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Exercises in high-dimensional sampling: maximal poisson-disk sampling and k -d darts
In this paper, we review our recent progress on efficient algorithms for generating well-spaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. Lastly, we summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.
Distributed Energy Management for Networked Microgrids Using Online ADMM With Regret
We propose a distributed algorithm for online energy management in networked microgrids with a high penetration of distributed energy resources (DERs). A high penetration of DERs introduces high uncertainty of power generation to the microgrids. In general, the state-of-the-art forecasting for non-dispatchable DERs such as solar energy is not sufficiently accurate, which results in inaccurate energy scheduling. To address the high uncertainty issue in the networked microgrids, we propose an online energy management based on the online alternating direction method of multipliers algorithm with the past power generation information from the DERs. The online algorithm provides less conservative schedule than the robust optimization-based approach. The effectiveness of the proposed algorithm is verified by various numerical examples.
Impacts of Distributed Speed Harmonization and Optimal Maneuver Planning on Multi-Lane Roads
A commonly proposed method for improving traffic flow on freeways is speed harmonization. The effectiveness of current speed harmonization approaches, such as variable speed limits, is extremely reliant on human driver compliance. Connected and automated vehicles (CAVs) are expected to come to market within this decade, offering the opportunity to eliminate or reduce the reliance on human compliance. However, extending current roadside infrastructure-based approaches of assigning centrally computed harmonization speeds to individual vehicles is, costly. An alternative approach is to have individual vehicles estimate the traffic state on-board and make distributed decisions to achieve the harmonization goal autonomously. In this work, we present a distributed algorithm for estimating the current average speed of traffic. We couple this with a distributed 2D maneuver planning approach. Then, we study the impact on traffic efficiency in terms of energy consumption and travel time at varying CAV penetration rates.
Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration
Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using highperformance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. Finally, we evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.
Distributed Optimal Dispatch of Distributed Energy Resources Over Lossy Communication Networks
In this paper, we consider the economic dispatch problem (EDP), where a cost function that is assumed to be strictly convex is assigned to each of distributed energy resources (DERs), over packet dropping networks. The goal of a standard EDP is to minimize the total generation cost while meeting total demand and satisfying individual generator output limit. We propose a distributed algorithm for solving the EDP over networks. The proposed algorithm is resilient against packet drops over communication links. Under the assumption that the underlying communication network is strongly connected with a positive probability and the packet drops are independent and identically distributed (i.i.d.), we show that the proposed algorithm is able to solve the EDP. Numerical simulation results are used to validate and illustrate the main results of the paper.
Distributed Flexibility Characterization and Resource Allocation Strategies for Multi-zone Commercial Buildings in the Smart Grid
The HVAC (Heating, Ventilation, and Air- Conditioning) system of commercial buildings is a complex system with a large number of dynamically interacting components. In particular, the thermal dynamics of each zone are coupled with those of the neighboring zones. In this paper, we study a multi-agent based approach to model and control commercial building HVAC system for providing grid services. In the multi-agent system (MAS), individual zones are modeled as agents that can communicate, interact, and negotiate with one another to achieve a common objective. We first propose a distributed characterization method on the aggregated airflow (and thus fan power) flexibility that the HVAC system can provide to the ancillary service market. Then, we propose a Nash-bargaining based airflow allocation strategy to track a dispatch signal (that is within the offered flexibility limit) while respecting the preference and flexibility of individual zones. Moreover, we devise a distributed algorithm to obtain the Nash bargaining solution via dual decomposition and average consensus. Numerical simulations illustrate that the proposed distributed protocols are much more scalable than the centralized approaches especially when the system becomes larger and more complex.
Arrangements for communicating data in a computing system using multiple processors
Systems and methods for reducing data movement in a computer system. The systems and methods use information or knowledge about the structure of an algorithm, operations to be executed at a receiving processing unit, variables or subsets or groups of variables in a distributed algorithm, or other forms of contextual information, for reducing the number of bits transmitted from at least one transmitting processing unit to at least one receiving processing unit or storage device.
Arrangements for communicating and processing data in a computing system
Systems and methods for reducing data movement in a computer system. The systems and methods use information or knowledge about the structure of an algorithm, operations to be executed at a receiving processing unit, variables or subsets or groups of variables in a distributed algorithm, or other forms of contextual information, for reducing the number of bits transmitted from at least one transmitting processing unit to at least one receiving processing unit or storage device.
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.
Distributed Restoration for Integrated Transmission and Distribution Systems With DERs
Not provided.
