Numerical Precision Research Articles

Improved Design for Hardware Implementation of Graph-Based Large Margin Classifiers for Embedded Edge Computing.

The number of connected embedded edge computing Internet of Things (IoT) devices has been increasing over the years, contributing to the significant growth of available data in different scenarios. Thereby, machine learning algorithms arise to enable task automation and process optimization based on those data. However, due to some learning methods' computational complexity implementing geometric classifiers, it is a challenge to map these on embedded systems or devices with limited resources in size, processing, memory, and power, to accomplish the desired requirements. This hampers the applicability of these methods to complex industrial embedded edge applications. This work evaluates strategies to reduce classifiers' implementation costs based on the CHIP-clas model, independent of hyperparameter tuning and optimization algorithms. The proposal aims to evaluate the tradeoff between numerical precision and model performance and analyze the hardware implementations of a distance-based classifier. Two 16 -b floating-point formats were compared to the 32 -b floating-point precision implementation. Also, a new hardware architecture was developed and then compared to the state-of-the-art reference. The results indicate that the model is robust to low precision computation, providing statistically equivalent results compared to the baseline model, also pointing out statistically equivalent performance and a global speed-up factor of approx 4.39 in processing time.

Numerical simulation and experimental application of a 300 MW boiler combustion system

In the actual operation of a 300 MW boiler, there are some problems such as unstable combustion, high combustible material of fly ash and slag, and large thermal deviation on both sides of steam. The Cooper method is used to divide the three parts of the furnace by a hexahedral structured grid, which can reduce the grid number and improve the numerical simulation calculation precision. The Realization k-ε turbulent model is used to simulate the gas-solid two-phase flow in the furnace before and after reconstruction. The boundary of the calculation model adopts the actual operating parameters, and the numerical calculation adopts the three-dimensional steady-state calculation - Simple algorithm. The conclusions are as follows: the amount of pulverized coal powder falling into the cold ash hopper is reduced from 0.077 kg/m3 before the reconstruction to 0.045 kg/m3 after the reconstruction, with a decrease of about 42%. The secondary air concentration arrangement in the lowest two layers strengthened the secondary air supporting capacity. The residence time of pulverized coal particles in the furnace is increased from 30.59 s before the reconstruction to 39.97 s after the reconstruction, and the time is extended by about 9.4 s, which is beneficial to the combustion of pulverized coal particles. The centralized arrangement of primary air in the lowest two layers is beneficial to the initial ignition and stable combustion of pulverized coal gas. The downdip of the tertiary air incidence angle reduces the rotational momentum of the tertiary airflow, and the increase of the rotational momentum of the over-fire air angle is conducive to weakening the residual rotation at the furnace outlet. After the implementation of the reconstruction measures, the boiler can be stably burned at 150 MW, the combustible material of fly ash and slag are reduced to the controllable range, the steam thermal deviation is significantly reduced, and the boiler operating parameters are stable.

Localized Evaluation for Constructing Discrete Vector Fields.

Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. We couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.

Comparison of numerical and exact analyses in a neutron activation and decay chain

A method for solving a set of coupled linear first-order ordinary differential equations as it applies to neutron activation and subsequent radioisotope decay chains was developed that is easy to implement and accurate enough for most preliminary engineering design calculations. The method is applied to a specific radioisotope production scheme to evaluate the yield of the desired isotope as well as production of secondary and tertiary contaminant radioisotopes. An analytical closed-form solution was also derived for the same activation and decay chain to provide a basis for comparison; the analytical solution was benchmarked against several limiting cases to validate the equations. Results of the simulation involving the numerical approach were compared to the exact analytical solution. The numerical solution, while obviously not exact, is found to be close enough for engineering purposes. A discussion of the numerical precision of the result for the particular case are discussed.

On evanescent waves and blowing-ups of the finite series technique in spherical wave expansion of shaped beams

In generalized Lorenz-Mie theory, the beam shape coefficients of Gauss-like beams obtained with finite series method blow up when the wave order is high. The blowing-ups caused by the loss of significant digits may be suppressed by increasing numerical precisions. Once the elimination of such blowing-ups is carried out, blowing-up phenomena still occur whose origin is still not clear to us. The work presented here attempts to provide an explanation on this issue. Based on the angular spectrum representation of the beam field, it is found that the blowing-up originates from the contribution of evanescent waves.

Koios 2.0: Open-Source Deep Learning Benchmarks for FPGA Architecture and CAD Research

With the prevalence of deep learning (DL) in many applications, researchers are investigating different ways of optimizing FPGA architecture and CAD to achieve better quality-of-results (QoR) on DL-based workloads. In this optimization process, benchmark circuits are an essential component; the QoR achieved on a set of benchmarks is the main driver for architecture and CAD design choices. However, current academic benchmark suites are inadequate, as they do not capture any designs from the DL domain. This work presents the second version of our suite of DL acceleration benchmark circuits for FPGA architecture and CAD research, called Koios. This suite of 40 circuits covers a wide variety of accelerated neural networks, design sizes, implementation styles, abstraction levels, and numerical precisions. These benchmarks include 32 DL designs and 8 synthetic (proxy) benchmarks. The Koios benchmarks are larger, more data parallel, more heterogeneous, more deeply pipelined, and utilize more FPGA architectural features compared to existing open-source benchmarks. This enables researchers to pinpoint architectural inefficiencies for this class of workloads and optimize CAD tools on more representative benchmarks that stress the CAD algorithms in different ways. In this paper, we describe the Koios designs, compare their characteristics to prior FPGA benchmark suites, and present results of running them through the Verilog-to-Routing (VTR) flow using a recent FPGA architecture model. Finally, we present case studies showing how exploration of DL-optimized FPGA architecture and CAD algorithms can be performed using our new benchmark suite.

Assimilation of Additional Radiosonde Observation Helps Improve the Prediction of Typhoon-Related Rainfall in the Pearl River Delta

Abstract Typhoons frequently hit the Pearl River Delta (PRD), threatening the region’s dense population and assets. Typhoon precipitation forecasting in this region is challenging, in part because of the complex hydrometeorological effects over the coast and the scarcity of upstream marine meteorological observations. Typhoon Mun was formed in the South China Sea on 2 July 2019, and it brought heavy rainfall to the PRD when its center moved to the Beibu Gulf. During Typhoon Mun, an additional sounding was conducted offshore in the PRD every 12 h to assess the incremental impact on the skill of precipitation forecasting. A precipitation prediction based on the Weather Research and Forecasting (WRF) Model underestimated the 12-h accumulated precipitation over the PRD by 87%, with the Final Analysis (FNL) data from the National Centers for Environmental Prediction in the United States as initial fields. To address this issue, we implemented a solution by reconstructing the initial field through the assimilation of the additional radiosonde observations using the WRF three-dimensional variational (3D-Var) method. The prediction with the new initial fields reduced the rainfall underestimation by 24%. A difference analysis indicates that the planetary boundary layer scheme used in FNL underestimates the low-level temperature and humidity, especially after the rainfall peak. In contrast, assimilation gives a more realistic lower-tropospheric structure, significantly enhancing the moisture flux convergence around 925 hPa and divergence around 700 hPa around the PRD. Sensitivity experiments show that assimilating atmospheric thermal (i.e., temperature and humidity) profiles is more helpful than dynamic (wind) profiles in improving the rainfall prediction of the typhoon. Significance Statement The impact of typhoon-related precipitation in the Pearl River Delta (PRD) is significant. Improving the numerical forecast precision in this region poses challenges, partly due to the influences of land–sea thermal and topographic factors near the boundary layer, as well as the scarcity of upstream observational data. This study proposes a practical method to improve typhoon-related precipitation prediction from a case study of Typhoon Mun. By assimilating additional sounding observations, we obtain a more realistic structure of the lower atmosphere, better spatial patterns of water vapor fluxes, and, ultimately, better precipitation forecasts. The results of our study suggest that a more advanced observing system of vertical atmospheric structure, especially the thermal one, over the South China Sea is important for improving typhoon predictions.

