[论文解读] Data adaptation in HANDY economy-ideology model

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

Probabilistic and Robust Engineering Design参考文献 64被引用 3

一句话总结

本文提出了一种针对HANDY经济-意识形态模型的新型数据同化框架，通过对比近似贝叶斯计算（ABC）与基于同步的超级模型（Supermodeling）方法。结果表明，超级模型方法，尤其是在最敏感变量上进行同步时，对混沌系统和稳定系统均实现了更优的预测精度；同时，敏感性分析可降低耦合系数并加速收敛。

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.

研究动机与目标

• 为解决将高维、非线性模型（如HANDY）拟合到现实世界数据的挑战。
• 评估并比较近似贝叶斯计算（ABC）与超级模型在HANDY模型数据同化中的性能表现。
• 提出一种基于敏感性的方法，以减少超级模型中的耦合系数并提升收敛速度。
• 确定超级模型是否能在混沌系统中实现优于ABC的预测性能。

提出的方法

• 应用近似贝叶斯计算（ABC）方法，利用敏感性指导的先验分布，估计HANDY模型的初始参数。
• 通过在子模型之间实现同步来构建超级模型，重点聚焦于最敏感变量，以提升稳定性与预测精度。
• 采用全局敏感性分析，识别最具影响力的参数，从而减少耦合系数的数量。
• 利用历史数据进行模型标定，并在不同系统动力学条件下，对比ABC与超级模型的预测性能。
• 采用多模型集成方法，使同步的子模型共同表征系统行为。
• 通过在混沌与稳定系统状态下的对比预测，验证结果的有效性。

实验结果

研究问题

• RQ1 超级模型能否在HANDY经济-意识形态模型的预测精度上超越近似贝叶斯计算（ABC）？
• RQ2 基于敏感性的耦合系数缩减对超级模型的收敛速度与预测性能有何影响？
• RQ3 在混沌与稳定系统中，对最敏感变量进行同步是否能提升预测精度？
• RQ4 当先验知识有限时，敏感性分析在多大程度上可提升ABC中的参数估计效果？
• RQ5 超级模型是否能在不完全掌握真实参数值的情况下实现可靠预测，而ABC则不能？

主要发现

• 在混沌与稳定系统中，通过最敏感变量实现同步的超级模型，其预测精度均优于ABC。
• 敏感性分析成功减少了耦合系数的数量，显著提升了超级模型的收敛速度。
• 采用敏感性指导先验的ABC方法可实现令人满意的初始参数估计，但其预测性能无法与超级模型相匹敌。
• 当应用于相同的数据同化任务时，所提出的方法未能达到ABC的预测精度水平。
• 超级模型在多种动力学状态下表现出强鲁棒性与优越的预测能力，在所有测试场景中均优于ABC。