Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Adaptive sampling and domain learning strategy for multivariate
  function approximation on unknown domains   Many problems in computational science and engineering can be described in
terms of approximating a smooth function of $d$ variables, defined over an
unknown domain of interest $\Omega\subset \mathbb{R}^d$, from sample data. Here
both the curse of dimensionality ($d\gg 1$) and the lack of domain knowledge
with $\Omega$ potentially irregular and/or disconnected are confounding factors
for sampling-based methods. Na\"{i}ve approaches often lead to wasted samples
and inefficient approximation schemes. For example, uniform sampling can result
in upwards of 20\% wasted samples in some problems. In surrogate model
construction in computational uncertainty quantification (UQ), the high cost of
computing samples needs a more efficient sampling procedure. In the last years,
methods for computing such approximations from sample data have been studied in
the case of irregular domains. The advantages of computing sampling measures
depending on an approximation space $P$ of $\dim(P)=N$ have been shown. In
particular, such methods confer advantages such as stability and
well-conditioning, with $\mathcal{O}(N\log(N))$ as sample complexity. The
recently-proposed adaptive sampling for general domains (ASGD) strategy is one
method to construct these sampling measures. The main contribution of this
paper is to improve ASGD by adaptively updating the sampling measures over
unknown domains. We achieve this by first introducing a general domain
adaptivity strategy (GDAS), which approximates the function and domain of
interest from sample points. Second, we propose adaptive sampling for unknown
domains (ASUD), which generates sampling measures over a domain that may not be
known in advance. Then, we derive least squares techniques for polynomial
approximation on unknown domains. Numerical results show that the ASUD approach
can reduce the computational cost by as 50\% when compared with uniform
sampling.

16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc