High-precision Calculations Research Articles

Self-aware face emotion accelerated recognition algorithm: a novel neural network acceleration algorithm of emotion recognition for international students.

With an increasing number of human-computer interaction application scenarios, researchers are looking for computers to recognize human emotions more accurately and efficiently. Such applications are desperately needed at universities, where people want to understand the students' psychology in real time to avoid catastrophes. This research proposed a self-aware face emotion accelerated recognition algorithm (SFEARA) that improves the efficiency of convolutional neural networks (CNNs) in the recognition of facial emotions. SFEARA will recognize that critical and non-critical regions of input data perform high-precision computation and convolutive low-precision computation during the inference process, and finally combine the results, which can help us get the emotional recognition model for international students. Based on a comparison of experimental data, the SFEARA algorithm has 1.3× to 1.6× higher computational efficiency and 30% to 40% lower energy consumption than conventional CNNs in emotion recognition applications, is better suited to the real-time scenario with more background information.

The Standard Model Theory of Neutron Beta Decay

We review the status of the Standard Model theory of neutron beta decay. Particular emphasis is put on the recent developments in the electroweak radiative corrections. Given that some existing approaches give slightly different results, we thoroughly review the origin of discrepancies, and provide our recommended value for the radiative correction to the neutron and nuclear decay rates. The use of dispersion relation, lattice Quantum Chromodynamics, and an effective field theory framework allows for high-precision theory calculations at the level of 10−4, turning neutron beta decay into a powerful tool to search for new physics, complementary to high-energy collider experiments. We offer an outlook to the future improvements.

Application of the Improved Entry and Exit Method in Slope Reliability Analysis

The entry and exit method is a simple and practical method to decide the critical slip surface of slope. Nevertheless, it has the drawback of sacrificing computational efficiency to improve search accuracy. To solve this problem, this paper proposes an improved entry and exit approach to search for the critical slip surface. On basis of the random fields produced by applying the Karhunen–Loève expansion approach, the simplified Bishop’s method combined with the improved entry and exit method is used to decide the critical slip surface and its relevant minimum factor of security. Then, the failure probability is calculated by conducting Monte Carlo simulation. Two instances are reanalyzed to validate the precision and efficiency of the method. Meaningful comparisons are made to show the calculating precision and calculating efficiency of the improved entry and exit method in searching for the minimum security factor of slope, based on which the effect of the reduced searching range on slope reliability was explored. The outcomes suggest that the approach offers a practical device for assessing the reliability of slopes in spatially variable soils. It can significantly enhance the computational efficiency in relatively high-computational precision of slope reliability analysis.

Analysis of the ammunition explosion seismic wave propagation law

The seismic wave generated in the ammunition explosion process is one of the important technical indicators to evaluate the ammunition damage power. It is of great significance to evaluate the ammunition damage power and study the targets damage characteristics. In this study, experimental studies were carried out with TNT explosive mass of 1.25 kg, 5.25 kg, 10.5 kg and 30.75 kg, and the ground vibration velocity time-history curves at different measuring points were obtained. The functional relationship between ground particle vibration acceleration and TNT explosive mass was established by dimensional analysis method, and the functional relationship calculation accuracy was verified by the measured test data. The results show that the particle vibration acceleration peak value is positively correlated with the TNT explosive mass, and negatively correlated with the measuring point distance; The particle vibration acceleration calculation function established by the dimensional analysis method has high fitting accuracy for the existing test data, and can be used to calculate the ammunition explosion ground vibration acceleration peak value. The research results provide a high-precision calculation method for the peak value of explosion seismic wave ground vibration acceleration.

Extreme field calculations for Penning ion traps and corresponding strong laser field scenarios

The extreme forces of highly charged ions and their trapping within high-precision experimental devices allow for challenging fundamental theories in yet unexplored territory. Here we focus on the theoretical side employing ab initio fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods to precisely calculate the bound-state energies of complex atoms and ions, as well as on presenting state-of-the-art high-precision g-factor calculations. In combination with similarly accurate experiments, one can competitively determine fundamental constants like the masses of the neutrino and the electron as well as setting new limits for physics beyond the standard model. Scenarios involving extreme laser pulses hold comparable potential but still require especially advances in the precision of the associated experiments.

Effect of Magnesium Substitution on Structural Features and Properties of Hydroxyapatite.

