Performance comparison of physics-based and machine learning assisted multi-fidelity methods for the management of coastal aquifer systems

Abstract

In this work we investigate the performance of various lower-fidelity models of seawater intrusion in coastal aquifer management problems. The variable density model is considered as the high-fidelity model and a pumping optimization framework is applied on a hypothetical coastal aquifer system in order to calculate the optimal pumping rates which are used as a benchmark for the lower-fidelity approaches. The examined lower-fidelity models could be classified in two categories: (1) physics-based models, which include several widely used variations of the sharp-interface approximation and (2) machine learning assisted models, which aim to improve the efficiency of the SI approach. The Random Forest method was utilized to create a spatially adaptive correction factor for the original sharp-interface model, which improves its accuracy without compromising its efficiency as a lower-fidelity model. Both the original sharp-interface and Machine Learning assisted model are then tested in a single-fidelity optimization method. The optimal pumping rated which were calculated using the Machine Learning based SI model sufficiently approximate the solution from the variable density model. The Machine Learning assisted approximation seems to be a promising surrogate for the high-fidelity, variable density model and could be utilized in multi-fidelity groundwater management frameworks.

Ensemble Learning for Blending Gridded Satellite and Gauge-Measured Precipitation Data

“…The latter are referred to as "base learners" throughout the work and include the multivariate adaptive regression splines (MARS), multivariate adaptive polynomial splines (poly-MARS), RF, gradient boosting machines (GBM), extreme gradient boosting (XGBoost) and Bayesian regularized neural networks (BRNN), which are briefly described in Appendix A. These learners are regularly applied in hydrology (see, e.g., the applications by [52][53][54][55]). Also notably, they are largely diverse with each other and exhibit considerably good performances for the task of interest according to [30].…”

“…boosting machines (GBM), extreme gradient boosting (XGBoost) and Bayesian regularized neural networks (BRNN), which are briefly described in Appendix A. These learners are regularly applied in hydrology (see, e.g., the applications by [52][53][54][55]). Also notably, they are largely diverse with each other and exhibit considerably good performances for the task of interest according to [30].…”

“…• Linear regression (LR): In LR, the dependent variable is a function of a linear weighted sum of the predictors ( [17], pp. [43][44][45][46][47][48][49][50][51][52][53][54][55]. The weights are estimated by minimizing the mean squared error.…”