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

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, 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 (Ghanem et al., 2017).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 (Bezanson et al., 2017) 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 multiindex stochastic collocation algorithm is also possible (Haji-Ali et al., 2016;John D. Jakeman et al., 2019;Piazzola et al., 2022).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.)