Hybrid minimization algorithm for computationally expensive multi-dimensional fitting

Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a predetermined set of positions in the parameter space and th...

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Bibliographic Details
Published in:arXiv.org 2021-12
Main Authors: Rubtsov, Evgenii, Chilingarian, Igor, Katkov, Ivan, Grishin, Kirill, Goradzhanov, Vladimir, Borisov, Sviatoslav
Format: Article
Language:English
Subjects:
Algorithms
Astrophysics
Interpolation
Mathematical models
Optimization
Parameters
Online Access:Get full text
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Summary:Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a predetermined set of positions in the parameter space and then interpolating. Here we present a hybrid minimization approach based on the local quadratic approximation of the \(\chi^2\) profile from a discrete set of models in a multidimensional parameter space. The main idea of our approach is to eliminate the interpolation of models from the process of finding the best-fitting solution. We present several examples of applications of our minimization technique to the analysis of stellar and extragalactic spectra.
ISSN:2331-8422