Data adaptation in HANDY economy-ideology model
This addresses the data assimilation challenge for researchers working with complex mathematical models in fields like environmental science and economics, though it appears to be an incremental improvement on existing methods.
The researchers tackled the problem of fitting high-dimensional nonlinear models to ground truth data by comparing Approximate Bayesian Computation and Supermodeling approaches on the HANDY economy-ideology model, demonstrating that Supermodeling with synchronization via the most sensitive variable provides better forecasting for both chaotic and stable systems than Approximate Bayesian Computation.
The concept of mathematical modeling is widespread across almost all of the fields of contemporary science and engineering. Because of the existing necessity of predictions the behavior of natural phenomena, the researchers develop more and more complex models. However, despite their ability to better forecasting, the problem of an appropriate fitting ground truth data to those, high-dimensional and nonlinear models seems to be inevitable. In order to deal with this demanding problem the entire discipline of data assimilation has been developed. Basing on the Human and Nature Dynamics (HANDY) model, we have presented a detailed and comprehensive comparison of Approximate Bayesian Computation (classic data assimilation method) and a novelty approach of Supermodeling. Furthermore, with the usage of Sensitivity Analysis, we have proposed the methodology to reduce the number of coupling coefficients between submodels and as a consequence to increase the speed of the Supermodel converging. In addition, we have demonstrated that usage of Approximate Bayesian Computation method with the knowledge about parameters' sensitivities could result with satisfactory estimation of the initial parameters. However, we have also presented the mentioned methodology as unable to achieve similar predictions to Approximate Bayesian Computation. Finally, we have proved that Supermodeling with synchronization via the most sensitive variable could effect with the better forecasting for chaotic as well as more stable systems than the Approximate Bayesian Computation. What is more, we have proposed the adequate methodologies.