Reduction In CPU Time Research Articles

Analysis of The Influence of Models of Individual Physical Processes and Phenomena on the Calculation Time of the Source Term in Severe Accidents

Dependence of the CPU time needs for calculation of the source term during a severe accident at nuclear power plants with WWER reactors from the individual physical processes and phenomena used as part of the calculation tools similar to the SOСRAT/V3 severe accident code is investigated. This analysis allows revealing the most expensive models in terms of runtime. The simplification of these models can ensure the greatest acceleration of the calculation. The relevance of the task draws from the need to develop new or adapt existing calculation tools for assessing the intensity of radioactive emission sources for the tasks of emergency preparedness and response considering the specific requirements for the accuracy of numerical estimates and time to obtain them. The paper demonstrates the possibility of reducing CPU time without significant loss of accuracy of the numerical estimates by simplifying the spectrum of aerosols sizes. The efficiency of the proposed approach is demonstrated by the example of modeling the Phebus FPT1 experiment.

Improving the computational performance of district heating network simulation

ABSTRACT District heating and cooling (DHC) systems are gaining importance due to their ability to integrate renewable and waste heat sources and connect with other infrastructures. However, the complexity of DHC systems rises as technical components and potential interactions grow, and energy demands increase. Heat transportation via water flow involves time- and temperature-dependent changes based on mass flow rates and heat losses, influenced by the dynamic properties of consumers and distribution pipes. To optimise DHC operations and simulate their complexities, dynamic modelling tools are necessary. However, dynamically simulating large-scale DHC networks are computationally demanding. One method to improve district heating networks (DHNs) is to replace dynamic pipe models with static models, simplifying the network's topological complexities. This paper proposes a framework for simulating DHNs using the NetworkX Python package to create and manipulate complex networks and the Modelica environment to simulate physical systems. The study highlights the constraints of the pipe replacement workflow due to its dependence on seasonal variation. The findings indicate that replacing pipe models can reduce CPU time by 30% to 65% in simulations, depending on the required accuracy during the summer season.

A cortical surface template for human neuroscience

Neuroimaging data analysis relies on normalization to standard anatomical templates to resolve macroanatomical differences across brains. Existing human cortical surface templates sample locations unevenly because of distortions introduced by inflation of the folded cortex into a standard shape. Here we present the onavg template, which affords uniform sampling of the cortex. We created the onavg template based on openly available high-quality structural scans of 1,031 brains—25 times more than existing cortical templates. We optimized the vertex locations based on cortical anatomy, achieving an even distribution. We observed consistently higher multivariate pattern classification accuracies and representational geometry inter-participant correlations based on onavg than on other templates, and onavg only needs three-quarters as much data to achieve the same performance compared with other templates. The optimized sampling also reduces CPU time across algorithms by 1.3–22.4% due to less variation in the number of vertices in each searchlight.

Model order reduction in parallel of discrete-time linear systems based on Meixner and Krawtchouk polynomials

Abstract In this paper, based on the partition technique, we use Meixner and Krawtchouk polynomials to present an input-independent model order reduction method. Our main contributions are twofold. First, the explicit difference relations of Meixner polynomials and Krawtchouk polynomials are expressed in an unified form. The parallel computation is carried out on the partitioned subsystems using the Krylov subspaces by which one can generate reduced systems independent of the expansion coefficients of input and can save the computation time. Second, a parallel adaptive enrichment strategy is used to choose the reduced order of reduced systems. Theoretical analysis shows that the proposed method characterizes the property of invariable coefficients. Finally, two numerical examples demonstrate that the proposed method achieves good reduction results in terms of accuracy and reduced CPU time.

