Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient-Based Estimation of Uncertain Parameters for Elliptic Partial
  Differential Equations   This paper addresses the estimation of uncertain distributed diffusion
coefficients in elliptic systems based on noisy measurements of the model
output. We formulate the parameter identification problem as an infinite
dimensional constrained optimization problem for which we establish existence
of minimizers as well as first order necessary conditions. A spectral
approximation of the uncertain observations allows us to estimate the infinite
dimensional problem by a smooth, albeit high dimensional, deterministic
optimization problem, the so-called finite noise problem in the space of
functions with bounded mixed derivatives. We prove convergence of finite noise
minimizers to the appropriate infinite dimensional ones, and devise a
stochastic augmented Lagrangian method for locating these numerically. Lastly,
we illustrate our method with three numerical examples.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc