Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Goal-based sensitivity maps using time windows and ensemble
  perturbations   We present an approach for forming sensitivity maps (or sensitivites) using
ensembles. The method is an alternative to using an adjoint, which can be very
challenging to formulate and also computationally expensive to solve. The main
novelties of the presented approach are: 1) the use of goals, weighting the
perturbation to help resolve the most important sensitivities, 2) the use of
time windows, which enable the perturbations to be optimised independently for
each window and 3) re-orthogonalisation of the solution through time, which
helps optimise each perturbation when calculating sensitivity maps. These novel
methods greatly reduce the number of ensembles required to form the sensitivity
maps as demonstrated in this paper. As the presented method relies solely on
ensembles obtained from the forward model, it can therefore be applied directly
to forward models of arbitrary complexity arising from, for example,
multi-physics coupling, legacy codes or model chains. It can also be applied to
compute sensitivities for optimisation of sensor placement, optimisation for
design or control, goal-based mesh adaptivity, assessment of goals (e.g. hazard
assessment and mitigation in the natural environment), determining the worth of
current data and data assimilation.
  We analyse and demonstrate the efficiency of the approach by applying the
method to advection problems and also a non-linear heterogeneous multi-phase
porous media problem, showing, in all cases, that the number of ensembles
required to obtain accurate sensitivity maps is relatively low, in the order of
10s.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom