Enabling Bayesian uncertainty quantification for multiscale systems and network models via mutual likelihood-informed dimension reduction (A06+)

蒙特卡罗方法是应用于整个物理科学中的逆问题的统计推断的计算主力，但在推断高维或耦合参数时可能变得过于昂贵。 这是与SFB 1114感兴趣的多尺度系统相关联的许多状态或参数推断问题的设置，例如降水和飓风动力学。 我们建议使用的组合策略，从既定的传统，如多级和自适应蒙特卡罗，和新的贡献，如似然知情的主动子空间降维和转移算子堆叠，以减少有效的计算维数，从而加速收敛和降低计算成本，同时也研究和控制的影响所产生的近似误差。

Monte Carlo methods are the computational workhorse of statistical inference as applied to inverse problems throughout the physical sciences, but can become prohibitively costly when inferring high-dimensional or coupled parameters. This is the setting of many state or parameter inference problems associated to multiscale systems of interest to SFB 1114, such as precipitation and hurricane dynamics. We propose to use a combination of strategies drawn from established traditions such as multilevel and adaptive Monte Carlo, and novel contributions such as likelihood-informed active subspace dimension reduction and transfer operator stacking, to reduce the effective computational dimension, thereby accelerating convergence and reducing computational cost, while also studying and controlling the impact of the approximation errors incurred.