Publications (54)
Maximum Throughput Problem in Dissipative Flow Networks with Application to Natural Gas Systems
Sidhant Misra, Marc Vuffray, Michael Chertkov
We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. W…
Finite Sample Bounds for Learning with Score Matching
Devin Smedira, Abhijith Jayakumar, Sidhant Misra +2
Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high-dimensional statistics…
Quantum Algorithm Implementations for Beginners
Abhijith J., Adetokunbo Adedoyin, John Ambrosiano +31
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer prog…
Bounds states of the Schrödinger-Newton model in low dimensions
Joachim Stubbe, Marc Vuffray
We prove the existence of quasi-stationary symmetric solutions with exactly n>=0 zeros and uniqueness for n=0 for the Schrödinger-Newton model in one dimension and in two dimensio…
The Impacts of Convex Piecewise Linear Cost Formulations on AC Optimal Power Flow
Carleton Coffrin, Bernard Knueven, Jesse Holzer +1
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal pow…
Forced oscillation source localization from generator measurements
Melvyn Tyloo, Marc Vuffray, Andrey Y. Lokhov
Malfunctioning equipment, erroneous operating conditions or periodic load variations can cause periodic disturbances that would persist over time, creating an undesirable transfer…
Efficient Learning of Discrete Graphical Models
Marc Vuffray, Sidhant Misra, Andrey Y. Lokhov
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least…
Natural Gas Flow Solutions with Guarantees: A Monotone Operator Theory Approach
Krishnamurthy Dvijotham, Marc Vuffray, Sidhant Misra +1
We consider balanced flows in a natural gas transmission network and discuss computationally hard problems such as establishing if solution of the underlying nonlinear gas flow equ…
The Inviscid, Compressible and Rotational, 2D Isotropic Burgers and Pressureless Euler-Coriolis Fluids; Solvable models with illustrations
Philippe Choquard, Marc Vuffray
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burge…
Learning Energy-Based Representations of Quantum Many-Body States
Abhijith Jayakumar, Marc Vuffray, Andrey Y. Lokhov
Efficient representation of quantum many-body states on classical computers is a problem of enormous practical interest. An ideal representation of a quantum state combines a succi…
High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware
Jon Nelson, Marc Vuffray, Andrey Y. Lokhov +2
Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experi…
Autoregressive pairwise Graphical Models efficiently find ground state representations of stoquastic Hamiltonians
Yuchen Pang, Abhijith Jayakumar, Evan McKinney +3
We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show…
Learning response functions of analog quantum computers: analysis of neutral-atom and superconducting platforms
Cenk Tüysüz, Abhijith Jayakumar, Carleton Coffrin +2
Analog quantum computation is an attractive paradigm for the simulation of time-dependent quantum systems. Programmable analog quantum computers have been realized in hardware usin…
Monotone Order Properties for Control of Nonlinear Parabolic PDE on Graphs
Sidhant Misra, Marc Vuffray, Anatoly Zlotnik +1
We derive conditions for the propagation of monotone ordering properties for a class of nonlinear parabolic partial differential equation (PDE) systems on metric graphs. For such s…
Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation
Sidhant Misra, Marc Vuffray, Anatoly Zlotnik
We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the ed…
Fast and Robust Determination of Power System Emergency Control Actions
Sidhant Misra, Line Roald, Marc Vuffray +1
This paper outlines an optimization framework for choosing fast and reliable control actions in a transmission grid emergency situation. We consider contractual load shedding and g…
Monotonicity of Actuated Flows on Dissipative Transport Networks
Anatoly Zlotnik, Sidhant Misra, Marc Vuffray +1
We derive a monotonicity property for general, transient flows of a commodity transferred throughout a network, where the flow is characterized by density and mass flux dynamics on…
Online Learning of Power Transmission Dynamics
Andrey Y. Lokhov, Marc Vuffray, Dmitry Shemetov +2
We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a max…
Computationally sufficient statistics for Ising models
Abhijith Jayakumar, Shreya Shukla, Marc Vuffray +2
Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms fo…
Single-Qubit Cross Platform Comparison of Quantum Computing Hardware
Adrien Suau, Jon Nelson, Marc Vuffray +3
As a variety of quantum computing models and platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importa…
Real-time Anomaly Detection and Classification in Streaming PMU Data
Christopher Hannon, Deepjyoti Deka, Dong Jin +2
Ensuring secure and reliable operations of the power grid is a primary concern of system operators. Phasor measurement units (PMUs) are rapidly being deployed in the grid to provid…
Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing
Zachary Morrell, Marc Vuffray, Andrey Lokhov +3
We propose a quantum annealing protocol that more effectively probes the dynamics of a single qubit on D-Wave's quantum annealing hardware. This protocol uses D-Wave's h-gain sched…
Learning Continuous Exponential Families Beyond Gaussian
Christopher X. Ren, Sidhant Misra, Marc Vuffray +1
We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical mo…
Lossy Source Coding via Spatially Coupled LDGM Ensembles
Vahid Aref, Nicolas Macris, Rudiger Urbanke +1
We study a new encoding scheme for lossy source compression based on spatially coupled low-density generator-matrix codes. We develop a belief-propagation guided-decimation algorit…
Stationary solutions of the Schrödinger-Newton model - An ODE approach
Philippe Choquard, Joachim Stubbe, Marc Vuffray
We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schrödinger-Newton model in any space dimension . Our result is based on an…
Learning of Discrete Graphical Models with Neural Networks
Abhijith J., Andrey Y. Lokhov, Sidhant Misra +1
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a disc…
On the Emerging Potential of Quantum Annealing Hardware for Combinatorial Optimization
Byron Tasseff, Tameem Albash, Zachary Morrell +4
Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies h…
Monotonicity of Dissipative Flow Networks Renders Robust Maximum Profit Problem Tractable: General Analysis and Application to Natural Gas Flows
Marc Vuffray, Sidhant Misra, Michael Chertkov
We consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials. Edge flows in a…
Universal framework for simultaneous tomography of quantum states and SPAM noise
Abhijith Jayakumar, Stefano Chessa, Carleton Coffrin +3
We present a general denoising algorithm for performing simultaneous tomography of quantum states and measurement noise. This algorithm allows us to fully characterize state prepar…
Graphical Models for Optimal Power Flow
Krishnamurthy Dvijotham, Pascal Van Hentenryck, Michael Chertkov +2
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly N…
Locating the source of forced oscillations in transmission power grids
Robin Delabays, Andrey Y. Lokhov, Melvyn Tyloo +1
Forced oscillation event in power grids refers to a state where malfunctioning or abnormally operating equipment causes persisting periodic disturbances in the system. While power…
Vector Field Visualization of Single-Qubit State Tomography
Adrien Suau, Marc Vuffray, Andrey Y. Lokhov +2
As the variety of commercially available quantum computers continues to increase so does the need for tools that can characterize, verify and validate these computers. This work ex…
Discrete distributions are learnable from metastable samples
Abhijith Jayakumar, Andrey Y. Lokhov, Sidhant Misra +1
Physically motivated stochastic dynamics are widely used to sample from high-dimensional distributions. However, such samplers often get trapped in metastable states, approximately…
Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems
David Métivier, Marc Vuffray, Sidhant Misra
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the ris…
Information Theoretic Optimal Learning of Gaussian Graphical Models
Sidhant Misra, Marc Vuffray, Andrey Y. Lokhov
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower boun…
Symmetric Linear Dynamical Systems are Learnable from Few Observations
Minh Vu, Andrey Y. Lokhov, Marc Vuffray
We consider the problem of learning the parameters of a -dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time . We…
Selecting Optimal Variable Order in Autoregressive Ising Models
Shiba Biswal, Marc Vuffray, Andrey Y. Lokhov
Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization…
QuantumAnnealing: A Julia Package for Simulating Dynamics of Transverse Field Ising Models
Zachary Morrell, Marc Vuffray, Sidhant Misra +1
Analog Quantum Computers are promising tools for improving performance on applications such as modeling behavior of quantum materials, providing fast heuristic solutions to optimiz…
Polymer Expansions for Cycle LDPC Codes
Nicolas Macris, Marc Vuffray
We prove that the Bethe expression for the conditional input-output entropy of cycle LDPC codes on binary symmetric channels above the MAP threshold is exact in the large block len…
Graphical Models and Belief Propagation-hierarchy for Optimal Physics-Constrained Network Flows
Michael Chertkov, Sidhant Misra, Marc Vuffray +2
In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science…
Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
Javier Gonzalez-Conde, Zachary Morrell, Marc Vuffray +2
Demonstrations of quantum advantage for certain sampling problems have generated considerable excitement for quantum computing and have further spurred the development of circuit-m…
Potential Applications of Quantum Computing at Los Alamos National Laboratory
Andreas Bärtschi, Francesco Caravelli, Carleton Coffrin +16
The emergence of quantum computing technology over the last decade indicates the potential for a transformational impact in the study of quantum mechanical systems. It is natural t…
Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models
Marc Vuffray, Sidhant Misra, Andrey Y. Lokhov +1
We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimat…
Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics
Arkopal Dutt, Andrey Y. Lokhov, Marc Vuffray +1
The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probab…
Programmable Quantum Annealers as Noisy Gibbs Samplers
Marc Vuffray, Carleton Coffrin, Yaroslav A. Kharkov +1
Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning…
The Bethe Free Energy Allows to Compute the Conditional Entropy of Graphical Code Instances. A Proof from the Polymer Expansion
Nicolas Macris, Marc Vuffray
The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting…
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
Vahid Aref, Nicolas Macris, Marc Vuffray
We investigate an encoding scheme for lossy compression of a binary symmetric source based on simple spatially coupled Low-Density Generator-Matrix codes. The degree of the check n…
The Potential of Quantum Annealing for Rapid Solution Structure Identification
Yuchen Pang, Carleton Coffrin, Andrey Y. Lokhov +1
The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated h…
Concentration to Zero Bit-Error Probability for Regular LDPC Codes on the Binary Symmetric Channel: Proof by Loop Calculus
Marc Vuffray, Theodor Misiakiewicz
In this paper we consider regular low-density parity-check codes over a binary-symmetric channel in the decoding regime. We prove that up to a certain noise threshold the bit-error…
General Revenue Adequacy Conditions for Energy Transport Networks
Sidhant Misra, Marc Vuffray, Anatoly Zlotnik +1
Optimization is widely used to determine the physical and financial exchange of wholesale electricity in organized markets. Guarantees of solution optimality and feasibility rest l…
Beyond the Bethe Free Energy of LDPC Codes via Polymer Expansions
Nicolas Macris, Marc Vuffray
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansi…
An Efficient Quantum Algorithm for Linear System Problem in Tensor Format
Zeguan Wu, Sidhant Misra, Tamás Terlaky +2
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution…
Optimal structure and parameter learning of Ising models
Andrey Y. Lokhov, Marc Vuffray, Sidhant Misra +1
Reconstruction of structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics…
Single-Qubit Fidelity Assessment of Quantum Annealing Hardware
Jon Nelson, Marc Vuffray, Andrey Y. Lokhov +1
As a wide variety of quantum computing platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. I…