SU-E-T-164: Evaluation of Electron Dose Distribution Using Two Algorithms
Purpose: To appreciate the difference of electron dose distributions calculated from the Monte Carlo and Electron 3D algorithms of radiotherapy in a heterogeneous phantom. Methods: A phantom consisted of two different materials (lungs mimicked by low-density cork and others by polystyrene) with an 11x16 cm field size (SSD = 100 cm) was utilized to estimate the two-dimensional dose distributions under 6 and 18 MeV beams. On behalf of two different types of tissue, the heterogeneous phantom was comprised of 3 identical slabs in the longitudinal direction with a thickness of 1 cm for each slab and 2 with a thickness of 2.5 cm. The Monte Carlo/MCTP application package constituted of five codes was performed to simulate the electron beams of a Varian Clinac 23IX. A 20x20 cm2 type III (open walled) applicator was used in these simulations. It has been shown elsewhere that the agreement of the phase space data between the calculation results of MCTP application package and the measured data were within 2% on depth-dose and transverse profiles, as well as output factor calculations. The electron 3D algorithm owned by Pinnacle 8.0m and the MCTP application package were applied for the two-dimensional dose distributions calculation. The curves at 50% and 100%-prescribed dose were observed for 6 and 18 MeV beams, respectively. Results: The MC calculations results were compared with the electron 3D calculations in terms of two-dimensional dose distributions for 6 and 18 MeV beams showed excellent agreement except in distal boundary where it was the very junction of the high and low-density region. Conclusions: The Monte Carlo/MCTP method could be used to better reflect the dose variation caused by heterogeneous tissues. Conclusion: A case study showed that the Monte Carlo/MCTP method could be used to better reflect the dose variation caused by heterogeneous tissues.
Fast neural network training on a cluster of GPUs for action recognition with high accuracy
In this work, we propose algorithms and techniques to accelerate training of deep neural networks for action recognition on a cluster of GPUs. The convergence analysis of our algorithm shows it is possible to reduce communication cost and at the same time minimize the number of iterations needed for convergence. We customize the Adam optimizer for our distributed algorithm to improve efficiency. In addition, we employ transfer-learning to further reduce training time while improving validation accuracy. For the UCF101 and HMDB51 datasets, the validation accuracies achieved are 93.1% and 67.9% respectively. With an additional end-to-end trained temporal stream, the validation accuracies achieved for UCF101 and HMDB51 are 93.47% and 81.24% respectively. As far as we know, these are the highest accuracies achieved with the two-stream approach using ResNet that does not involve computationally expensive 3D convolutions or pretraining on much larger datasets.
Residential Demand Side Aggregation of Privacy-Conscious Consumers
The increasing adoption of smart meters has led to growing concerns regarding privacy risks stemming from the high resolution measurements. This has given rise to privacy protection techniques that physically alter the consumer's energy load profile, masking private information by using localised devices, e.g. batteries or flexible loads. Meanwhile, there has also been increasing interest in aggregating the distributed energy resources (DERs) of residential consumers to provide services to the grid. In this paper, we propose an online distributed algorithm to aggregate the DERs of privacy-conscious consumers to provide services to the grid, whilst preserving their privacy. Results show that the optimisation solution from the distributed method converges to one close to the optimum computed using an ideal centralised solution method, balancing between grid service provision, consumer preferences and privacy protection. More importantly, the distributed method preserves consumer privacy, and does not require high-bandwidth two-way communications infrastructure.
Novel Geometric Operations for Linear Programming
This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.
Streaming Matching and Edge Cover in Practice
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a $1/(2+\varepsilon)$-approximation of the weight while using $O( n \log W /\epsilon)$ memory (here $n$ is the number of vertices and $W$ is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best $1/2$-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require $O(n \log n)$ memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass $3/2+\epsilon$-approximate algorithm with the memory requirement of Paz and Schwartzman's semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of the semi-streaming algorithm by computing a matching using linearly bounded memory on item intersection graphs derived from three machine learning datasets, whereas the existing offline algorithms could not complete on one of these datasets since their memory requirements exceeded 1TB.
Enabling DER Participation in Frequency Regulation Markets
Distributed energy resources (DERs) are playing an increasing role in ancillary services for the bulk grid, particularly in frequency regulation. In this article, we propose a framework for collections of DERs, combined to form microgrids and controlled by aggregators, to participate in frequency regulation markets. Our approach covers both the identification of bids for the market clearing stage and the mechanisms for the real-time allocation of the regulation signal. The proposed framework is hierarchical, consisting of a top layer and a bottom layer. The top layer consists of the aggregators communicating in a distributed fashion to optimally disaggregate the regulation signal requested by the system operator. The bottom layer consists of the DERs inside each microgrid whose power levels are adjusted so that the tie line power matches the output of the corresponding aggregator in the top layer. The coordination at the top layer requires the knowledge of cost functions, ramp rates, and capacity bounds of the aggregators. We develop meaningful abstractions for these quantities respecting the power flow constraints and taking into account the load uncertainties and propose a provably correct distributed algorithm for optimal disaggregation of regulation signals among the microgrids.
Cabana
Physics simulations that use particles in their algorithms are ubiquitous on modern high performance computers. Cabana is a C++ library for developing particle-based simulations on heterogeneous high performance computing platforms. Cabana provides general data structures and algorithms for common particle operations in a way that is both performant and portable on HPC systems. This includes particle data structure allocatable and configurable on GPU and CPU architectures, and threaded and distributed algorithms for sorting particles, halo exchanges, neighbor list generation, and other basic particle operations.