From c4e57cad68b18c2c5ec076a9c6d77b619c74d5be Mon Sep 17 00:00:00 2001 From: Mehmet Hakan Satman Date: Mon, 22 Sep 2025 19:25:20 +0300 Subject: [PATCH 1/2] fix minor issues in the manuscript --- paper/paper.md | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 31606e5..a84b669 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -22,19 +22,19 @@ bibliography: paper.bib # Summary Approximating functions with high-dimensional domains is crucial in modern scientific and engineering problems. -An example of this is constructing surrogate models for quantities of interest in high-dimensional, parametrized PDE problems. +An example of this is constructing surrogate models for quantities of interest in high-dimensional, parameterized PDE problems. These surrogate models are constructed to provide computationally inexpensive yet accurate approximations that can be used in applications such as uncertainty quantification, optimization, and parameter estimation [@UQHandbook2017]. For suitably smooth functions, accurate surrogates can be constructed using global polynomial approximation techniques over the parameter domain, and a common approach is the use of sparse grid polynomial approximation. In particular, sparse grid polynomial interpolation techniques enable practitioners to approximate solutions to parametric problems in a non-intrusive manner using existing numerical solvers. -`SparseGridsKit.jl` provides a Julia toolbox to manually and adaptively construct sparse grid polynomial approximations [@julia]. +`SparseGridsKit.jl` provides a Julia [@julia] toolbox to manually and adaptively construct sparse grid polynomial approximations. Interpolation and quadrature routines allow evaluation and integration of the surrogate models. Multi-fidelity approximation via the multi-index stochastic collocation algorithm is also possible [@HajiAli2016; @Jakeman2019; @Piazzola2022]. -Approximations can be represented either in a basis of global Lagrange interpolation polynomials or in a basis of domain appropriate spectral-type global polynomials (e.g.\ Legendre, Chebyshev, Hermite...). +Approximations can be represented either in a basis of global Lagrange interpolation polynomials or in a basis of domain appropriate spectral-type global polynomials (e.g.\ Legendre, Chebyshev, Hermite, etc.). # Statement of need -Sparse grid approximation is a well-developed methodology and is featured in many survey articles and textbook chapters, e.g., [@Bungartz2004; @LeMaitre2010; @Schwab2011; @Cohen2015; @Sullivan2015]. -The need for sparse grid surrogate modelling is demonstrated by its use in many applications, from simpler elliptic and parabolic PDEs to complex practical engineering problems, e.g., \ [@Piazzola2021; @Piazzola2022; @Li2024]. +Sparse grid approximation is a well-developed methodology and is featured in many survey articles and textbook chapters [@Bungartz2004; @LeMaitre2010; @Schwab2011; @Cohen2015; @Sullivan2015]. +The need for sparse grid surrogate modelling is demonstrated by its use in many applications, from simpler elliptic and parabolic PDEs to complex practical engineering problems [@Piazzola2021; @Piazzola2022; @Li2024]. The `SparseGridsKit.jl` implementation offers a rich set of features to enable this. Specifically, `SparseGridsKit.jl` is a Julia implementation of adaptive sparse grid global polynomial approximation methods. @@ -46,7 +46,7 @@ The functionality includes: - Multi-index set construction and manipulation. - Combination technique sparse grid approximations, and functionality for interpolation, integration and derivatives of the surrogate model. - Adaptive sparse grid approximation construction based on the ubiquitous Gerstner-Griebel dimensional adaptive algorithm [@Gerstner2003]. -This implementation uses profit indicators as described in [@Nobile2016]. +This implementation uses profit indicators as described in @Nobile2016. - Adaptive multi-fidelity approximation via the Multi-Index Stochastic Collocation (MISC) algorithm [@HajiAli2016; @Jakeman2019; @Piazzola2022]. - Conversion to and from Polynomial Chaos / spectral polynomial series representation. - Limited support for surrogate model differentiation via