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60Co (Type M) and 131I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method (expm). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

To be precise (imprecise) in utilitarian (hedonic) contexts: Examining the influence of numerical precision on consumer reactions to artificial intelligence‐based recommendations

AbstractThe precision of artificial intelligence (AI)‐generated information has been suggested in the past as a method of nudging consumers' evaluations and intentions, but little is known about whether such effects are also context‐sensitive. Based on four studies, we find a matched condition under which consumers are more likely to make a positive response when precise (imprecise) numbers presented by AI recommenders are used in a utilitarian (hedonic) consumption context (Study 1). Additionally, we show that consumer conceptual fluency also mediates this matching effect on consumer purchase decision‐making (Studies 2). We further show the matching effect is moderated by the recommender type (Study 3) and consumer lay beliefs about the AI and human recommenders (Study 4). This study shows that when consumers' lay belief changes from “AI performs objective tasks well” and “Human performs subjective tasks well” to “AI performs subjective tasks well” and “Human performs objective tasks well,” it can change the difference in the matching relationship between human and AI recommenders.

Blowing-ups of beam shape coefficients of Gaussian beams using finite series in generalized Lorenz–Mie theory

Compact closed-form expressions of the beam shape coefficients (BSCs) of Gaussian beams are obtained in the generalized Lorenz–Mie theory through the finite series (FS) method. As a result, such expressions have made it possible to more deeply understand the behaviour of the BSCs and, therefore, the scattering of Gaussian beams beyond the paraxial approximation. The blowing up, in particular, of FS BSCs which has been observed for several paraxial beams is now mathematically justified as a phenomenon that is independent of numerical precision. Furthermore, numerical results demonstrate how such blow ups are related to the ratio between the beam waist radius and its wavelength.

Curl condition: Existence of sub‐Hilbert space for molecular species or chemical processes

AbstractThe “accuracy” of diabatic Hamiltonian matrix elements solely depends on the level of ab initio calculation and on the included set of coupled electronic manifold forming a “true” sub‐Hilbert space (SHS). If ab initio calculations are performed with enough accuracy, existence of SHS can be validated only when the Curl Condition attains zero within numerical precision. For the first time, we depict a theoretical and algorithmic formulation on the calculation of Curl Condition to demonstrate the existence of SHS on molecular processes or chemical reactions.

ADRC for a piezoelectric plate with delays and disturbances via frequency response method: Design, analysis and experiments

A large number of uncertainties such as external excitement, model parameter perturbation, complex boundary conditions, time delays, seriously impact the operation of the piezoelectric plate structure. Therefore, an active disturbance rejection controller is designed and implemented based on an extended state observer to address such issues. The controller designed is analyzed in frequency-domain to address the time delays introduced by the sensors, actuators, communicational networks, computational delays, etc. Knowing that the accurate models are difficult to build, the Lissajous graphics and frequency test methods, hence, are implemented to estimate the delay and model parameters of the system. The stability characteristics and performance are verified via two intuitive frequency response methods, the small gain theorem and the Nyquist diagram. Bedsides, the relationship between time delays and control parameters is quantified, which enables controller parameters to be adjusted according to frequency index. This is the first attempt to use the small-gain theorem, which is favored for its numerical precision and computational efficiency, to analyze the active disturbance rejection control of time-delay systems. A case of a disturbed all-clamped piezoelectric plate with delays is, in particular, tested under a hardware-in-the-loop benchmark. Theoretical and experimental results show the effectiveness of the proposed approach to suppress the structure vibration in the presence of delays and disturbances.

Rate and memory effects in bifurcation-induced tipping.

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution, or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exchange occurs at a parameter value beyond the bifurcation value. This is what we call, here, the shifted stability exchange. We perform a systematic study on how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical simulations and partly analytical results for different types of bifurcations and different paradigmatic systems. We show that the nonautonomous dynamics can be split into two regimes. Depending on whether we exceed the numerical or experimental precision or not, the system may enter the nondeterministic or the deterministic regime. This is determined solely by the conditions of the drift. Finally, we deduce the scaling laws governing this phenomenon and we observe very similar behavior for different systems and different bifurcations in both regimes.

Discrete-Time Frequency-Domain Disturbance Observer to Mitigate Harmonic Current in PMSM Drives and the Implementation With Reduced Delay

The disturbance observer (DOB) can be employed in electric drives to improve disturbance rejection. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -filter of classical frequency-domain DOBs to attenuate multiple harmonic disturbances is high-order and faces issues including discretization, numerical precision, and frequency adaption, thus its realization in variable-speed drives would be challengeable. This paper proposes a discrete-time multi-frequency DOB (MFDOB) to address these issues. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -filter of the proposed design is constructed with an integrator and several parallel resonators in a closed-loop structure. It uses a single parameter per harmonic to control the disturbance rejection bandwidth and the performance is guaranteed under various fundamental frequencies. The impact of the computation delay on the MFDOB-based current control is studied, and the system with less computation delay exhibits a higher stability margin and a wider range of low sensitivity. To eliminate the computation delay, a real-time pulse-width-modulation (PWM) update scheme is also developed for the DOB-based two-degree-of-freedom (2DOF) controller. The proposed method is evaluated on a laboratory permanent magnet synchronous machine platform.

Research on spot market price forecasting method considering the electricity‐purchase gain for demand side

AbstractThe clearing price in electricity spot market is an important reference guiding market participants to purchase energy. Current electricity price forecasting methods mainly focus on improving numerical accuracy, and the need to optimize economic benefits is ignored. However, higher numerical precision sometimes leads to lower electricity‐purchase gain. To deal with that, this paper proposes a price forecasting method that optimizes economic benefits together with numerical accuracies. A revenue‐optimizing term evaluating the relationship between the predicted price and the cost reference price is introduced to the loss function of the prosumers’ forecasting model. A sequence comparison neural network structure is proposed and added to consumers’ model, so the forecasting model is trained by also considering price trend. By co‐optimizing numerical precision and electricity‐purchase gain, the prediction is more conducive to reducing the cost of purchasing power. Price data in actual electricity market are used to verify the feasibility and improvement of the proposed method.

Two-grid algorithms based on FEM for nonlinear time-fractional wave equations with variable coefficient

In this paper, a fully discrete finite element scheme is established with L1 approximation for solving the nonlinear time-fractional wave equation with a variable coefficient. The stability of the scheme is analyzed and the optimal error estimates are derived. To improve the computational efficiency, we propose a two-grid algorithm based on the fully discrete finite element scheme. With the proposed technique, a small-scale nonlinear problem is calculated by iteration in a coarse-grid space with mesh size H, and then a linearized problem is solved in a fine-grid space with mesh size h, H≫h. This technique not only maintains the numerical precision, but also saves a lot of computing time. The stability and optimal convergence order are considered. Using the Taylor expansion, the second two-grid algorithm is constructed to improve the optimal convergence order. The similar properties are discussed in detail. Numerical experiments are provided to illustrate the theoretical analysis and test the performance of the proposed algorithms.

An overview of a posteriori error estimation and post-processing methods for nonlinear eigenvalue problems

In this article, we present an overview of different a posteriori error analysis and post-processing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising in electronic structure calculations for the calculation of the ground state and compare them. We provide two equivalent error reconstructions based either on a second-order Taylor expansion of the minimized energy, or a first-order expansion of the nonlinear eigenvalue equation. We then show how several a posteriori error estimations as well as post-processing methods can be formulated as specific applications of the derived reconstructed errors, and we compare their range of applicability as well as numerical cost and precision.

