Sparse Grids Matlab Kit

The Sparse Grids Matlab Kit is a collection of Matlab functions for high-dimensional quadrature and interpolation, based on the combination technique version of sparse grids.

It is lightweight, high-level and (hopefully) easy to use, good for quick prototyping and teaching. It comes with a very extensive documentation and examples (8800 lines of code, 4800 lines of comments).

It is somehow geared towards Uncertainty Quantification (UQ), but it is flexible enough for other purposes.


Contributors

  • Lorenzo Tamellini (main developer, maintainer) - CNR-IMATI, Pavia, Italy

  • Fabio Nobile - École Polytechnique Fédérale de Lausanne, Switzerland

  • Chiara Piazzola - CNR-IMATI, Pavia, Italy

  • Björn Sprungk - Technische Universität Bergakademie Freiberg, Germany

  • Giovanni Porta - Politecnico di Milano, Italy

  • Diane Guignard - University of Ottawa, Canada

  • Francesco Tesei - Credit Suisse, Switzerland


License

The Sparse Grids Matlab Kit is distributed with a BSD2 License


Download


Features

  • Sparse-grid-based quadrature and interpolation for several measures/pdf

    • uniform: Gauss-Legendre, Leja, Clenshaw-Curtis, midpoints, equispaced points

    • normal: Gauss-Hermite, Leja, Genz-Keister

    • exponential: Gauss-Laguerre, Leja

    • gamma: Gauss-Laguerre (generalized), Leja

    • beta: Gauss-Jacobi, Leja

  • Dimension-adaptive sparse grid algorithm

  • Conversion of a sparse-grid interpolant to a Polynomial Chaos Representation (Legendre, Chebyshev, Hermite, Laguerre, Generalized Laguerre, Jacobi polynomials supported)

  • Sparse-grid-based global and local sensitivity analysis (by computation of Sobol Indices and gradients of a sparse grid interpolant)

  • Computation of Hessians

  • Export of sparse grid collocation points and weights to ASCII file

  • Visualization functions (plot of sparse grid points and sparse grid interpolant)


Cite us

Please cite our toolbox by mentioning the webpage containing the package and adding the following references to your work:


1) C. Piazzola, L. Tamellini. The Sparse Grids Matlab kit - a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification, ArXiv 2203.09314, 2022.
Paper available at this link
Codes available here


@article{piazzola.tamellini:SGK,

author = {Piazzola, C. and Tamellini, L.},

title = {{The Sparse Grids Matlab kit - a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification}},

journal= {ArXiv},

year = {2022},

volume = {},

number = {2203.09314},

pages = {},

note = {}

}



2) J. Bäck, F. Nobile, L. Tamellini, and R. Tempone. Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison. In J.S. Hesthaven and E.M. Ronquist, editors, Spectral and High Order Methods for Partial Differential Equations, volume 76 of Lecture Notes in Computational Science and Engineering, pages 43–62. Springer, 2011. Available at this link


@InCollection{back.nobile.eal:comparison,

author = {B\"ack, J. and Nobile, F. and Tamellini, L. and Tempone, R.},

title = {Stochastic spectral {G}alerkin and collocation methods for {PDE}s with random coefficients: a numerical comparison},

booktitle = {Spectral and High Order Methods for Partial Differential Equations},

pages = {43--62},

publisher = {Springer},

year = 2011,

volume = 76,

series = {Lecture Notes in Computational Science and Engineering},

editor = {Hesthaven, J.S. and Ronquist, E.M.},

note = {Selected papers from the ICOSAHOM '09 conference, June 22-26, Trondheim, Norway}

}


selected PUBLICATIONs USING THE SPARSE GRIDS MATLAB KIT - with code


  • Chiara Piazzola, Lorenzo Tamellini, Raúl Tempone. A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology, Mathematical Biosciences, 2022.
    Paper available here.
    Matlab code available
    here


  • Jesús Martínez-Frutos, Francisco Periago Esparza. Optimal Control of PDEs under Uncertainty - An Introduction with Application to Optimal Shape Design of Structures. Springer International Publishing, 2018.
    Book available
    here.
    Matlab code available here


Get in touch

For any questions or to report a bug, send an email to tamellini AT imati DOT cnr DOT it .

Send us your email if you want to be notified when a new version is released online