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Any literature that extensively discusses the ability to strongly inter-/extrapolate computationally on little empirical data?

This topic has fascinated me, but I find that it seems a bit novel.

Particulary, instead of gathering large amounts of empirical observations, is there something that could guide interpolating a lot of empirical result from very limited but "skillfully" selected or manipulated data?

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    $\begingroup$ What does "strongly interpolate" mean? $\endgroup$ Oct 25, 2021 at 19:09
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    $\begingroup$ Look up krigging and radial basis functions. You can also see bbanerjee.github.io/ParSim/assets/tech_reports/… for a concise discussion of the basic ideas. $\endgroup$ Oct 25, 2021 at 19:36
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    $\begingroup$ That sounds like you just want to estimate the parameters of a model. If you don't have a model, there is nothing you can do with small amounts of data. $\endgroup$ Oct 26, 2021 at 11:50
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    $\begingroup$ Extrapolation, for example predicting future states, based on sparse data tends to be dicey even if you have a model of your system, process, etc. $\endgroup$ Nov 26, 2021 at 13:21
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    $\begingroup$ Polynomial interpolation in the non-scalar case is usually rather ill-conditioned, getting worse with higher dimension. Or said another way, given a set of monomials, it is or at least was some 10 years ago a topic of research to find point-sets where interpolation using these monomials is well-conditioned. $\endgroup$ Nov 26, 2021 at 13:47

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