Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs

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Exponential ReLU DNN Expression of Holomorphic Maps in High Dimension (2021, methodology): “This criterion is not always met in practice [4].”
Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients (2015, unknown): “Ideally, one would like to design numerical methods that are immune to the growth of J , which in principle amounts to treat the case of countably many variables, that is, This problem has been the object of much attention in recent years [3, 4, 7, 8, 9, 16, 13, 19].”
Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “ods for computing low-rank approximations. Remark 6.16 Note that results on the convergence of best r-term approximations on a polynomial basis for particular classes of parameter-dependent equations [29, 52, 24], which exploit the anisotropy of the solution map u: Ξ → V, provide as a by-product upp”