Moon, Gordon M.; Kwon, Hyoukjun K.; Jeong, Geonhwa J.; Chatarsi, Prasanth C.; Rajamanickam, Sivasankaran R.; Krishna, Tushar K.
There is a growing interest in custom spatial accelerators for machine learning applications. These accelerators employ a spatial array of processing elements (PEs) interacting via custom buffer hierarchies and networks-on-chip. The efficiency of these accelerators comes from employing optimized dataflow (i.e., spatial/temporal partitioning of data across the PEs and fine-grained scheduling) strategies to optimize data reuse. The focus of this work is to evaluate these accelerator architectures using a tiled general matrix-matrix multiplication (GEMM) kernel. To do so, we develop a framework that finds optimized mappings (dataflow and tile sizes) for a tiled GEMM for a given spatial accelerator and workload combination, leveraging an analytical cost model for runtime and energy. Our evaluations over five spatial accelerators demonstrate that the tiled GEMM mappings systematically generated by our framework achieve high performance on various GEMM workloads and accelerators.
We present an adaptive algorithm for constructing surrogate models for integrated systems composed of a set of coupled components. With this goal we introduce ‘coupling’ variables with a priori unknown distributions that allow approximations of each component to be built independently. Once built, the surrogates of the components are combined and used to predict system-level quantities of interest (QoI) at a fraction of the cost of interrogating the full system model. We use a greedy experimental design procedure, based upon a modification of Multi-Index Stochastic Collocation (MISC), to minimize the error of the combined surrogate. This is achieved by refining each component surrogate in accordance with its relative contribution to error in the approximation of the system-level QoI. Our adaptation of MISC is a multi-fidelity procedure that can leverage ensembles of models of varying cost and accuracy, for one or more components, to produce estimates of system-level QoI. Several numerical examples demonstrate the efficacy of the proposed approach on systems involving feed-forward and feedback coupling. For a fixed computational budget, the proposed algorithm is able to produce approximations that are orders of magnitude more accurate than approximations that treat the integrated system as a black-box.
We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.
Potassium channels modulate various cellular functions through efficient and selective conduction of K+ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K+ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated byab initiocalculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations.
We present a theoretical framework for designing and assessing the performance of algorithms executing in networks consisting of spiking artificial neurons. Although spiking neural networks (SNNs) are capable of general-purpose computation, few algorithmic results with rigorous asymptotic performance analysis are known. SNNs are exceptionally well-motivated practically, as neuromorphic computing systems with 100 million spiking neurons are available, and systems with a billion neurons are anticipated in the next few years. Beyond massive parallelism and scalability, neuromorphic computing systems offer energy consumption orders of magnitude lower than conventional high-performance computing systems. We employ our framework to design and analyze neuromorphic graph algorithms, focusing on shortest path problems. Our neuromorphic algorithms are message-passing algorithms relying critically on data movement for computation, and we develop data-movement lower bounds for conventional algorithms. A fair and rigorous comparison with conventional algorithms and architectures is challenging but paramount. We prove a polynomial-factor advantage even when we assume an SNN consisting of a simple grid-like network of neurons. To the best of our knowledge, this is one of the first examples of a provable asymptotic computational advantage for neuromorphic computing.
dos Santos, Gonzalo; Meyer, Robert; Aparicio, Romina; Tranchida, Julien G.; Bringa, Eduardo M.; Urbassek, Herbert M.
Magnetization of clusters is often simulated using atomistic spin dynamics for a fixed lattice. Coupled spin-lattice dynamics simulations of the magnetization of nanoparticles have, to date, neglected the change in the size of the atomic magnetic moments near surfaces. We show that the introduction of variable magnetic moments leads to a better description of experimental data for the magnetization of small Fe nanoparticles. To this end, we divide atoms into a surface-near shell and a core with bulk properties. It is demonstrated that both the magnitude of the shell magnetic moment and the exchange interactions need to be modified to obtain a fair representation of the experimental data. This allows for a reasonable description of the average magnetic moment vs cluster size, and also the cluster magnetization vs temperature.