GE 2 : A General and Efficient Knowledge Graph Embedding Learning System

Graph embedding learning computes an embedding vector for each node in a graph and finds many applications in areas such as social networks, e-commerce, and medicine. We observe that existing graph embedding systems (e.g., PBG, DGL-KE, and Marius) have long CPU time and high CPU-GPU communication overhead, especially when using multiple GPUs. Moreover, it is cumbersome to implement negative sampling algorithms on them, which have many variants and are crucial for model quality. We propose a new system called GE 2 , which achieves both <u>g</u>enerality and <u>e</u>fficiency for <u>g</u>raph <u>e</u>mbedding learning. In particular, we propose a general execution model that encompasses various negative sampling algorithms. Based on the execution model, we design a user-friendly API that allows users to easily express negative sampling algorithms. To support efficient training, we offload operations from CPU to GPU to enjoy high parallelism and reduce CPU time. We also design COVER, which, to our knowledge, is the first algorithm to manage data swap between CPU and multiple GPUs for small communication costs. Extensive experimental results show that, comparing with the state-of-the-art graph embedding systems, GE 2 trains consistently faster across different models and datasets, where the speedup is usually over 2x and can be up to 7.5x.

Toward Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo.

We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N2 dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.

A POD based extrapolation DG time stepping space-time FE method for parabolic problems

Based on the proper orthogonal decomposition technique, a new reduced-order discontinuous time stepping space-time finite element extrapolation iterative scheme is constructed to solve two-dimensional parabolic problems, which includes very few degrees of freedom but holds sufficiently high accuracy. A reduced space-time projection operator is defined, and its related error estimations are discussed. Then, the error estimate between the classical scheme solution and the reduced-basis scheme solution, and the a priori error estimate for the reduced-basis scheme are derived, respectively. These error estimates are analyzed by using the technique of combining Radau quadrature rule with finite element method, without considering any dual problems. The algorithm implementation of the reduced-order extrapolation iterative scheme is also provided. Finally, a numerical example is presented. The numerical results are consistent with theoretical ones. Moreover, it is shown that the new reduced-order extrapolation iterative scheme, by comparing to the standard approach, can reduce CPU time without loss of accuracy. Therefore, it is feasible and efficient for solving parabolic problems.

First train timetabling and passenger transfer routing problems in urban rail transit networks

This paper incorporates the shortest passenger travel paths into the first train timetabling problem in urban rail transit networks. We first propose a path-based first train timetabling problem, which is formulated as a mixed-integer nonlinear programming model to reduce the travel time for passengers. To solve this model, we present a tailored branch-and-bound combined with the timetable-based Dijkstra algorithm. To further enhance the efficiency of the exact algorithm, we design a rolling time heuristic algorithm as a substitute for the branch-and-bound algorithm. Then, we proved that the rolling time heuristic combined with the timetable-based Dijkstra algorithm achieves 97.86% and 99.39% reductions in CPU time while sacrificing only 0.007% and 0.057% of optimality gap by two numerical experiments. Finally, the results based on two test networks with different structures demonstrate that the path-based first train timetabling model effectively improves passenger travel efficiency. Specifically, the travel times are reduced by 744 mins and 761 mins, while the transfer waiting times are reduced by 37.87% and 58.91% compared to the existing timetables. Moreover, the results also demonstrate that loop line networks will increase the difficulty of timetabling and lead to many passengers taking detours. To further enhance the efficiency of commuting for passengers who take the first train, URT operators may consider relaxing the limitations on the departure time of the depot stations.

Fully higher-order coupling of finite element and level set methods for two-phase flow with a new explicit projection method

This work presents the development of a higher-order finite element method for modeling unsteady, incompressible and inviscid two-phase flows using the level set method. A new explicit projection method is introduced to solve the incompressible Euler equation, where the pressure and the velocity fields are solved separately. To implement high order temporal schemes, the Hodge decomposition in this projection method is not applied to the velocity but to its time derivative. A discontinuous Galerkin discretization is used to solve both the level set and the nonlinear advection terms present in the Euler equations, while a Galerkin discretization is used to solve the pressure Poisson equation. The present method is a fully high order numerical approach, both in space and temporal dimensions. Numerical results provided by several 2D benchmark test cases in naval hydrodynamics (i.e hydrostatic equilibrium, sloshing and dam break) validate the computational code, illustrating the power of the proposed method. Compared to the CFD codes based on low order VOF/finite-volume methods, the present approach demonstrates greater accuracy on coarse meshes, leading to reduced CPU time.

