A very fast simulated re-annealing algorithm is presented for statistically finding the best global fit of a nonlinear, non-convex cost function in a D-dimensional parameter space. The algorithm uses an exponentially decreasing temperature schedule, $ T = T_0 \exp(-c k^{1/D}) $, which is faster than fast Cauchy annealing ($ T = T_0/k $) and Boltzmann annealing ($ T = T_0/\ln k $). This method is enhanced with re-annealing, allowing adaptation to changing sensitivities in multi-dimensional parameter spaces, resulting in the very fast re-annealing (VFR) algorithm. The algorithm is based on a generating function that samples the parameter space efficiently, with a probability distribution that allows for faster convergence to the global minimum. The method is applied to fit empirical data to Lagrangians representing nonlinear Gaussian-Markovian systems. It is particularly useful for complex systems where the cost function is nonlinear and non-convex, such as in combat models, neuroscience, and nuclear physics. The VFR algorithm is statistically shown to find a global minimum by using an annealing schedule that ensures the sum of probabilities over all annealing steps diverges, leading to a statistically significant result. The algorithm is also adaptable to different parameter sensitivities by periodically rescaling the annealing time based on the current minimum value of the cost function. Applications of the VFR algorithm include fitting combat systems to exercise data, modeling economic markets, and fitting human EEG data to Lagrangians derived from mesoscopic neocortical interactions. The algorithm is also used in the analysis of long-time probability distributions, where it provides a sensitive separation of models based on their long-time correlations. The VFR algorithm is efficient and effective for a wide range of problems, particularly those involving nonlinear, non-convex cost functions in high-dimensional spaces. It is a powerful tool for statistical modeling and optimization in various scientific and engineering disciplines.A very fast simulated re-annealing algorithm is presented for statistically finding the best global fit of a nonlinear, non-convex cost function in a D-dimensional parameter space. The algorithm uses an exponentially decreasing temperature schedule, $ T = T_0 \exp(-c k^{1/D}) $, which is faster than fast Cauchy annealing ($ T = T_0/k $) and Boltzmann annealing ($ T = T_0/\ln k $). This method is enhanced with re-annealing, allowing adaptation to changing sensitivities in multi-dimensional parameter spaces, resulting in the very fast re-annealing (VFR) algorithm. The algorithm is based on a generating function that samples the parameter space efficiently, with a probability distribution that allows for faster convergence to the global minimum. The method is applied to fit empirical data to Lagrangians representing nonlinear Gaussian-Markovian systems. It is particularly useful for complex systems where the cost function is nonlinear and non-convex, such as in combat models, neuroscience, and nuclear physics. The VFR algorithm is statistically shown to find a global minimum by using an annealing schedule that ensures the sum of probabilities over all annealing steps diverges, leading to a statistically significant result. The algorithm is also adaptable to different parameter sensitivities by periodically rescaling the annealing time based on the current minimum value of the cost function. Applications of the VFR algorithm include fitting combat systems to exercise data, modeling economic markets, and fitting human EEG data to Lagrangians derived from mesoscopic neocortical interactions. The algorithm is also used in the analysis of long-time probability distributions, where it provides a sensitive separation of models based on their long-time correlations. The VFR algorithm is efficient and effective for a wide range of problems, particularly those involving nonlinear, non-convex cost functions in high-dimensional spaces. It is a powerful tool for statistical modeling and optimization in various scientific and engineering disciplines.