Hydroxyapatite (HAP) is the main mineral component of bones and teeth. It is widely used in medicine as a bone filler and coating for implants to promote new bone growth. Ion substitutions into the HAP structure highly affect its properties. One of the most important substituents is magnesium. This paper presents new results obtained using high-precision hybrid density functional theory calculations for Mg/Ca substitutions in HAP in a wide magnesium concentration range within a 2 × 2 × 2 supercell model. Experimental data on the mechanochemical synthesis of HAP-Mg samples with different Mg concentrations are also presented. A comparison between the experiment and the theory showed good agreement: the HAP-Mg unit cell parameters and volume decreased with increasing degree of Mg/Ca substitution. The changes in the distances between the Ca and O, Ca and H, and Mg and O ions upon Mg/Ca substitution in different calcium positions was analyzed. The resulting asymmetry and distortion of the cell parameters were evaluated. It was shown that bulk modulus, energy levels, and band gap depend on the degree of Mg substitutions in the Ca1 and Ca2 positions. The formation energies of Mg/Ca substitutions showed non-monotonic behavior that was different for Ca1 and Ca2 positions. The Ca2 position had a slightly higher probability (~5 meV/f.u.) of substitution than Ca1 position at a Mg concentration x = 0.5. At x = 1, substitution in both positions can coexist. The simulated IR spectra for different Mg/Ca substitutions showed that Mg in the Ca2 position changes the IR spectrum more significantly than Mg in the Ca1 position. Similar changes were recorded in the IR spectra of the synthesized samples. The electronic structure is shown to be sensitive to the number and position of substitutions, which may be used to tweak the optical properties of the HAP-Mg material.

Multi-physics coupling simulation of small mobile nuclear reactor with finite element-based models

This paper describes the multi-physics coupling simulation of a small transportable nuclear reactor, SIMONS, using the neutronics/thermo-mechanics coupling three-dimensional high-fidelity code platform FEMAS (FEM-based Multiphysics Analysis Software for Nuclear Reactor). FEMAS builds multi-physics field models utilizing the open-source finite element codes deal.II and FEniCS. Using coupling simulations of neutronics, thermal-conduction, and thermo-mechanics, the SIMONS micro mobile reactor is examined. For the generation of cross-sections libraries, the open-source Monte Carlo code OpenMC is utilized, and the (n,xn) correction and SPH method is developed to maintain neutron equilibrium and eliminate homogenization errors. The approaches yield neutronic solutions that are in good agreement with the reference solutions, as the keff error decreases from 5066 pcm to 7.2 pcm and the maximum relative power error decreases from 5.2% to 0.3%. With a thermal power of 240 kW, the local temperature difference of the entire reactor is 354.68 K, and the deformation rate due to thermal stress is 2.4%, resulting in a reactivity feedback of 4459.6 pcm. At the wall in contact with the outermost fuel rods, where the temperature gradient grows substantially and thermal stress rises, the monolith stress is measured to peak at 9.65 MPa. This research has paved the way for a more thorough multi-physics examination of micro nuclear reactors in the era of high-precision computation.

Deep learning-driven super-resolution reconstruction of two-dimensional explosion pressure fields

Precise and rapid calculation of explosive loads on structures in specific explosion scenarios is crucial for blast-resistant design, emergency response and safety assessments of structures after disasters. However, available methods such as empirical models and numerical simulations are inadequate in meeting the fast computation demands for diverse explosion scenarios due to limitations in accuracy or computational cost. In order to obtain high-precision explosion pressure fields and overpressure time histories with low computational cost, this study presents a deep learning-based framework for reconstructing two-dimensional explosion pressure fields, which transforms low-resolution numerical simulation results into super-resolution outputs equivalent to high-resolution numerical simulation results. A super-resolution strategy, which concatenates high-resolution channels that record flow field information with the low-resolution channel, is proposed to improve the network performance. Based on the constructed dataset, a comparative study of three different networks is presented to assess their super-resolution applicability. Finally, the performance and generalization ability of the trained model is evaluated with super-resolution evaluation metrics, statistical evaluation metrics, and relative error distribution. The findings indicate that the super-resolution strategy can effectively improve the prediction accuracy of the network. The super-resolution model can not only provide high-credibility super-resolution pressure fields and pressure time histories, but also exhibits excellent generalization capabilities for explosive scenarios beyond the training dataset, therefore providing a new approach for realizing high-precision calculation of explosive flow fields and loads under diverse blast scenarios.

