The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates sequentially in time as observations are being collected. The updating step is based on the experimental covariances computed from an ensemble of realizations and the updates are given as linear combinations of the differences between observations and forecasted system state values. The ERFF replaces the linear combination in the update step with a non-linear function represented by a random forest. In this way, the non-linear relationships between the parameters to be updated and the observations can be captured and a better update produced. The ERFF is demonstrated for the purpose of log-conductivity identification from piezometric head observations in a number of scenarios with varying degrees of heterogeneity (log-conductivity variances going from 1 up to 6.25 (ln m/d)2), number of realizations in the ensemble (50 or 100), and number of piezometric head observations (18 or 36). In all scenarios, the ERFF works well, being able to reconstruct the log-conductivity spatial heterogeneity while matching the observed piezometric heads at selected control points. For benchmarking purposes the ERFF is compared to the restart EnKF to find that the ERFF is superior to the EnKF for the number of ensemble realizations used (small in typical EnKF applications). Only when the number of realizations grows to 500, the restart EnKF is able to match the performance of the ERFF, albeit at triple the computational cost.
翻译:集合随机森林过滤器(ERFF) 被展示为用于反向建模的全套 Kalman 过滤器(EnKF) 的替代。 EnKF 是一种数据同化方法,在观测收集过程中,在时间上连续预测并更新参数估计值。更新步骤的基础是从一系列实现和更新的组合中计算出来的实验共变变量,作为观测和预测系统状态值差异的线性组合。ERFF 仅将更新步骤中的线性组合替换为由随机森林代表的非线性功能。在这种方式中,要更新的参数与观测结果之间的非线性离线性关系可以被捕获并进行更好的更新。 ERFF 显示该更新步骤是为了在一系列不同程度的情景中,通过对正偏差头观察来进行逻辑-导辨别(从1到6.25(m/d)之间,只有500个线性差值),更新的应用程序中的实现次数(50或100个),以及用于Stencial-F 头观测结果的数值(18或36个),在所观测到所观测到的直径直径直径方的内。