Some form of sparse grids might be useful.  See for example: - https://people.sc.fsu.edu/~jburkardt/m_src/spinterp/help/polynomial.html - https://ins.uni-bonn.de/media/public/publication-media/sparsegrids_j8NLaMi.pdf?name=sparsegrids.pdf - https://link.springer.com/article/10.1007/s00024-017-1606-y
