[Paper Review] Data adaptation in HANDY economy-ideology model

Marcin Sendera|arXiv (Cornell University)|Apr 8, 2019

Probabilistic and Robust Engineering Design64 references3 citations

TL;DR

This paper proposes a novel data assimilation framework for the HANDY economy-ideology model by comparing Approximate Bayesian Computation (ABC) with Supermodeling, a synchronization-based approach. It demonstrates that Supermodeling, especially when synchronizing on the most sensitive variable, achieves superior forecasting accuracy for both chaotic and stable systems, while sensitivity analysis reduces coupling coefficients and accelerates convergence.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of fitting high-dimensional, nonlinear models like HANDY to real-world data.
• To evaluate and compare the performance of Approximate Bayesian Computation (ABC) and Supermodeling in data assimilation for the HANDY model.
• To develop a sensitivity-based methodology to reduce coupling coefficients and improve convergence speed in Supermodeling.
• To determine whether Supermodeling can achieve better forecasting than ABC, especially in chaotic systems.

Proposed method

• Applying Approximate Bayesian Computation (ABC) to estimate initial parameters in the HANDY model using sensitivity-informed priors.
• Implementing Supermodeling by coupling submodels through synchronization, with emphasis on the most sensitive variable to enhance stability and accuracy.
• Using global sensitivity analysis to identify the most influential parameters and reduce the number of coupling coefficients.
• Calibrating the model using historical data and comparing forecast performance between ABC and Supermodeling across different system dynamics.
• Employing a multi-model ensemble approach where synchronized submodels collectively represent the system behavior.
• Validating results through comparative forecasting on both chaotic and stable system regimes.

Experimental results

Research questions

• RQ1 Can Supermodeling outperform Approximate Bayesian Computation (ABC) in forecasting accuracy for the HANDY economy-ideology model?
• RQ2 How does sensitivity-based reduction of coupling coefficients affect convergence speed and forecasting performance in Supermodeling?
• RQ3 Does synchronizing on the most sensitive variable improve forecasting accuracy in both chaotic and stable systems?
• RQ4 To what extent can sensitivity analysis enhance parameter estimation in ABC when prior knowledge is limited?
• RQ5 Can Supermodeling achieve reliable predictions without full knowledge of the true parameter values, unlike ABC?

Key findings

• Supermodeling with synchronization via the most sensitive variable achieved better forecasting accuracy than ABC for both chaotic and stable systems.
• Sensitivity analysis successfully reduced the number of coupling coefficients, significantly improving convergence speed in Supermodeling.
• ABC with sensitivity-informed priors provided satisfactory initial parameter estimation but failed to match the forecasting performance of Supermodeling.
• The proposed methodology did not achieve comparable predictive accuracy to ABC when applied to the same data assimilation task.
• Supermodeling demonstrated robustness and superior predictive capability across diverse dynamical regimes, outperforming ABC in all tested scenarios.