Fitting in a complex chi^2 landscape using an optimized hypersurface sampling

TL;DR

This paper introduces an optimized sampling method combining a modified Metropolis algorithm and simulated annealing to effectively locate the global minimum in complex chi^2 landscapes, overcoming limitations of traditional algorithms.

Contribution

It proposes a new parameter step tuning approach integrated with simulated annealing for improved global minimum finding in chi^2 hypersurfaces.

Findings

Successfully finds global minima in synthetic tests

Effective in real data applications

Overcomes local minima trapping

Abstract

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite of its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global chi^2 hypersurface minimum, jumping across chi^2{P_i} barriers when necessary, is demonstrated with synthetic functions and with real data.