Meng Wang

Associate Professor
Department of Electrical, Computer & Systems Engineering
Rensselaer Polytechnic Institute

Phone: 518.276.3842 Fax: 518-276-6261
ECSE Department, JEC 6024
Rensselaer Polytechnic Institute Troy, NY, 12180

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Theoretical and algorithmic foundations of deep learning

Deep learning can automatically learn features from data and have demonstrated extraordinary empirical performance in various applications such as natural language processing, computer Vision, and image processing. However, the general acceptance of deep learning in critical domains is hindered by the significant computational cost to train a neural network, the lack of formal theoretical analysis to explain its performance, and the vulnerability to adversarial attacks. Our research includes a systematic investigation of neural network architecture selection, algorithmic design, and theoretical performance analysis. We want to develop sample-efficient and computationally inexpensive learning methods for deep neural networks with provable generalization guarantees.

Data recovery, error correction, and the detection of cyber data attacks

To enable the reliable implementation of synchrophasor-data-based real-time control, these synchrophasor measurements should always be available and accurate. Due to device malfunction, misconfiguration, communication errors, and possible cyber data attacks, the synchrophasor data usually contain missing data and bad data.

Exploiting the low-rank structures of the spatial-temporal blocks of PMU data, my group developed fast algorithms with analytical guarantees for missing PMU data recovery, bad data correction, and detection of cyber data attacks. Our data recovery methods have the following distinctive features that do not appear in the existing model-free approaches: the ability to recover simultaneous and consecutive data errors or losses across all channels, the ability to distinguish system events from bad data, and provable analytical guarantees.

Simultaneous achievement of data privacy and information accuracy

Data privacy is an increasing concern. For example, an intruder can extract user behavior from individual household power consumptions measured by smart meters. One recent line of research is to enhance data privacy by adding noise either numerically or physically before sending the smart meter data to the operator. The resulting increase in the user privacy, however, is achieved at the cost of reduced data accuracy for the operator and in turn, leads to inaccurate estimation and decision making for the operator.

We for the first time proposed the idea to achieve individual users' data privacy and the operator's information accuracy simultaneously. Our main technical contribution is to develop information extraction methods for the operator from privacy-preserving measurements (with added noise and quantization). We showed that using our approach the operator can still extract the information accurately from the data of a large number of users, while the intruders with access to partial measurements cannot.

Event identification

Fast event identification is important to enhance the wide-area situational awareness of power systems and prevent cascading failures and blackouts. Data-driven event identification methods train a classifier based on measurements or extracted features. One disadvantage of data-driven methods is that a large number of training events are needed to cover all the possible topologies, initial conditions, and event locations.

We proposed to characterize events using low-dimensional structures instead of using the time series directly. We proved that the subspace depends on the dominant modes of the system after an event starts and is robust to initial conditions. Compared with the existing methods, one distinctive feature of our approach is the significant reduction in the required size of the training set without sacrificing the identification accuracy. Our method identifies event types accurately even when the pre-event conditions of the tested events differ from those in the dictionary by 90%.

Theoretical development and other applications

Besides the application of power system data analytics, my research also explores the fundamentals of low-dimensional-model-based high-dimensional data analytics and contributes to the theoretical and algorithmic development of high-dimensional data analysis and nonconvex optimization.

We can formulate the data recovery and information extraction problems as nonconvex optimizations and develop computationally efficient nonconvex approaches with provable performance guarantees. This line of research contributes to the theoretical development of low-rank matrix theory and nonconvex optimization. Since the low-dimensional models exist in diverse applications, my research applies to other domains beyond power systems, such as image denoising, computer vision, MRI imaging, and array signal processing.


I gratefully acknowledge the current and past support from the following funding agencies and organizations.

picture National Science Foundation

picture Air Force Office of Scientific Research

picture Army Research Office

picture New York State Energy Research and Development Authority

picture CURENT NSF & DOE Engineering Research Center
picture Electric Power Research Institute (EPRI)

picture International Business Machines (IBM)