Number Of Simulation Points Research Articles

Efficient simulation of fully nonstationary wind velocity field by an enhanced numerical truncation method

The spectral representation method (SRM) is widely utilized to simulate the fully nonstationary wind velocity field with time-varying coherence. The simulation samples are generated by double summation of harmonic functions. Despite the fast Fourier transform (FFT) technique has been employed to accelerate the summation in the frequency dimension, the computational efficiency is still constrained by the number of simulation points and samples due to the time-consuming summation operation in the spatial dimension. In this study, a numerical truncation method is presented to further quicken the SRM-based simulation of a fully nonstationary wind velocity field. The fundamental idea is that the harmonic functions with tiny amplitude are inconsequential and can be omitted. A novel diagonal decoupling approach is first developed to rearrange the double summation. Further, the frequency truncation scheme is established to simplify the summation in the spatial dimension. Meanwhile, the FFT operations to calculate the summation in the frequency dimension are also considerably reduced. Finally, the superior performance of the proposed method on precision and efficiency is demonstrated by numerical examples.

High-efficiency simulation of nonstationary wind velocity using diagonal POD of decomposed time-frequency interpolation node spectrum matrices

The classical spectral representation method (SRM) used extensively to simulate nonstationary wind fields suffers from lower efficiency. Although some tries can already accelerate SRM, the efficiency improvement is restricted when the number of simulation points is large. For this reason, this paper proposed a high-efficiency interpolation scheme to boost the efficiency of SRM. Firstly, the decomposed time-frequency interpolation node spectrum matrices can be approximately decouple into the products of time and frequency functions using diagonal proper orthogonal decomposition (POD). Specifically, the POD operation is just for the diagonal elements, which are low-dimensional matrices. Since Cholesky decomposition is merely needed in the time-frequency interpolation point, the time consumed by spectral decomposition will be significantly reduced. Then, one-dimensional (1D) interpolation is implemented for these decoupling terms in the time and frequency directions, respectively. The decoupling results only contains a few time terms, so the number of 1D interpolation operations can be considerably decreased. Moreover, by exchanging the summation order, very few fast Fourier transform operations are required to accelerate harmonic superposition. Therefore, the proposed method may further enhance the simulation efficiency. Finally, through numerical examples, the accuracy and superiority of the proposed method are demonstrated.

Detecting the phase behavior on cache performance using the reuse distance vectors

Abstract Previous studies proposed several code signatures, with large vector dimensions and time-consuming profiling processes, to detect phase transitions of the overall processor performance. However, there still lacks an effective and efficient method to detect and leverage the phase characteristics of memory access. In this paper, we propose the reuse distance vector (RDV), a new metric that tightly coupled with the cache performance, to summarize the phase behavior in the memory hierarchy. Different from the commonly seen huge dimensionality of other code signatures, RDVs are measured at very low dimensions. Meanwhile, the profiling overhead can be further reduced by our sampling technique. Based on RDVs, we can pick simulation points from the whole program via a clustering method to act as the representative subset to reduce the time consumption of cycle accurate simulations. Using the simulation points found by RDVs, the average relative error of cache miss rate estimation is as low as 1.08%, which outperforms the accuracies of BBVs and EIPVs by 79% and 22% (all compared methods use the same number of simulation points that takes merely 0.4% of the whole program). Meanwhile, the average errors of MLP and the cache miss service time are only 0.9% and 1.8%, respectively.

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

Simulation of Gaussian Random Fields With One Derivative

Circulant embedding provides a fast and exact algorithm for simulating stationary Gaussian random fields on grids. However, the method tends to work poorly for differentiable processes with correlation ranges comparable to the size of the simulation domain. This work describes an algorithm for simulating differentiable stationary Gaussian processes, with the focus on processes possessing exactly one derivative. The algorithm works by first simulating a filtered version of the process using circulant embedding and then recovering the original process from the filtered version. This recovery step is the slowest part of the computation, requiring many solutions of large systems of linear equations. Preconditioned conjugate gradient provides a viable method for obtaining essentially exact solutions to these linear equations. The memory requirements are linear in the number of simulation points and if more than one simulation under a model is needed, subsequent simulations are much faster than the first. The algorithm can be modified to simulate certain differentiable nonstationary intrinsic random functions, to which existing approaches to circulant embedding do not apply. A supplemental file contains code for simulating these intrinsic random functions.

A modified space charge routine for high intensity bunched beams

In 1991 a space charge calculation for bunched beam with a three-dimensional ellipsoid was proposed, replacing the usual SCHEFF routines. It removes the cylindrical symmetry required in SCHEFF and avoids the point to point interaction computation, whose number of simulation points is limited. This routine has now been improved with the introduction of two or three ellipsoids giving a good representation of the complex non-symmetrical form of the bunch (unlike the 3-d ellipsoidal assumption). The ellipsoidal density distributions are computed with a new method, avoiding the difficulty encountered near the centre (the axis in 2-d problems) by the previous method. It also provides a check of the ellipsoidal symmetry for each part of the distribution. Finally, the Fourier analysis reported in 1991 has been replaced by a very convenient Hermite expansion, which gives a simple but accurate representation of practical distributions. Comparisons with other space charge routines have been made, particularly with the ones applying other techniques such as SCHEFF. Introduced in the versatile beam dynamics code DYNAC, it should provide a good tool for the study of the various parameters responsible for the halo formation in high intensity linacs. Improvements of the method are under development by the authors. These improvements, which might lead to a new step in space charge computations, are however beyond the scope of this article.

COMPARISONS OF NUMERICAL RANDOM WAVE SIMULATORS

A review of unidimensional numerical random sea simulators is provided, centering the attention on the measurement of distortions introduced by the different simulation techniques. Simulators by wave superposition are analyzed, with the conclusion being that they generate significant distortions on the realizations when the number of simulated points are larger than two times the number of wave components. Composed simulators are proposed for the purpose of generating long non-periodic realizations using FFT algorithms. In order to qualify simulators, a justification, based on physical properties of random waves, is given to use mn> m1» Qp and mo as the best spectral parameters to characterize processes. Mean values and variabilities of wave heights and periods are controlled by these parameters. A new robust technique is developed to estimate the parameters of an AR(p) model corresponding to a given target spectrum, S 77 ( f ). MA(q) and ARMA(p,q) approximations are studied. The source of pseudo-random numbers to generate the input white noise has a critical impact on the statistical properties of the output.