automatic differentiation. @@ -55,9 +55,9 @@ The functionality described above is tested and documented with examples include Other sparse grid approximation packages in Julia include: - - [`DistributedSparseGrids.jl`](https://github.com/baxmittens/DistributedSparseGrids.jl) [@Bittens2023]: a Julia package providing adaptive sparse grid approximation using a local hierarchical basis and distributed computing functionality. - - [`Tasmanian.jl`](https://github.com/floswald/Tasmanian.jl): a Julia interface to the C++ [Tasmanian library](https://github.com/ORNL/Tasmanian). - - [`AdaptiveSparseGrids.jl`](https://github.com/jacobadenbaum/AdaptiveSparseGrids.jl): a Julia package offering sparse grid approximation using a local hierarchical basis. + - [`DistributedSparseGrids.jl`](https://github.com/baxmittens/DistributedSparseGrids.jl) [@Bittens2023]: A Julia package providing adaptive sparse grid approximation using a local hierarchical basis and distributed computing functionality. + - [`Tasmanian.jl`](https://github.com/floswald/Tasmanian.jl): A Julia interface to the C++ [Tasmanian library](https://github.com/ORNL/Tasmanian). + - [`AdaptiveSparseGrids.jl`](https://github.com/jacobadenbaum/AdaptiveSparseGrids.jl): A Julia package offering sparse grid approximation using a local hierarchical basis. As described above, `SparseGridsKit.jl` instead offers functionality based upon global polynomial approximation targeting problems in which the function is assumed to be suitably smooth. The adaptive approximation algorithm is also split cleanly into `SOLVE-ESTIMATE-MARK-REFINE` steps to aid adaptive algorithm development. @@ -71,7 +71,7 @@ Other popular software packages implementing sparse grid approximation include: - `PyApprox`: A Python package for high-dimensional approximation [@PyApprox]. - `Dakota`: A C++ library for optimisation and surrogate modelling [@Dakota]. - `UQTk`: A collection of C++/Python uncertainty quantification tools including sparse grid quadrature [@DebusschereUQTk:2017]. -- `Tasmanian`,`SG++`,: C++ sparse grid approximation implementations with wrappers for many popular software languages [@stoyanov2015tasmanian; @pflueger10spatially]. +- `Tasmanian`,`SG++`: C++ sparse grid approximation implementations with wrappers for many popular software languages [@stoyanov2015tasmanian; @pflueger10spatially]. `SparseGridsKit.jl` specifically offers a Julia toolkit sharing the ethos of the `Sparse Grids MATLAB Kit`: to be user-friendly and aid fast algorithm prototyping. Notably, `SparseGridsKit.jl` also provides an implementation of the multi-index stochastic collocation algorithm which is currently only available in `PyApprox`. From 5abd99a4c409d16b43cf3c1d265cb7ce48a9cd23 Mon Sep 17 00:00:00 2001 From: Mehmet Hakan Satman Date: Mon, 22 Sep 2025 19:30:49 +0300 Subject: [PATCH 2/2] minor fixes in bibtex --- paper/paper.bib | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 20d0f00..41d7000 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -104,7 +104,7 @@ @article{Piazzola2021 } @article{Li2024, - title = {Characterizing Aquifer Properties through a Sparse Grid-Based Bayesian Framework and InSAR Measurements: A Basin-Scale Application to {A}lto {G}uadalentín, {S}pain}, + title = {Characterizing Aquifer Properties through a Sparse Grid-Based {B}ayesian Framework and InSAR Measurements: A Basin-Scale Application to {A}lto {G}uadalentín, {S}pain}, url = {http://dx.doi.org/10.22541/essoar.172373105.53381390/v1}, DOI = {10.22541/essoar.172373105.53381390/v1}, publisher = {Authorea, Inc.}, @@ -241,7 +241,7 @@ @url{Dakota } @article{spinterp, - title = {Algorithm 847: {spinterp}: piecewise multilinear hierarchical sparse grid interpolation in {MATLAB}}, + title = {Algorithm 847: {Spinterp}: piecewise multilinear hierarchical sparse grid interpolation in {MATLAB}}, volume = {31}, ISSN = {1557-7295}, url = {http://dx.doi.org/10.1145/1114268.1114275}, @@ -356,7 +356,7 @@ @article{julia } @article{Bittens2023, - title = {DistributedSparseGrids.jl: A Julia library implementing + title = {DistributedSparseGrids.jl: A {J}ulia library implementing an Adaptive Sparse Grid collocation method}, volume = {8}, ISSN = {2475-9066},