Power and thermal management are critical components of High-Performance-Computing (HPC) systems, due to their high power density and large total power consumption. The assessment of thermal dissipation by means of compact models directly from the thermal response of the final device enables more robust and precise thermal control strategies as well as automated diagnosis. However, when dealing with large scale systems "in production", the accuracy of learned thermal models depends on the dynamics of the power excitation, which depends also on the executed workload, and measurement nonidealities, such as quantization. In this paper we show that, using an advanced system identification algorithm, we are able to generate very accurate thermal models (average error lower than our sensors quantization step of 1°C) for a large scale HPC system on real workloads for very long time periods. However, we also show that: 1) not all real workloads allow for the identification of a good model; 2) starting from the theory of system identification it is very difficult to evaluate if a trace of data leads to a good estimated model. We then propose and validate a set of techniques based on machine learning and deep learning algorithms for the choice of data traces to be used for model identification. We also show that deep learning techniques are absolutely necessary to correctly choose such traces up to 96 of the times.
Previous works have shown that the relation between the core temperature and the dissipated power can be described by a purely dynamic ARX model @cite_5 @cite_21 . ARX models are widely used in system identification since they constitute the simplest way of representing a dynamic process in the presence of uncertainties @cite_9 . Two important features of these models are the possibility of obtaining asymptotically unbiased estimates of their parameters by means of least squares and the absence of stability problems of the associated optimal one step-ahead predictors @cite_9 . Nevertheless, it has been shown in @cite_21 that the classic MISO ARX model is not able to describe properly the thermal dynamics of the system because the estimated models are characterized by relevant negative poles and or complex conjugate poles. This is in contrast with the physics of thermal systems, where only real positive poles can exist. As explained in @cite_21 , this problem is due to the presence of a significant level of measurement noise.
@cite_5 @cite_9 @cite_21
1893146140 2139019659 2020999234 2028633127
This is the second in a series of papers in which we derive a @math -expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase. In our previous paper, we computed the @math -limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order @math -limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg-Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Without thus appealing to the Euler-Lagrange equation, we establish for all configurations which have "almost minimal energy" the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of @math -equivalence, the obtained results also yield an expansion of the minimal energy for the original Ohta-Kawasaki energy. This leads to expecting to see triangular lattices of droplets as energy minimizers. High-performance microprocessor families employ dynamic-thermal-management techniques to cope with the increasing thermal stress resulting from peaking power densities. These techniques operate on feedback generated from on-die thermal sensors. The allocation and the placement of thermal-sensing elements directly impact the effectiveness of the dynamic management mechanisms. In this paper, we propose systematic techniques for determining the optimal locations for thermal sensors to provide high-fidelity thermal monitoring of a complex microprocessor system. Our strategies can be divided into two main categories: uniform sensor allocation and nonuniform sensor allocation. In the uniform approach, the sensors are placed on a regular grid. The nonuniform allocation identifies an optimal physical location for each sensor such that the sensor's attraction toward steep thermal gradients is maximized, which can result in uneven concentrations of sensors on different locations of the chip. We also present a hybrid algorithm that shows the tradeoffs associated with number of sensors and expected accuracy. Our experimental results show that our uniform approach using interpolation can detect the chip temperature with a maximum error of 5.47degC and an average maximum error of 1.05degC . On the other hand, our nonuniform strategy is able to create a sensor distribution for a given microprocessor architecture, providing thermal measurements with a maximum error of 3.18degC and an average maximum error of 1.63degC across a wide set of applications. We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states ( annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios. Random graph models with limited choice have been studied extensively with the goal of understanding the mechanism of the emergence of the giant component. One of the standard models are the Achlioptas random graph processes on a fixed set of (n ) vertices. Here at each step, one chooses two edges uniformly at random and then decides which one to add to the existing configuration according to some criterion. An important class of such rules are the bounded-size rules where for a fixed (K 1 ), all components of size greater than (K ) are treated equally. While a great deal of work has gone into analyzing the subcritical and supercritical regimes, the nature of the critical scaling window, the size and complexity (deviation from trees) of the components in the critical regime and nature of the merging dynamics has not been well understood. In this work we study such questions for general bounded-size rules. Our first main contribution is the construction of an extension of Aldous’s standard multiplicative coalescent process which describes the asymptotic evolution of the vector of sizes and surplus of all components. We show that this process, referred to as the standard augmented multiplicative coalescent (AMC) is ‘nearly’ Feller with a suitable topology on the state space. Our second main result proves the convergence of suitably scaled component size and surplus vector, for any bounded-size rule, to the standard AMC. This result is new even for the classical Erdős–Renyi setting. The key ingredients here are a precise analysis of the asymptotic behavior of various susceptibility functions near criticality and certain bounds from (The barely subcritical regime. Arxiv preprint, 2012) on the size of the largest component in the barely subcritical regime.