Gabitov I. V. Kolokolov В. В. Лебедев

This paper presents a method that allows evaluating the performance of an optical fiber system where bit errors result from a complex interplay of spontaneous noise generated in optical amplifiers and birefringent disorder of the transmission fiber. We demonstrate that in the presence of temporal fluctuations of birefringence characteristics, the bit-error rate (BER) itself is insufficient for characterizing system performance. Adequate characterization requires introducing the probability distribution function (PDF) of the BER obtained by averaging over many realizations of birefringent disorder. Our theoretical analysis shows that this PDF has an extended tail indicating the importance of anomalously large values of BER. We present the results of comprehensive analysis of the following issues: 1) The dependence of the PDF tail shape on detection details, such as filtering and regular temporal shift adjustment; 2) the changes in the PDF of BER that occur when the first- or higher order polarization mode dispersion (PMD) compensation techniques are applied; 3) an alternative PMD compensation method capable of providing more efficient suppression of extreme outages.

Amplified spontaneous emission

10.1109/jlt.2004.825237

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Citations (22)

Reducing the Error Floor

arXiv (Cornell University) (2007)

Michael Chertkov

We discuss how the loop calculus approach of [Chertkov, Chernyak '06], enhanced by the pseudo-codeword search algorithm of [Chertkov, Stepanov '06] and the facet-guessing idea from [Dimakis, Wainwright '06], improves decoding of graph based codes in the error-floor domain. The utility of the new, Linear Programming based, decoding is demonstrated via analysis and simulations of the model $[155,64,20]$ code.

Code (set theory)

Wainwright

Source

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Linear PDEs and eigenvalue problems corresponding to ergodic stochastic optimization problems on compact manifolds

arXiv (Cornell University) (2013)

Joris Bierkens Vladimir Chernyak Michael Chertkov Hilbert J. Kappen

We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the metric induced by the noise. The long term stochastic dynamics on the manifold will be completely characterized by the long term density $\rho$ and the long term current density $J$. As such, control problems may be reformulated as variational problems over $\rho$ and $J$. We discuss several optimization problems: the problem in which both $\rho$ and $J$ are varied freely, the problem in which $\rho$ is fixed and the one in which $J$ is fixed. These problems lead to different kinds of operator problems: linear PDEs in the first two cases and a nonlinear PDE in the latter case. These results are obtained through through variational principle using infinite dimensional Lagrange multipliers. In the case where the initial dynamics are reversible we obtain the result that the optimally controlled diffusion is also symmetrizable. The particular case of constraining the dynamics to be reversible of the optimally controlled process leads to a linear eigenvalue problem for the square root of the density process.

Variational principle

10.48550/arxiv.1303.0126

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Citations (2)

Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems

arXiv (Cornell University) (2021)

Laurent Pagnier Michael Chertkov

Parameter Estimation (PE) and State Estimation (SE) are the most wide-spread tasks in the system engineering. They need to be done automatically, fast and frequently, as measurements arrive. Deep Learning (DL) holds the promise of tackling the challenge, however in so far, as PE and SE in power systems is concerned, (a) DL did not win trust of the system operators because of the lack of the physics of electricity based, interpretations and (b) DL remained illusive in the operational regimes were data is scarce. To address this, we present a hybrid scheme which embeds physics modeling of power systems into Graphical Neural Networks (GNN), therefore empowering system operators with a reliable and explainable real-time predictions which can then be used to control the critical infrastructure. To enable progress towards trustworthy DL for PE and SE, we build a physics-informed method, named Power-GNN, which reconstructs physical, thus interpretable, parameters within Effective Power Flow (EPF) models, such as admittances of effective power lines, and NN parameters, representing implicitly unobserved elements of the system. In our experiments, we test the Power-GNN on different realistic power networks, including these with thousands of loads and hundreds of generators. We show that the Power-GNN outperforms vanilla NN scheme unaware of the EPF physics.

Trustworthiness

10.48550/arxiv.2102.06349

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Pseudo-codeword Landscape

Michael Chertkov Mikhail Stepanov

We discuss the performance of low-density-parity-check (LDPC) codes decoded by means of linear programming (LP) at moderate and large signal-to-noise-ratios (SNR). Utilizing a combination of the previously introduced pseudo-codeword-search method and a new "dendro" trick, which allows us to reduce the complexity of the LP decoding, we analyze the dependence of the frame-error-rate (FER) on the SNR. Under maximum-a-posteriori (MAP) decoding the dendro-code, having only checks with connectivity degree three, performs identically to its original code with high-connectivity checks. For a number of popular LDPC codes performing over the additive-white-Gaussian-noise (AWGN) channel we found that either an error-floor sets at a relatively low SNR, or otherwise a transient asymptote, characterized by a faster decay of FER with the SNR increase, precedes the error-floor asymptote. We explain these regimes in terms of the pseudo-codeword spectra of the codes.

Asymptote

Code (set theory)

Parity bit

10.1109/isit.2007.4557442

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Citations (39)

Options for Control of Reactive Power by Distributed Photovoltaic Generators

Proceedings of the IEEE (2011)

Konstantin Turitsyn Petr Šulc Scott Backhaus Michael Chertkov

High-penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit present several challenges and opportunities for distribution utilities. Rapidly varying irradiance conditions may cause voltage sags and swells that cannot be compensated by slowly responding utility equipment resulting in a degradation of power quality. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g., by minimizing thermal losses. We discuss and compare via simulation various design options for control systems to manage the reactive power generated by these inverters. An important design decision that weighs on the speed and quality of communication required is whether the control should be centralized or distributed (i.e., local). In general, we find that local control schemes are able to maintain voltage within acceptable bounds. We consider the benefits of choosing different local variables on which to control and how the control system can be continuously tuned between robust voltage control, suitable for daytime operation when circuit conditions can change rapidly, and loss minimization better suited for nighttime operation.

10.1109/jproc.2011.2116750

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Citations (733)