Matthew Rocklin

A Computational Framework for Uncertainty Quantification and Stochastic Optimization in Unit Commitment With Wind Power Generation

We present a computational framework for integrating a state-of-the-art numerical weather prediction (NWP) model in stochastic unit commitment/economic dispatch formulations that account for wind power uncertainty. We first enhance the NWP model with an ensemble-based uncertainty quantification strategy implemented in a distributed-memory parallel computing architecture. We discuss computational issues arising in the implementation of the framework and validate the model using real wind-speed data obtained from a set of meteorological stations. We build a simulated power system to demonstrate the developments.

Unit commitment with wind power generation: integrating wind forecast uncertainty and stochastic programming.

We present a computational framework for integrating the state-of-the-art Weather Research and Forecasting (WRF) model in stochastic unit commitment/energy dispatch formulations that account for wind power uncertainty. We first enhance the WRF model with adjoint sensitivity analysis capabilities and a sampling technique implemented in a distributed-memory parallel computing architecture. We use these capabilities through an ensemble approach to model the uncertainty of the forecast errors. The wind power realizations are exploited through a closed-loop stochastic unit commitment/energy dispatch formulation. We discuss computational issues arising in the implementation of the framework. In addition, we validate the framework using real wind speed data obtained from a set of meteorological stations. We also build a simulated power system to demonstrate the developments.

Latent clustering on graphs with multiple edge types

We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured by many different metrics. For instance, similarity between two papers can be based on common authors, where they were published, keyword similarity, citations, etc. As such, graphs with multiple edges give a more accurate model to describe similarities between objects than models using single-edge graphs. Each edge/metric provides only partial information about the data; recovering full information requires aggregation of all the similarity metrics. Clustering becomes much more challenging in this context, since in addition to the difficulties of the traditional clustering problem, we have to deal with a space of clusterings. Reducing the multidimensional space into a single dimension poses significant challenges. At the same time, the multidimensional space can contain latent structures, and searching this multidimensional space can reveal important information about the graph. We generalize the concept of clustering in single-edge graphs to multiedged graphs and investigate problems such as the following: Can we find a clustering that remains good, even if we change the relative weights of metrics? How can we describe the space of clusterings efficiently? Can we find unexpected clusterings (a good clustering that is distant from all given clusterings)? If we are given the ground-truth clustering, can we recover how the weights for edge types were aggregated?

Symbolic Statistics with SymPy

Replacing symbols with random variables makes it possible to naturally add statistical operations to complex physical models. Three examples of symbolic statistical modeling are considered here, using new features from the popular SymPy project.

Computing an Aggregate Edge-Weight Function for Clustering Graphs with Multiple Edge Types

We investigate the community detection problem on graphs in the existence of multiple edge types. Our main motivation is that similarity between objects can be defined by many different metrics and aggregation of these metrics into a single one poses several important challenges, such as recovering this aggregation function from ground-truth, investigating the space of different clusterings, etc. In this paper, we address how to find an aggregation function to generate a composite metric that best resonates with the ground-truth. We describe two approaches: solving an inverse problem where we try to find parameters that generate a graph whose clustering gives the ground-truth clustering, and choosing parameters to maximize the quality of the ground-truth clustering. We present experimental results on real and synthetic benchmarks.