Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstructing high-dimensional Hilbert-valued functions via compressed
  sensing   We present and analyze a novel sparse polynomial technique for approximating
high-dimensional Hilbert-valued functions, with application to parameterized
partial differential equations (PDEs) with deterministic and stochastic inputs.
Our theoretical framework treats the function approximation problem as a joint
sparse recovery problem, where the set of jointly sparse vectors is possibly
infinite. To achieve the simultaneous reconstruction of Hilbert-valued
functions in both parametric domain and Hilbert space, we propose a novel
mixed-norm based $\ell_1$ regularization method that exploits both energy and
sparsity. Our approach requires extensions of concepts such as the restricted
isometry and null space properties, allowing us to prove recovery guarantees
for sparse Hilbert-valued function reconstruction. We complement the enclosed
theory with an algorithm for Hilbert-valued recovery, based on standard
forward-backward algorithm, meanwhile establishing its strong convergence in
the considered infinite-dimensional setting. Finally, we demonstrate the
minimal sample complexity requirements of our approach, relative to other
popular methods, with numerical experiments approximating the solutions of
high-dimensional parameterized elliptic PDEs.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an