Design and Evaluation of GPU-FPX: A Low-Overhead tool forFloating-Point Exception Detection in NVIDIA GPUs
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Linear solver packages are central to many scientific, engineering, and machine learning applications. When floating-point exceptions occur in these solvers, e.g., division by zero or overflow, numerical results are compromised and become unreliable. Existing static and dynamic analysis tools can detect such exceptions, but they do not explain why the exceptions occur in terms of the solver inputs. Here, we present a study to characterize the inputs that cause numerical exceptions in linear solver packages. Our approach uses explainable AI (XAI) to find the most relevant characteristics of input matrices that explain the occurrence of exceptions in the solvers. Since training data in this domain is scarce, we perform extensive data gathering and data augmentation to obtain exception-inducing inputs. Our approach uses a repair strategy on the features blamed by XAI to validate that such features indeed explain the exceptions. We compare the LIME and SHAP XAI techniques using a dozen matrix features with three classifiers. We evaluate the approach on three widely used linear solver packages and find that some input characteristics can explain the occurrence of exceptions 100% of the time, in specific solvers and preconditioners.
Techniques for improving performance of accelerated processing devices (“APDs”) when exceptions occur are provided. In APDs, the very large number of parallel processing execution units, and the complexity of the hardware used to execute a large number of work-items in parallel, means that APDs typically stall when an exception occurs (unlike in central processing units (“CPUs”), which are able to execute speculatively and out-of-order). However, the techniques provided herein allow at least some execution to occur past exceptions. Execution past an exception generating instruction occurs by executing instructions that would not lead to a corruption while skipping those that would lead to a corruption. After the exception has been satisfied, execution occurs in a replay mode in which the potentially exception-generating instruction is executed and in which instructions that did not execute in the exception-wait mode are executed. A mask and counter are used to control execution in replay mode.
Embodiments may include systems and methods to create and edit a representation of a worksite, to create various data objects, to classify such objects as various types of pre-defined “features” with attendant properties and layout constraints. As part of or in addition to classification, an embodiment may include systems and methods to create, associate, and edit intrinsic and extrinsic properties to these objects. A design engine may apply of design rules to the features described above to generate one or more solar collectors installation design alternatives, including generation of on-screen and/or paper representations of the physical layout or arrangement of the one or more design alternatives. In some embodiments, metadata about the design process, including the process of classifying features and providing user input, generating layouts, and then modifying those layouts, may be generated. The metadata may include information about exceptional conditions in the project state information or design. A list of exceptions corresponding to exceptional conditions may be generated, and the designer may interact with these exceptions in a variety of ways, such as by complying with rules to remove an item from the exceptions list or overriding the application of the rules. The exceptions may be non-blocking relative to other user actions.
Testing code for floating-point exceptions is crucial as exceptions can quickly propagate and produce unreliable numerical answers. The state-of-the-art to test for floating-point exceptions in heterogeneous systems is quite limited and solutions require the application’s source code, which precludes their use in accelerated libraries where the source is not publicly available. We present an approach to find inputs that trigger floating-point exceptions in black-box CPU or GPU functions, i.e., functions where the source code and information about input bounds are unavailable. Our approach is the first to use Bayesian optimization (BO) to identify such inputs and uses novel strategies to overcome the challenges that arise in applying BO to this problem. Here, we implement our approach in the XSCOPE framework and demonstrate it on 58 functions from the CUDA Math Library and 81 functions from the Intel Math Library. XSCOPE is able to identify inputs that trigger exceptions in about 73% of the tested functions.
This paper introduces the special collection in Geophysical Research Letters and Journal of Geophysical Research: Atmospheres on the exceptional stratospheric polar vortex in 2019/2020. Papers in this collection show that the 2019/2020 stratospheric polar vortex was the strongest, most persistent, and coldest on record in the Arctic. The unprecedented Arctic chemical processing and ozone loss in spring 2020 have been studied using numerous satellite and ground-based data sets and chemistry-transport models. Quantitative estimates of chemical loss are broadly consistent among the studies and show profile loss of about the same magnitude as in the Arctic in 2011, but with most loss at lower altitudes; column loss was comparable to or larger than that in 2011. Several papers show evidence of dynamical coupling from the mesosphere down to the surface. Studies of tropospheric influence and impacts link the exceptionally strong vortex to reflection of upward propagating waves and show coupling to tropospheric anomalies, including extreme heat, precipitation, windstorms, and marine cold air outbreaks. Predictability of the exceptional stratospheric polar vortex in 2019/2020 and related predictability of surface conditions are explored. The exceptionally strong stratospheric polar vortex in 2019/2020 highlights the extreme interannual variability in the Arctic winter/spring stratosphere and the far-reaching consequences of such extremes.
Electromagnetic coupling is ubiquitous in photonic systems and transfers optical signals from one device to the other, creating crosstalk between devices. While this allows the functionality of some photonic components such as couplers, it limits the integration density of photonic chips, and many approaches have been proposed to reduce the crosstalk. However, due to the wave nature of light, complete elimination of crosstalk between closely spaced, identical waveguides is believed to be impossible and has not been observed experimentally. Here we show an exceptional coupling that can completely suppresses the crosstalk utilizing highly anisotropic photonic metamaterials. The anisotropic dielectric perturbations in the metamaterial mutually cancel the couplings from different field components, resulting in an infinitely long coupling length. We demonstrate the extreme suppression of crosstalk via exceptional coupling on a silicon-on-insulator platform, which is compatible with a complementary metal-oxide-semiconductor process. The idea of exceptional coupling with anisotropic metamaterials can be applied to many other electromagnetic devices, and it could drastically increase the integration density of photonic chips.
We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counterpropagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the strength of a perturbing cross-coupling between the two modes. Partially reflecting the output of one mode into the other creates a non-Hermitian Hamiltonian that exhibits a family of EPs, creating an exceptional surface (ES). We use a fully quantum treatment of field inputs and noise sources to obtain a quantitative bound on the estimation error by calculating the quantum Fisher information (QFI) in the output fields, whose inverse gives the Cramér-Rao lower bound on the mean-squared error of any unbiased estimator. We determine the bounds for two input states, namely, a semiclassical coherent state and a highly nonclassical NOON state. We find that the QFI is enhanced in the presence of an EP for both of these input states and that both states can saturate the Cramér-Rao bound. We then identify idealized yet experimentally feasible measurements that achieve the minimum bound for these two input states. We also investigate how the QFI changes for parameter values that do not lie on the ES, finding that these can have a larger QFI, suggesting alternative routes to optimize the parameter estimation for this problem.
Abstract Orienting polymer semiconductors is desirable to optimize device characteristics, provide insight into microstructure, and magnify subtle phase behavior. Here, a combination of uniaxial strain and subsequent heating of the donor–acceptor (DA) polymer PBnDT‐FTAZ is discovered to lead to exceptional optical dichroic ratios of up to 38 (and close to 50 near the polymer's absorption edge). This alignment is achieved due to the existence of a previously undetected thermotropic liquid crystal (LC) mesophase. The LC transition, not discernable through calorimetry, is uncovered through a combination of in situ UV–vis spectroscopy, X‐ray scattering, and dynamic mechanical analysis (DMA). Comparing PBnDT‐FTAZ to the non‐fluorinated PBnDT‐HTAZ and the homo polymer PBnDT, all of which show similar thermal transitions, reveals that exceptional alignment is only found in PBnDT‐FTAZ. This is attributed to the PBnDT‐FTAZ film having two distinct liquid crystal populations, and the polymer templating to a highly aligned, high‐clearing temperature population when heated. The DMA thermal relaxation behavior observed here is also seen in other DA conjugated polymers suggesting that such thermotropic LC mesophases may be common in these materials. These findings demonstrate a polymer semiconductor with remarkable alignment and uncover phase behavior with broad implications for process‐structure‐property relationships in polymer semiconductors.
CoCrFeMnNi high-entropy alloy (HEA) was additively manufactured (AM) by laser powder-bed fusion (L-PBF). The AM CoCrFeMnNi has prominent cellular dislocation structures with a small number of Mn-rich oxides. The thermal stability of the AM CoCrFeMnNi was investigated by isochronal annealing treatment at various temperatures from 400 to 1300°C for 1h. Microstructural analysis shows slow dislocation recovery, retarded recrystallization process, and precipitation of additional Cr-Mn based oxides during thermal annealing, resulting in exceptional thermal stability and retained high hardness at elevated temperatures. Further, by thermodynamic calculations, a low stored energy of 1.31 MJ/m 3 and a high activation energy of 353 kJ/mol for recrystallization were estimated for the AM CoCrFeMnNi. The exceptional thermal stability of the AM CoCrFeMnNi HEA is mechanistically attributed to the low crystallographic misorientations across the dislocation cell walls, sluggish atomic diffusion, and the pinning effects of the oxide nanoprecipitates.
We present a comprehensive study of axion condensed neutron stars that arise in models of an exceptionally light axion that couples to quantum chromodynamics (QCD). These axions solve the strong-charge-parity (𝐶𝑃) problem, but have a mass-squared lighter than that due to QCD by a factor of 𝜖 < 1. Inside dense matter, the axion potential is altered, and much of the matter in neutron stars resides in the axion condensed phase where the strong-𝐶𝑃 parameter 𝜃 = 𝜋 and 𝐶𝑃 remains a good symmetry. In these regions, masses and interactions of nucleons are modified, in turn changing the equation of state (EOS), structure, and phenomenology of the neutron stars. We take the first steps toward the study of the EOS of neutron star matter at 𝜃 = 𝜋 within chiral effective field theory and use relativistic mean field theory to deduce the resulting changes to nuclear matter and the neutron star low-density EOS. We derive constraints on the exceptionally light axion parameter space based on observations of the thermal relaxation of accreting neutron stars, isolated neutron star cooling, and pulsar glitches, excluding the region up to 5 ×10 −7 ≲ 𝜖 ≲ 0.2 for 𝑚 𝑎 ≳ 2 × 10 −9 eV. We comment on potential changes to the neutron star mass-radius relationship, and discuss the possibility of novel, nuclear-density compact objects with 𝜃 = 𝜋 that are stabilized not by gravity but by the axion potential.