Sobol Quasi-random Sequence Research Articles

A data-driven deep learning model of radiative heat transfer in dense granular systems

Radiative heat transfer has attracted increasing research interest in various dense granular systems, including large-scale nuclear pebble-bed reactors, fusion breeder blankets, packed beds, metal powder beds and granular lunar regolith simulants. The optimised ray tracing method (ORTM) with a Sobol quasi-random sequence is proposed to calculate the obstructed view factor between spheres, and it converges much faster than that with the traditional pseudorandom number sampling method. Based on discrete particle packing of nuclear pebble bed HTR-PM and random particle generation, a large obstructed view factor dataset of thermal radiation is generated by parallel CUDA computing for training a deep learning regression model to discuss the packing-property linkage for radiative heat transfer in the large-scale particle bed. Compared with other approaches, the deep residual neural network (ResNet) with the swish activation function applied in this paper is found to be the best neural network architecture for view factor prediction without vanishing gradients or model degradation problems during training. The testing error of the trained deep learning model is <1.0 × 10-4 for over 99.96% view-factor cases in nuclear pebble beds, and it has proven to be 7.3 × 105 times faster than the traditional numerical method in view-factor calculations. This makes it feasible to explore the local and macroscopic thermal radiation behaviours in large-scale pebble beds filled with up to 1.0 × 107 spheres.

QUASI-MONTE CARLO METHODS BASED ON SOBOL AND HALTON SEQUENCES FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS APPLIED IN SECURITY SYSTEMS

In this paper we implement and analyze the performance of Sobol quasi-random sequence and compare the results with the Halton quasi-random sequence has been done. We consider a case study with a non-smooth integrand function with applications in financial mathematics. We show that the Sobol sequence has some advantageous over the Halton sequence. It is established that Sobol sequence performs bett er than other sequences for higher dimensions.

A COMPARISON OF QUASI MONTE CARLO METHODS BASED ON FAURE AND SOBOL SEQUENCES FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS

In this paper we implement and analyze the performance of Faure quasi-random sequence. We compare the results with the Sobol quasi-random sequence which is the most widely used quasi-Monte Carlo method. Also some experiments between Faure sequence and the plain (Crude) Monte Carlo method are given. We consider a case study with a non-smooth integrand function. We show that the Sobol sequence has some adv antageous over the Faure sequence.

On Non-Poissonian Voronoi Tessellations

&lt;p&gt;The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern ”random”, Poisson-Voronoi tessellations (PVT), or ”non-random”, Non Poisson-Voronoi tessellations. In this note we shall consider properties of Voronoi tessellations with centers gener-ated by Sobol quasi random sequences which produce a more ordered disposition of the centers with respect to the PVT case. A probability density function for volumes of these Sobol Voronoi tessellations (SVT) will be proposed and compared with results of numerical simulations. An application will be presented concerning the local struc-ture of gas (CO&lt;sub&gt;2&lt;/sub&gt;) in the liquid-gas coexistence phase. Furthermore a probability distribution will be computed for the length of chords resulting from the intersections of random lines with a three-dimensional SVT. The agreement of the analytical formula with the results from a computer simulation will be also investigated. Finally a new type of Voronoi tessellation based on adjustable positions of seeds has been introduced which generalizes both PVT and SVT cases.&lt;/p&gt;

Topographical global optimization applied to nuclear reactor core design: Some preliminary results

The nuclear reactor core design optimization problem consists in adjusting several reactor cell parameters, such as dimensions, enrichment and materials, in order to minimize the average peak-factor in a three-enrichment-zone reactor, considering restrictions on the average thermal flux, criticality and sub-moderation. This problem is highly multimodal, requiring optimization techniques that overcome local optima. In order to do so, we use a clustering optimization technique based on the topographical information on the objective function called Topographical Global Optimization (TGO). This algorithm consists of three steps: a uniform random sampling of solutions in the search space, the construction of the topograph, and the application of a local optimization algorithm using the topograph minima as starting points. In this work, we use the Sobol quasi-random sequence to perform the first step and the Hooke–Jeeves direct search method (HJ), which is one of the less sophisticated algorithms of this type, for the third step. In spite of HJ’s simplicity, the results are competitive in terms of fitness function values, being obtained at a computational cost one order of magnitude lower than the efforts required for achieving the best results so far. This fact suggests that better results can be obtained employing more modern and effective direct search methods. Nevertheless, as the problem attacked is quite challenging, the preliminary results show the potential of TGO to be applied to other nuclear science and engineering problems. For the best of our knowledge, this is the first time that TGO is applied to an engineering optimization problem.

An Improved Algorithm for Pricing Derivatives Using Sobol Quasirandom Sequences

It is often argued that Quasi-Monte Carlo Methods (QMC ) only work for problems of low effective dimension that encompass most of financial problems. We will show here some evidence that, with the Sobol construction, they can be suited for problems with high effective dimension in the truncation sense as well as (moderately) high effective dimension in the superposition sense. We propose a methodology for obtaining the initial direction integers that are a central piece for generation of good Sobol sequences and show several examples both financial and nonfinancial where they can be used. Our sequences can deal with up to 35,000-dimensional problems.

Enhancement of the Global Convergence of Using Iterative Dynamic Programming To Solve Optimal Control Problems

Although iterative dynamic programming (IDP) has been well recognized as a powerful method for finding the true optimal solution to a nonlinear dynamic optimization problem, the global optimality of the IDP solution is still not guaranteed completely. This paper explores enhancing the global convergence of using iterative dynamic programming to solve optimal control problems. Two approaches are employed to enhance the possibility of obtaining the true optimum while reducing the required computation efforts. One approach employs Sobol's quasi-random sequence generator to generate allowable controls and the other utilizes multipass computation. Numerical examples show that the use of multipass IDP computation with small numbers of state grid points and allowable control values can indeed enhance the possibility of obtaining a true optimum. This is particularly true when the allowable control values are generated by using Sobol's quasi-random sequence generator.

Use of Sobol's Quasirandom Sequence Generator for Integration of Modified Uncertainty Importance Measure

Use of Sobol's Quasirandom Sequence Generator for Integration of Modified Uncertainty Importance Measure

Use of Sobol's Quasirandom Sequence Generator for Integration of Modified Uncertainty Importance Measure.

Sensitivity analysis of model output is relevant to a number of practices, including verification of models and computer code quality assurance. It deals with the identification of influential model parameters, especially in complex models implemented in computer programs with many uncertain input variables. In a recent article a new method for sensitivity analysis, named HIM* based on a rank transformation of the uncertainty importance measure suggested by Hora and Iman was proved very powerful for performing automated sensitivity analysis of model output, even in presence of model non-monotonicity. The same was not true of other widely used non-parametric techniques such as standardized rank regression coefficients. A drawback of the HIM* method was the large dimension of the stochastic sample needed for its estimation, which made HIM* impracticable for systems with large number of uncertain parameters. In the present note a more effective sampling algorithm, based on Sobol's quasirandom generator is co...