Constructing Sobol Sequences with Better Two-Dimensional Projections

By Stephen Joe, Frances Y. Kuo. SIAM Journal on Scientific Computing, 2008

448 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A unified deep artificial neural network approach to partial differential equations in complex geometries (2017, background): “A common choice is the Sobol sequence [34] which is described in detail in [2] for N ≤ 40, and later extended in [14] and [15] for N ≤ 1111, and N ≤ 21201, respectively.”
Design of computer experiments: A review (2017, methodology): “MSD: Maximin Scaled Distance MSE: Mean Squared Error MSE: Maximum Sampling Error MST: Minimum Spanning Tree NLP: Nonlinear Programming NN: Nearest Neighbor OA: Optimization Algorithms OAS: Orthogonal Array Sampling PerGA: Permuted Genetic Algorithm PE: Potential Energy PSO: Particle Swarm Optimizati”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “Direction numbers for s > 50 that also satisfy certain equidistribution properties can be found in [203, 207, 208, 279].”
Crowdsourcing in Computer Vision (2016, unknown): “4(b) shows the first 500 samples from a Sobol sequence [56, 36] in dimensions 14 and 15.”
Efficient training of physics‐informed neural networks via importance sampling (2021, background): “Among the popular lowdiscrepancy sequences are the generalized Halton sequences [45, 46], the Sobol sequences [47, 48], and the Hammersley sets [49, 50].”