Covariance Matrix Adaptation Evolution Research Articles

Influence of GEOTRACES data distribution and misfit function choice on objective parameter retrieval in a marine zinc cycle model

Abstract. Biogeochemical model behaviour for micronutrients is typically hard to constrain because of the sparsity of observational data, the difficulty of determining parameters in situ, and uncertainties in observations and models. Here, we assess the influence of data distribution, model uncertainty, and the misfit function on objective parameter optimisation in a model of the oceanic cycle of zinc (Zn), an essential micronutrient for marine phytoplankton with a long whole-ocean residence time. We aim to investigate whether observational constraints are sufficient for reconstruction of biogeochemical model behaviour, given that the Zn data coverage provided by the GEOTRACES Intermediate Data Product 2017 is sparse. Furthermore, we aim to assess how optimisation results are affected by the choice of the misfit function and by confounding factors such as analytical uncertainty in the data or biases in the model related to either seasonal variability or the larger-scale circulation. The model framework applied herein combines a marine Zn cycling model with a state-of-the-art estimation of distribution algorithm (Covariance Matrix Adaption Evolution Strategy, CMA-ES) to optimise the model towards synthetic data in an ensemble of 26 optimisations. Provided with a target field that can be perfectly reproduced by the model, optimisation retrieves parameter values perfectly regardless of data coverage. As differences between the model and the system underlying the target field increase, the choice of the misfit function can greatly impact optimisation results, while limitation of data coverage is in most cases of subordinate significance. In cases where optimisation to full or limited data coverage produces relatively distinct model behaviours, we find that applying a misfit metric that compensates for differences in data coverage between ocean basins considerably improves agreement between optimisation results obtained with the two data situations.

A Study on Performace of Levenberg-Marquardt and CMA-ES Optimization Methods for Atlas-based 2D/3D Reconstruction

Abstract: In this study, we compare the performance of our previously proposed deformable 2D/3D registration approach based on the Levenberg-Marquardt optimization with methods exploiting Covariance Matrix Adaptation (CMA) and Covariance Matrix Self Adaptation (CMSA) evolution strategies. The aim of the registration is to reconstruct a patient-specifc 3D bone model from a small set of plain 2D X-ray images what is achieved by ftting a deformable bone atlas onto the X-ray images. The comparison of diferent optimization methods is focused on both the robustness and the speed. The results were obtained using a large-scale data set of synthetic X-ray images. We show that our method is several times faster in comparison with the approaches based on evolution strategies while the robustness of the reconstruction is preserved. To speed-up the reconstruction process, certain parts of the registration pipeline are accelerated using graphics hardware. The median error of our proposed method was 1.12mm and the median reconstruction time was 7.2s. The median time reached by the CMA-ES and CMSA-ES methods was 48.5 s and 138.5 s respectively.