Novel framework for the three-dimensional NLTE inverse problem

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