Research and Hardware Implementation of a Reduced-Latency Quadruple-Precision Floating-Point Arctangent Algorithm

In the field of digital signal processing, such as in navigation and radar, a significant number of high-precision arctangent function calculations are required. Lookup tables, polynomial approximation, and single/double-precision floating-point Coordinate Rotation Digital Computer (CORDIC) algorithms are insufficient to meet the demands of practical applications, where both high precision and low latency are essential. In this paper, based on the concept of trading area for speed, a four-step parallel branch iteration CORDIC algorithm is proposed. Using this improved algorithm, a 128-bit quad-precision floating-point arctangent function is designed, and the hardware circuit implementation of the arctangent algorithm is realized. The results demonstrate that the improved algorithm can achieve 128-bit floating-point arctangent calculations in just 32 cycles, with a maximum error not exceeding 2×10−34 rad. It possesses exceptionally high computational accuracy and efficiency. Furthermore, the hardware area of the arithmetic unit is approximately 0.6317 mm2, and the power consumption is about 40.6483 mW under the TSMC 65 nm process at a working frequency of 500 MHz. This design can be well suited for dedicated CORDIC processor chip applications. The research presented in this paper holds significant value for high-precision and rapid arctangent function calculations in radar, navigation, meteorology, and other fields.

One-loop gauge invariant amplitudes with a space-like gluon

Nowadays the particle physics has entered an era where high precision calculations are required in order to compare the theoretical predictions with the experimental data. In this paper, we explicitly compute the virtual contributions for the space-like one-jet processes, ∅→g⋆gg,∅→g⋆qq¯,∅→g⋆gH and ∅→g⋆q¯qe+e− within the auxiliary parton method. Our results, which are expected to play an important role in high precision description of small x physics, explicitly confirm the conjecture developed in Ref. [1], thus helping to bridge the gap between lowest order calculations and NLO corrections within hybrid kT-factorization scheme.

Guided Intelligent Hyper-Heuristic Algorithm for Critical Software Application Testing Satisfying Multiple Coverage Criteria

This paper proposes a novel algorithm that combines symbolic execution and data flow testing to generate test cases satisfying multiple coverage criteria of critical software applications. The coverage criteria considered are data flow coverage as the primary criterion, software safety requirements, and equivalence partitioning as sub-criteria. black The characteristics of the subjects used for the study include high-precision floating-point computation and iterative programs. The work proposes an algorithm that aids the tester in automated test data generation, satisfying multiple coverage criteria for critical software. The algorithm adapts itself and selects different heuristics based on program characteristics. The algorithm has an intelligent agent as its decision support system to accomplish this adaptability. Intelligent agent uses the knowledge base to select different low-level heuristics based on the current state of the problem instance during each generation of genetic algorithm execution. The knowledge base mimics the expert’s decision in choosing the appropriate heuristics. black The algorithm outperforms by accomplishing 100% data flow coverage for all subjects. In contrast, the simple genetic algorithm, random testing and a hyper-heuristic algorithm could accomplish a maximum of 83%, 67% and 76.7%, respectively, for the subject program with high complexity. black The proposed algorithm covers other criteria, namely equivalence partition coverage and software safety requirements, with fewer iterations. black The results reveal that test cases generated by the proposed algorithm are also effective in fault detection, with 87.2% of mutants killed when compared to a maximum of 76.4% of mutants killed for the complex subject with test cases of other methods.

Low-lying electronic states of osmium monoxide OsO

The ground state of osmium monoxide (OsO) has long been controversial. In this paper, the low-lying Λ–S and Ω electronic states of OsO have been comprehensively studied by the high-precision multi-reference calculations. The ground state of OsO is unexpectedly the closed-shell 1Σ+ state with a double bond instead of the previously reported 3Φ or 5Σ+ state; after including the spin–orbit coupling effects, the ground state becomes 3Π2. With the help of the theoretical spectroscopic constants and transition dipole moments, the emission spectra in the region of 405 nm–875 nm are assigned. Our results will facilitate the future studies of absorption and emission spectra of OsO.

Optimisation of layered shell model for analysis of reinforced concrete shear walls based on machine learning

Layered shell modelling is an effective tool for the efficient simulation of two-dimensional structural members. As machine learning (ML) provides a novel alternative for the optimisation analysis of the traditional layered shell model, it has been widely used in civil engineering applications. This study focuses on the accurate numerical simulation of reinforced concrete (RC) shear wall structures using the ML method. The user subprogram interface HYPELA2 based on the implicit solver of Marc software was compiled to implement a program package to consider the precise constitutive model of concrete. Additionally, different ML methods and loss functions were compared, and the adopted optimisation method was based on the particle swarm optimisation and L1 loss function. The analysis of constitutive parameters was realised according to the optimisation of the ML algorithm. Multiple numerical models were used to verify the stability and accuracy of the proposed layered shell model and ML method. Finally, the results obtained from comprehensive experimental research and numerical simulations were used to determine the recommended values of parameters for finite element analysis of RC shear walls to produce a novel high-precision, efficient, and universal calculation model.

