Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Novel framework for the three-dimensional NLTE inverse problem   The inversion of spectropolarimetric observations of the solar upper
atmosphere is one of the most challenging goals in solar physics. If we account
for all relevant ingredients of the spectral line formation process, such as
the three-dimensional (3D) radiative transfer out of local thermodynamic
equilibrium (NLTE), the task becomes extremely computationally expensive.
Instead of generalizing 1D methods to 3D, we have developed a new approach to
the inverse problem. In our meshfree method, we do not consider the requirement
of 3D\,NLTE consistency as an obstacle, but as a natural regularization with
respect to the traditional pixel-by-pixel methods. This leads to more robust
and less ambiguous solutions. We solve the 3D\,NLTE inverse problem as an
unconstrained global minimization problem that avoids repetitive evaluations of
the $\Lambda$ operator. Apart from the 3D\,NLTE consistency, the method allows
us to easily include additional conditions of physical consistency such as the
zero divergence of the magnetic field. Stochastic ingredients make the method
less prone to ending up within the local minima of the loss function. Our
method is capable of solving the inverse problem faster by several orders of
magnitude than by using grid-based methods. The method can provide accurate and
physically consistent results if sufficient computing time is available, along
with approximate solutions in the case of very complex plasma structures or
limited computing time.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th