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SparseGridsKit.jl: Adaptive single- and multi-fidelity sparse grid approximation in Julia

SparseGridsKit.jl: Adaptive single- and multi-fidelity sparse grid approximation in Julia - Published in JOSS (2025)

https://github.com/benmkent/sparsegridskit.jl

Science Score: 93.0%

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Repository

Simple sparse grid interpolation Julia implementation

Basic Info
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  • Stars: 1
  • Watchers: 1
  • Forks: 2
  • Open Issues: 9
  • Releases: 3
Created over 1 year ago · Last pushed 9 months ago
Metadata Files
Readme License

README.md

SparseGridsKit.jl

Documentation Test codecov Aqua QA DOI

A simple implementation of sparse grid polynomial interpolation and corresponding interpolation.

To add the package use the following command: ] add SparseGridsKit The construction is based upon the sparse operators introduced by Smolyak (Smolyak, 1963). Key papers defining the approximation formulation include (Barthelmann, 2000), (Gerstner, 1998) and (Gerstner, 2003). This construction of the approximation is inspired by the Sparse Grids MATLAB Kit (Piazzola, 2024).

This documentation is example driven, with full documentation for each subset of functions given at the end of the relevant example. This is not a thorough mathematical description of sparse grid approximation, but a practical guide to using the software.

The package is still under development and by no means complete.

Statement of Need

This Julia implementation closely follows the mathematical description in the adaptive sparse grid approximation literature. This package aims to aid fast algorithm development and analysis, with an emphasis on applications in uncertainty quantification.

Contribution Guidelines

To report bugs, seek support or submit request features, please use the GitHub issue tracker. Please feel free to contribute and submit pull requests.

Example

In the simplest case one often wants to create a sparse grid using a sequence of nested sets Clenshaw--Curtis points and a Smolyak type multi-index set. To this end, one uses create_sparsegrid with the desired Smolyak multi-index set. In this case we choose a grid with dimension n=3 and Smolyak level w=3. ```julia using SparseGridsKit, Plots, LaTeXStrings

Test create_sparsegrid

n,k =3,3 knots = [GaussHermitePoints(), CCPoints(), UniformPoints()] rules = [Linear(), Doubling(), Doubling()] miset = createsmolyakmiset(n,k) sg = createsparsegrid(miset, knots=knots, rule=rules) nsteps = 100 @gif for i in range(0, stop = 2π, length = nsteps) plot(sg) plot!( title="Sparse Grid n,k="string(n)","*string(k), xlabel=L"y1", ylabel=L"y2", zlabel=L"y3", camera = (20 * (1 + cos(i)),10 * (1 + cos(i))) ) end ``` Example Sparse Grid

Bibliography

  • Smolyak, S. (1963). Quadrature and interpolation formulae on tensor products of certain function classes. Soviet Math. Dokl., 4(5), 240–243.
  • Volker Barthelmann, Erich Novak, & Klaus Ritter (2000). High dimensional polynomial interpolation on sparse grids. Advances in Computational Mathematics, 12(4), 273–288.
  • Gerstner, T., & Griebel, M. (1998). Numerical integration using sparse grids. Numerical algorithms, 18(3), 209–232.
  • Gerstner, T., & Griebel, M. (2003). Dimension–Adaptive Tensor–Product Quadrature. Computing, 71(1), 65–87.
  • Piazzola, C., & Tamellini, L. (2024). Algorithm 1040: The Sparse Grids MATLAB Kit - a MATLAB implementation of sparse grids for high-dimensional function approximation and uncertainty quantification. ACM Transactions on Mathematical Software, 50(1), 1–22.

Owner

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JOSS Publication

SparseGridsKit.jl: Adaptive single- and multi-fidelity sparse grid approximation in Julia
Published
September 25, 2025
DOI
Volume 10, Issue 113, Page 8300
Authors
Benjamin M. Kent ORCID
CNR-IMATI, Pavia, Italy
Editor
Mehmet Hakan Satman ORCID
Tags
numerical approximation surrogate modelling sparse grids multi-fidelity uncertainty quantification
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GitHub Events

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  • Issue comment event: 18
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  • Pull request review event: 1
  • Pull request event: 27
  • Fork event: 3
Last Year
  • Create event: 22
  • Commit comment event: 6
  • Release event: 3
  • Issues event: 25
  • Watch event: 1
  • Delete event: 15
  • Issue comment event: 18
  • Public event: 1
  • Push event: 146
  • Pull request review event: 1
  • Pull request event: 27
  • Fork event: 3

Issues and Pull Requests

Last synced: 9 months ago

All Time
  • Total issues: 16
  • Total pull requests: 18
  • Average time to close issues: 25 days
  • Average time to close pull requests: 3 days
  • Total issue authors: 3
  • Total pull request authors: 4
  • Average comments per issue: 0.31
  • Average comments per pull request: 0.56
  • Merged pull requests: 14
  • Bot issues: 0
  • Bot pull requests: 0
Past Year
  • Issues: 16
  • Pull requests: 18
  • Average time to close issues: 25 days
  • Average time to close pull requests: 3 days
  • Issue authors: 3
  • Pull request authors: 4
  • Average comments per issue: 0.31
  • Average comments per pull request: 0.56
  • Merged pull requests: 14
  • Bot issues: 0
  • Bot pull requests: 0
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Top Authors
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  • benmkent (14)
  • dannys4 (1)
  • JuliaTagBot (1)
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  • benmkent (14)
  • jbytecode (2)
  • baxmittens (1)
  • danielskatz (1)
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Packages

  • Total packages: 1
  • Total downloads:
    • julia 2 total
  • Total dependent packages: 0
  • Total dependent repositories: 0
  • Total versions: 2
juliahub.com: SparseGridsKit

Simple sparse grid interpolation Julia implementation

  • Versions: 2
  • Dependent Packages: 0
  • Dependent Repositories: 0
  • Downloads: 2 Total
Rankings
Dependent repos count: 8.2%
Dependent packages count: 35.2%
Average: 37.4%
Forks count: 40.0%
Stargazers count: 66.2%
Last synced: 9 months ago

Dependencies

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.github/workflows/test.yaml actions
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  • julia-actions/julia-runtest v1.11.1 composite
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