MFFT: A GPU Accelerated Highly Efficient Mixed-Precision Large-Scale FFT Framework

Fast Fourier transform (FFT) is widely used in computing applications in large-scale parallel programs, and data communication is the main performance bottleneck of FFT and seriously affects its parallel efficiency. To tackle this problem, we propose a new large-scale FFT framework, MFFT, which optimizes parallel FFT with a new mixed-precision optimization technique, adopting the “high precision computation, low precision communication” strategy. To enable “low precision communication”, we propose a shared-exponent floating-point number compression technique, which reduces the volume of data communication, while maintaining higher accuracy. In addition, we apply a two-phase normalization technique to further reduce the round-off error. Based on the mixed-precision MFFT framework, we apply several optimization techniques to improve the performance, such as streaming of GPU kernels, MPI message combination, kernel optimization, and memory optimization. We evaluate MFFT on a system with 4,096 GPUs. The results show that shared-exponent MFFT is 1.23 × faster than that of double-precision MFFT on average, and double-precision MFFT achieves performance 3.53× and 9.48× on average higher than open source library 2Decomp&FFT (CPU-based version) and heFFTe (AMD GPU-based version), respectively. The parallel efficiency of double-precision MFFT increased from 53.2% to 78.1% compared with 2Decomp&FFT, and shared-exponent MFFT further increases the parallel efficiency to 83.8%.

High-precision calculation and experiments on the thermal blooming of high-energy lasers.

Thermal blooming (TB) is one of the important factors affecting the quality of high-energy laser beams. Reasonable simulation of thermal blooming is important to the application of a high-energy laser. However, reported investigations on TB simulation are mainly based on one method, such as the perturbation method or the phase screen method, which often leads to obvious errors in some conditions. In the paper, the reasonable ranges of optical generalized distortion parameters for both methods are determined based on the reported experimental data, which solves the problem of accurate TB simulations for the first time. In addition, the dynamic effect of thermal blooming is also calculated. Finally, the formula method is presented to extract the phase of thermal blooming distortion. We then use LC-SLM (Liquid crystal spatial light modulator) to emulate thermal blooming effect in the lab. The experimental results are more consistent with the numerical simulation results than conventional phase extraction methods. Our work provides a quantitatively and programmable way to accurately simulate TB with LC-SLM in the lab.

QPA: A Quantization-Aware Piecewise Polynomial Approximation Methodology for Hardware-Efficient Implementations

Piecewise polynomial approximation (PPA) on nonlinear functions plays an important role in high-precision computing. In this article, we proposed QPA, an integration of error-flattened quantization-aware PPA methods, to generate the optimized coefficients for efficient hardware implementations targeting any polynomial order. QPA incorporated four key features to minimize the fitting error and the hardware cost, including using the Remez algorithm to compute the minimax fitting polynomial, combining the fitting and quantization operations to get an error-flattened characteristic, assigning specific coefficient bit width to each multiplier to reduce the hardware cost, and fine-tuning the truncated coefficients to further reduce the fitting error. Experimental results showed that our methods consistently achieved the lowest fitting error compared with the state-of-the-art error-flattened piecewise approximation methods. We synthesized the proposed designs with 28-nm TSMC CMOS technology. The results showed that the proposed designs achieved up to 37.0% area reduction and 50.5% power consumption reduction compared to the state-of-the-art error-flattened piecewise linear (PWL) method, and up to 27.0% area reduction, 21.4% delay reduction, and 20.8% power consumption reduction compared to the state-of-the-art error-flattened piecewise quadratic (PWQ) method.

Model-dependent analysis method for energy budget of the cosmological first-order phase transition

The kinetic energy of the fluid shell in the cosmological first-order phase transition is crucial for predicting the gravitational wave signals generated by the sound wave mechanism. We propose a model-dependent method to calculate the kinetic energy fraction by dividing the bubble-fluid system into three distinct regions: the symmetric phase, the broken phase, and the bubble wall. By solving the local equation of motion of the scalar field with a phenomenological friction term, the bubble wall velocity and the boundary conditions of the fluid equations of both phases can be derived simultaneously. Then, for a given particle physics model, the fluid profiles of different hydrodynamical modes and the corresponding kinetic energy fraction can be obtained. Our method can also capture the temperature dependency of the sound speed of the plasma. Compared with the conventional model-independent method, our approach is based on an accurate equation of state derived directly from the effective potential and takes into account the contribution of the bubble wall to the energy-momentum tensor. Therefore, our method in-principle provides a more consistent and accurate result, which is crucial for high-precision calculations of the gravitational waves induced by the first-order phase transition.

Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code

In this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schrödinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used for nonlinear problems. The semi-global algorithm is briefly presented, the C++ implementation is described and five sample simulations are shown. The accompanying C++ source code package is included. The high precision benchmark (long double and float128) shows the estimated calculation costs. The presented method turns out to be faster and more accurate than the global Chebyshev propagator. Program summaryProgram Title: SemiGlobalCppCPC Library link to program files:https://doi.org/10.17632/429rszyc65.1Developer's repository link:http://gitlab.com/cosurgi/SemiGlobalCppLicensing provisions: GNU General Public License 2Programming language: C++Nature of problem: The femto- and attosecond chemistry requires fast and high precision computation tools for quantum dynamics. Conventional software has problems with providing high precision calculation results (up to 33 significant digits), especially when the computation has to be as fast as possible.Solution method: This software fills in the gap by providing the semi-global algorithm [1–3] for arbitrary number of coupled electronic states for the time dependent Hamiltonian and nonlinear inhomogeneous source term. It is implemented in a way that allows computation with precision of 15, 18 or 33 significant digits, where the computation speed can be directly controlled by setting the required error tolerance. The semi-global algorithm [1–3] is implemented in C++ providing a 10× speed boost compared to original publication of semi-global algorithm implemented in Matlab/Octave [1–3].

Accuracy of a Recent Regularized Nuclear Potential.

F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [Gygi J. Chem. Theory Comput. 2023, 19, 1300-1309.]. This potential V(r) is determined by inverting the Schrödinger equation for the wave function Ansatz ϕ(r) = exp[-h(r)]/√π with h(r) = r erf(ar) + b exp(-a2r2), where a and b are parameters. Gygi fixes b by demanding ϕ to be normalized, with the value b(a) depending on the strength of the regularization controlled by a. We begin this work by re-examining the determination of b(a) and find that the original 10-decimal tabulations of Gygi are only correct to 5 decimals, leading to normalization errors in the order of 10-10. In contrast, we show that a simple 100-point radial quadrature scheme not only ensures at least 10 correct decimals of b but also leads to machine-precision level satisfaction of the normalization condition. Moreover, we extend Gygi's plane-wave study by examining the accuracy of V(r) with high-precision finite element calculations with Hartree-Fock and LDA, GGA, and meta-GGA functionals on first- to fifth-period atoms. We find that although the convergence of the total energy appears slow in the regularization parameter a, orbital energies and shapes are indeed reproduced accurately by the regularized potential even with relatively small values of a, as compared to results obtained with a point nucleus. The accuracy of the potential is furthermore studied with s-d excitation energies of Sc-Cu as well as ionization potentials of He-Kr, which are found to converge to sub-meV precision with a = 4. The findings of this work are in full support of Gygi's contribution, indicating that all-electron plane-wave calculations can be accurately performed with the regularized nuclear potential.

Electric-dipole transition amplitudes for atoms and ions with one valence electron

Motivated by recent measurements for several alkali-metal atoms and alkali-metal-like ions, we perform a detailed study of electric dipole ($E1$) transition amplitudes in K, $\mathrm{Ca}{}^{+}$, Rb, $\mathrm{Sr}{}^{+}$, Cs, $\mathrm{Ba}{}^{+}$, Fr, and $\mathrm{Ra}{}^{+}$, which are of interest for studies of atomic parity violation, electric dipole moments, and polarizabilities. Using the all-orders correlation potential method, we perform high-precision calculations of $E1$ transition amplitudes between low-lying $s, p$, and $d$ states. We perform a robust error analysis, and compare our calculations to many amplitudes for which there are high-precision experimental determinations. We find excellent agreement, with deviations at the level of $\ensuremath{\sim}0.1$%. We also compare our results to other theoretical evaluations, and discuss the implications for uncertainty analyses. Further, combining calculations of branching ratios with recent measurements, we extract high-precision values for several $E1$ amplitudes of $\mathrm{Ca}{}^{+}, \mathrm{Sr}{}^{+}$, Cs, Fr, and $\mathrm{Ra}{}^{+}$.