Isotropic and anisotropic mesh adaptation for RANS simulations of a nacelle under crosswind conditions

Mesh adaptation of unstructured meshes for aerodynamic simulations, that typically resolve the Reynolds Averaged Navier-Stokes (RANS) equations, is a promising approach to enable high numerical precision on complex geometries. Its objective is to minimize the discretization error without using empirical meshing guidelines. The most common approach of mesh adaptation is the “feature-based” isotropic mesh adaptation: from an initial flow prediction on an isotropic unstructured mesh, a local error estimator is computed using a flow variable. It is then used to adapt the mesh using isotropic tetrahedra. Additional near-wall resolution can be achieved by extruding prism layers from the walls. A more efficient approach is to use anisotropic mesh adaptation purely with tetrahedra that are stretched to follow the flow's preferential directions. In this work, we demonstrate the abilities of feature-based isotropic and anisotropic mesh adaptation on a complex flow phenomenon of importance for jet engines: flow separation in a nacelle under crosswind conditions. Two different solvers, adapted for either isotropic or anisotropic meshes, are employed. Results are compared with standard unstructured simulations with user-imposed mesh refinements and highlight the ability of mesh adaptation to automatically capture all the relevant flow phenomena without any user input and at reduced mesh size.

Constant advance replicas method for locating minimum energy paths and transition states.

The chain-of-states (CoS) constant advance replicas (CAR) method and its climbing image variant (CI-CAR) for locating minimum energy paths (MEPs) and transition states are reported. The CAR algorithm applies the Lagrange multiplier method for imposing holonomic constraints on a chain-of-replicas, aiming to maintain equal mass-weighted/scaled root-mean-square (RMS) distances between the adjacent replicas by removing the sliding-down displacements contributed by the potential gradients during path optimization. Two contextual regularization schemes with clear geometrical interpretations are implemented to jointly promote high convergence and numerical robustness of the CAR algorithm. We show that the constrained reaction path can be solved normally within 5 steps of Lagrange multiplier updates with remarkably high numerical precision via the CAR approach. The efficacy of the CAR methods is demonstrated by testing on multiple analytical, classical, and quantum mechanical transition paths: the Müller potential, the alanine dipeptide isomerization, the helix unwinding of the VIVITLVMLKKK 12-mer peptide, and the Baker set of reactions. We also explore the potential of applying adaptive momentum (AdaM) optimizers for locating optimal transition paths under complex conformational changes. Most importantly, we discuss extensively the differences and connections between our newly proposed CAR methods and several related methods, with focuses on the reaction path with holonomic constraints (RPCons) approach of Brokaw et al. [J. Chem. Theory Comput. 2009, 5 (8), 2050-2061] and the state-of-the-art string method (SM) of E et al. [J. Chem. Phys. 2007, 126 (16), 164103]. The CAR approach represents a latest update to the general theoretical framework of reaction path finding algorithms in the two-ended CoS regime.

A data-driven persistence test for robust (probabilistic) quality control of measured environmental time series: constant value episodes

Abstract. Robust quality control is a prerequisite and an essential component in any data application. That is especially important for time series of environmental observations such as air quality due to their dynamic and irreversible nature. One of the common issues in these data is constant value episodes (CVEs), where a set of consecutive data values remains constant over a given period. Although CVEs are often considered to be an indicator of sensor failure or other measurement errors and are removed during quality control procedures, there are situations when CVEs reflect natural environmental phenomena, and they should not be removed from the data or analysis. Assessing whether the CVEs are erroneous data or valid observations is a challenge. As there are no formal procedures established for this, their classification is based on subjective judgment and is therefore uncertain and irreproducible. This paper presents a novel test procedure, i.e., constant value test, to estimate the probability of CVEs being valid data. The theoretical foundation of this test is based on statistical characteristics and probability theory and takes into account the numerical precision of the data values. The test is a data-driven (parametric) approach, which makes it usable for time series analysis in different environmental research domains, as long as serial dependency is given and the data distribution is not too different from Gaussian. The robustness of the test was demonstrated with sensitivity studies using synthetic data with different distributions. Example applications to measured air temperature and ozone mixing ratio data confirm the versatility of the test.