Adjustable THz Absorber Exploiting Nested Graphene Disk-Ring

This work introduces a THz dual-band absorber with the capability of being tuned via external stimulation. A nested disk-ring graphene pattern is proposed on top of the lossless substrate while the other side of the substrate is coated by a thick layer of gold. The proposed absorber is modeled using an equivalent circuit model (ECM) and also simulated by the full wave method. A perfect match between the circuit model and numerical full wave simulation highlights the developed circuit modeling. Since the circuit modeling can reduce CPU time and need memory considerably. The impedance-matching concept interpretations are discussed in detail. Ample simulation results show the dual-band operation of the proposed absorber at 2THz and 10THz, while an interesting tuning capability is provided by changing chemical potentials. Such a simple and adjustable wave absorber is in demand for numerous applications ranging from medical imaging to indoor communication.

SHyTCWaves: A stop-motion hybrid model to predict tropical cyclone induced waves

Waves produced by tropical cyclones (TCs) can be estimated using non-stationary wave models forced with time-varying wind fields. However, dynamical simulations are time and computationally demanding at regional-scale domains since high temporal and spatial resolutions are required to correctly simulate TC-induced wave propagation processes. Applications such as early warning systems, coastal risk assessments and future climate projections benefit from fast and accurate estimates of wave fields induced by close-to-real storm tracks geometry. The proposed SHyTCWaves methodology constitutes a novel tool capable of estimating the spatio-temporal variability of directional wave spectra produced by TCs in deep waters, using a hybrid approach and statistical techniques to reduce CPU time effort. This work demonstrates that TC-induced waves can be reconstructed using a stop-motion approach based on the addition of successive 6 h periods of time-varying storm conditions. The developed hybrid model reduces a TC track to a number of segments that are parameterized in terms of 10 representative TC features, and generates a library of cases dynamically pre-computed which allow to ensemble consecutive 6 h analog segments representing the original TC track. The metamodel has been compared and corrected with available satellite data, and its applicability is exemplified for TC Ofa in the South Pacific.

A Hybrid Data‐Driven and Data Assimilation Method for Spatiotemporal Forecasting: PM2.5 Forecasting in China

AbstractSpatiotemporal forecasting involves generating temporal forecasts for system state variables across spatial regions. Data‐driven methods such as Convolutional Long Short‐Term Memory (ConvLSTM) are effective in capturing both spatial and temporal correlations, but they suffer from error accumulation and accuracy loss as forecasting time increases due to the nonlinearity and uncertainty in physical processes. To address this issue, we propose to combine data‐driven and data assimilation (DA) methods for spatiotemporal forecasting. The accuracy of the data‐driven ConvLSTM model can be improved by periodically assimilating real‐time observations using the ensemble Kalman filter (EnKF) approach. This proposed hybrid ConvLSTM‐EnKF method is demonstrated through PM2.5 forecasting in China, which is a challenging task due to the complexity of topographical and meteorological conditions in the region, the need for high‐resolution forecasting over a large study area, and the scarcity of observations. The results show that the ConvLSTM‐EnKF method outperforms conventional methods and can provide satisfactory operational PM2.5 forecasts for up to 1 month with spatially averaged RMSE below 20 μg/m3 and correlation coefficient (R) above 0.8. In addition, the ConvLSTM‐EnKF method shows a substantial reduction in CPU time when compared to the commonly used NAQPMS‐EnKF method, up to three orders of magnitude. Overall, the use of data‐driven models provides efficient forecasts and speeds up DA. This hybrid ConvLSTM‐EnKF is a novel operational forecasting technique for spatiotemporal forecasting and is used in real spatiotemporal forecasting for the first time.

Load Flow Calculation For Electrical Power System Based On Run Length Encoding Algorithm

This paper presents Data Compression Simulated algorithm for load flow calculation in electrical power systems. Real time monitor of grids required less computation time in calculation of power system analysis. Load flow problem is heart of this analysis and it basically required calculate active and reactive power flow in lines connected between buses in networks. Many topology and structures for Transmission and Distribution Systems has been proposed to reduce CPU times and memory. The proposed algorithm used Data compression technique tested different systems and results shows it is efficiency. More accuracy for large systems will need more iterations calculation which mean increasing time consumption, while Run Length Encoding (RLE) algorithm is fitness to optimized calculation numbers to exact number cause it has no zero values included. Network structure was represented as one dimension vector instead of 2D Matrix and it is effectiveness results was valid, by avoid exponential increased, by utilized this algorithm. Matlab results obtained by applied this algorithm match theoretical results.

A COMBINED ANALYTICAL/NUMERICAL APPROACH TO THE MODELING OF THE PROCESSES LEADING TO PUFFING AND MICRO-EXPLOSION IN A COMPOSITE MULTI-COMPONENT FUEL/WATER DROPLET

The previously developed analytical/numerical model for predicting heat transfer and component diffusion in composite multi-component droplets is adjusted for use in practical engineering applications related to the analysis of droplet heating and evaporation and the onset of puffing and micro-explosions in those droplets. This adjustment allowed us to gain new insights into the previously developed models of these processes. The focus of the analysis is on kerosene/water droplets. It is demonstrated that the number of terms in the series in the analytical solution to the heat transfer equation can be reduced to just one or two to ensure that the maximal error of the model prediction does not exceed 1%, unless we are interested in the processes at the very start of heating. At the same time, the minimal number of terms in the series in the analytical solution to the component diffusion equation should be at least seven to ensure that the errors of the prediction of the numerical code do not exceed 3%. It is shown that, to ensure that the analytical/numerical code predicts physically consistent results, the maximal absolute error of calculation of the eigenvalues based on the bisection method cannot exceed 10<sup>-7</sup>. It is shown that using these limiting values for each of these input parameters leads to about 50%-75% reduction in the CPU time required to obtain results close to those which were obtained using the nonoptimized version of the numerical code. The overall reduction in CPU time can be up to about 95%. The predictions of the adjusted analytical/numerical code are validated against in-house experimental data and data available in the literature.

Exact and heuristic approaches for maximizing flows in UAV-enabled wireless cellular networks with multi-hop backhauls

This paper investigates the problem of data routing in backhaul networks using Unmanned Aerial Vehicles (UAVs) to relay data from Small Cells (SCs) to the core network. The objective is to maximize the total fulfilled demand of data to be routed, while ensuring technical requirements such as hop constraints and edge capacity. The problem is formulated using a compact mixed-integer programming model, which can solve small- and medium-sized topologies. In addition, a fast constructive heuristic based on a maximal tree is developed to solve large-scale topologies, resulting in a significant reduction in CPU time. The quality of the heuristic is evaluated by using column generation for solving the linear programming relaxation of an exponential formulation. The computational study shows the effectiveness and value of the proposed compact model and constructive heuristic for various topology sizes. Furthermore, experiments demonstrate that by keeping the network setup constant and updating the demand vector only, the computational time of the compact model can be drastically reduced for all topology sizes.

Development of a computational fluid dynamics model adopting a nested grid system: Flow simulations for ideal and real urban settings

We incorporate a nested grid system into a computational fluid dynamics (CFD) model based on the Reynolds-averaged Navier-Stokes equations. First, we evaluate the CFD model by comparing the results simulated in an array of aligned buildings using one- and two-way nested and non-nested coarse (same grid size as the parent domain) and fine grid (same grid size as the child domain) systems. The two-way nested grid simulates double-eddy circulation, wind speeds, and turbulence kinetic energy (TKE) in a street canyon better than the one-way nested grid. The nested simulations produce similar results to the fine grid system but with a significantly reduced CPU time. We also apply the nested grid system to airflow simulations in a building-congested district and validate the simulated results against the wind speed and direction measured by an automated weather system. The nested simulation improves wind direction compared to the WRF model operated by the National Institute of Environmental Research of South Korea. The two-way nested grid successfully reproduces the measured wind speed. The two-way nested grid simulation well represents the continuous flow structure (a smooth flow transition) between the parent and child domains by considering the two-way flow interaction between the two domains.

New Two-Level Time-Mesh Difference Scheme for the Symmetric Regularized Long Wave Equation

The paper introduces a new two-level time-mesh difference scheme for solving the symmetric regularized long wave equation. The scheme consists of three steps. A coarse time-mesh and a fine time-mesh are defined, and the equation is solved using an existing nonlinear scheme on the coarse time-mesh. Lagrange’s linear interpolation formula is employed to obtain all preliminary solutions on the fine time-mesh. Based on the preliminary solutions, Taylor’s formula is utilized to construct a linear system for the equation on the fine time-mesh. The convergence and stability of the scheme is analyzed, providing the convergence rates of O(τF2+τC4+h4) in the discrete L∞-norm for u(x,t) and in the discrete L2-norm for ρ(x,t). Numerical simulation results show that the proposed scheme achieves equivalent error levels and convergence rates to the nonlinear scheme, while also reducing CPU time by over half, which indicates that the new method is more efficient. Furthermore, compared to the earlier time two-mesh method developed by the authors, the proposed scheme significantly reduces the error between the numerical and exact solutions, which means that the proposed scheme is more accurate. Additionally, the effectiveness of the new scheme is discussed in terms of the corresponding conservation laws and long-time simulations.

A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation

Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when grappling with their intricacies and varying scales. However, the transition from two dimensions (2D) to three dimensions (3D) poses a substantial challenge, as the computational demands of dynamically adaptive mesh techniques increase exponentially. Addressing this challenge effectively, we turn to the cutting-edge realm of artificial intelligence and neural networks. In our study, we harness the innovative power of a long short-term memory (LSTM) neural network as an error estimator for adapting unstructured meshes in both 2D and 3D scenarios. This LSTM network predicts the evolution of the adaptive grid based on specified variables, presenting itself as an artificial intelligence-driven architecture to optimize the adaptive criterion for the target variable. This is achieved by establishing a direct correspondence between the Riemann metric and these variables. To demonstrate the practical applicability of our approach, we seamlessly integrate the LSTM error estimator into the 3D adaptive atmospheric model Fluidity-Atmosphere (Fluidity-Atmos), thereby enabling real-time mesh adaptation during numerical simulations. We assess the effectiveness of this method in terms of simulation precision and computational efficiency through a series of experiments in both 2D and 3D settings. Our results not only reveal that the mesh patterns generated by the LSTM error estimator within Fluidity-Atmos closely resemble those produced by traditional error estimators but also underscore its superior performance in enhancing simulation accuracy. Notably, as the number of nodes increases, the LSTM mesh generator substantially reduces CPU time requirements by up to 50% in 3D cases compared to the conventional mesh generator within Fluidity-Atmos, highlighting its remarkable computational efficiency.

Advanced numerical techniques for predicting frequency response functions

Numerical methods have been widely used to predict Frequency Response Functions (FRF) of structures. The FRF can be used to characterize structural dynamics and support sound and vibration control. Generally, frequency sweep is conducted in the FRF calculations to identify damping and resonant frequencies of structures under excitations. However, as numerical models are getting complex and larger, the demands for computational resources (e.g., CPU time, memory, disk space) are greatly increased. Lately, high performance computing (HPC) at the DoD HPC center has been used with advanced numerical techniques to reduce the overall computational time. Those advanced numerical techniques include Krylov subspace and Galerkin Projection (KGP) and Pade Approximation. Significantly CPU time reduction has been demonstrated for relatively smaller FE models. This paper will further discuss adaptive KGP by automating the frequency sweep process via calculated relative residues, then combine with Finite Element Tearing and Interconnecting (FETI) to solve for FRF of a large FEM model in the order of 60M DOF. A flat plate with viscoelastic layer will serve as an example to demonstrate accuracy and efficiency of AKGP with FETI. The benefits of using HPC with advanced numerical techniques to solve for large FEM models are clearly displayed.

SHYTCWAVES: A STOP-MOTION HYBRID TC-INDUCED WAVES METAMODEL

Waves produced by tropical cyclones (TCs) can be estimated using numerical models and non-stationary simulations forced with vortex-type time-varying wind fields. However, dynamical simulations are time and computationally demanding at regional-scale domains since high temporal resolutions are required to correctly simulate wave propagation. Early warning systems, as well as risk induced assessments, would benefit from fast and accurate estimates of the wave climate induced by close-to-real tracks geometry. For this reason, the objective of the proposed methodology is to obtain a tool capable of estimating the spatial and temporal variability of directional wave spectra produced by TCs at regional scale in deep waters using a hybrid approach, and statistical techniques, to reduce CPU time effort. SHyTCWaves is a metamodel that provides estimates of the directional wave spectra produced by TCs, which can be used as boundary conditions for local-scale models at nearshore coastal areas, in addition to providing faster than dynamically simulated TC forecast predictions.