THE Sparse Grids Matlab Kit

The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be used for approximating high-dimensional functions and, in particular, for surrogate-model-based uncertainty quantification.

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). 

Contributors

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

• Chiara Piazzola (main developer, maintainer) - Technische Universität München, Germany

• Fabio Nobile - École Polytechnique Fédérale de Lausanne, Switzerland

• 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

Source code available at https://github.com/lorenzo-tamellini/sparse-grids-matlab-kit

Releases:

• 23-5 ("Robert")  - current release. 

  • User manual here, last update 9 Oct. 23 11 May 23. 

  • Codes for the manual here

• 22-2 ("California")

• 18-10 (“Esperanza”)

• 17-5 (“Trent”)

• 15-8 (“Woodstock”)

• 14-12 (“Fenice”)

• 14-4 (“Ritchie”)

Features

• Implementation based on the combination technique form of sparse grids

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

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

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

    • exponential: Gauss-Laguerre, weighted Leja

    • gamma: Gauss-Laguerre (generalized), weighted Leja

    • beta: Gauss-Jacobi, weighted Leja

    • triangular: weighted Leja

• Dimension-adaptive sparse grid algorithm that:

  • • supports non-nested knots

    • supports vector-valued functions

    • provides multiple profit definitions

    • implements a buffering strategy for reducing costs for high-dimensional functions

• Seamless integration of the Matlab Parallel Toolbox

• Can recycle function evaluations that might be already available

• 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 gradients and Hessians

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

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

• Fully compatible with UM-Bridge Matlab client for connecting with third-party model solvers (more info at https://github.com/UM-Bridge/umbridge and https://arxiv.org/abs/2304.14087)

• Testing unit available

• Several tutorials available

Cite us - sparse grids matlab kit paper (with code)

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

1) C. Piazzola, L. Tamellini. 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, 2023.
Paper available at this link
Codes available here 

@article{piazzola.tamellini:SGK,

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

 title  = {{Algorithm 1040: The Sparse Grids Matlab Kit - a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification}},

 journal= {ACM Transactions on Mathematical Software},

 year   = {2024},

 volume = {50},

 number = {1},

 doi = {10.1145/3630023}

}

OTHER selected PUBLICATIONs USING THE SPARSE GRIDS MATLAB KIT (with code)

• Linus Seelinger, Anne Reinarz et al. Democratizing Uncertainty Quantification, arXiv, 2024.
  Paper available here. 
  Codes available here

• 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

ACKNOWLEDGEMENTS

The projects listed below have supported the development of the Sparse Grids Matlab Kit (projects prior to 2017 not listed):

• Lorenzo Tamellini has been partially supported by ICSC—Centro Nazionale di Ricerca in High Performance Computing, Big Data, and Quantum Computing funded by European Union—NextGenerationEU.

• Lorenzo Tamellini and Chiara Piazzola have been partially supported by the PRIN 2017 project 201752HKH8 "Numerical Analysis for Full and Reduced Order Methods for the efficient and accurate solution of complex systems governed by Partial Differential Equations (NA-FROM-PDEs)". 

• Chiara Piazzola has been supported by the Alexander von Humboldt Foundation