A low-cost parallel implementation of direct numerical simulation of wall turbulence

A numerical method for the direct numerical simulation of incompressible wall turbulence in rectangular and cylindrical geometries is presented. The distinctive feature resides in its design being targeted towards an efficient distributed-memory parallel computing on commodity hardware. The adopted discretization is spectral in the two homogeneous directions; fourth-order accurate, compact finite-difference schemes over a variable-spacing mesh in the wall-normal direction are key to our parallel implementation. The parallel algorithm is designed in such a way as to minimize data exchange among the computing machines, and in particular to avoid taking a global transpose of the data during the pseudo-spectral evaluation of the non-linear terms. The computing machines can then be connected to each other through low-cost network devices. The code is optimized for memory requirements, which can moreover be subdivided among the computing nodes. The layout of a simple, dedicated and optimized computing system based on commodity hardware is described. The performance of the numerical method on this computing system is evaluated and compared with that of other codes described in the literature, as well as with that of the same code implementing a commonly employed strategy for the pseudo-spectral calculation.Comment: To be published in J. Comp. Physic

Feedback and time are essential for the optimal control of computing systems

The performance, reliability, cost, size and energy usage of computing systems can be improved by one or more orders of magnitude by the systematic use of modern control and optimization methods. Computing systems rely on the use of feedback algorithms to schedule tasks, data and resources, but the models that are used to design these algorithms are validated using open-loop metrics. By using closed-loop metrics instead, such as the gap metric developed in the control community, it should be possible to develop improved scheduling algorithms and computing systems that have not been over-engineered. Furthermore, scheduling problems are most naturally formulated as constraint satisfaction or mathematical optimization problems, but these are seldom implemented using state of the art numerical methods, nor do they explicitly take into account the fact that the scheduling problem itself takes time to solve. This paper makes the case that recent results in real-time model predictive control, where optimization problems are solved in order to control a process that evolves in time, are likely to form the basis of scheduling algorithms of the future. We therefore outline some of the research problems and opportunities that could arise by explicitly considering feedback and time when designing optimal scheduling algorithms for computing systems

Expander Graph and Communication-Efficient Decentralized Optimization

In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for different numbers of nodes and node degrees. Our numerical results show that the performance of decentralized optimization is significantly better on expander graphs than other regular graphs.Comment: 2016 IEEE Asilomar Conference on Signals, Systems, and Computer

DeepSecure: Scalable Provably-Secure Deep Learning

This paper proposes DeepSecure, a novel framework that enables scalable execution of the state-of-the-art Deep Learning (DL) models in a privacy-preserving setting. DeepSecure targets scenarios in which neither of the involved parties including the cloud servers that hold the DL model parameters or the delegating clients who own the data is willing to reveal their information. Our framework is the first to empower accurate and scalable DL analysis of data generated by distributed clients without sacrificing the security to maintain efficiency. The secure DL computation in DeepSecure is performed using Yao's Garbled Circuit (GC) protocol. We devise GC-optimized realization of various components used in DL. Our optimized implementation achieves more than 58-fold higher throughput per sample compared with the best-known prior solution. In addition to our optimized GC realization, we introduce a set of novel low-overhead pre-processing techniques which further reduce the GC overall runtime in the context of deep learning. Extensive evaluations of various DL applications demonstrate up to two orders-of-magnitude additional runtime improvement achieved as a result of our pre-processing methodology. This paper also provides mechanisms to securely delegate GC computations to a third party in constrained embedded settings