Emulation of CPU-demanding reactive transport models: a comparison of Gaussian processes, polynomial chaos expansion, and deep neural networks

摘要: This paper presents a detailed comparison between 3 methods for emulating CPU-intensive reactive transport models (RTMs): Gaussian processes (GPs), polynomial chaos expansion (PCE), and deep neural networks (DNNs). State-of-the-art open source libraries are used each emulation method while the CPU-time incurred by one forward run of considered RTMs varies from 1 h to 30 min 5 days. Besides direct simulated uranium concentration time series, replacing original RTM its emulator is also investigated global sensitivity analysis (GSA), uncertainty propagation, probabilistic calibration using Markov chain Monte Carlo (MCMC) sampling. The selected DNN found be superior both GPs PCE in reproducing input–output behavior 8-dimensional 13-dimensional RTMs. even though training sets small, 75 500 samples. Furthermore, two variants, standard sparse (sPCE), appear always provide least accuracy not differing much performance. As consequence better capabilities, outperforms other propagation. For GSA application, GP offer equally good approximations true first-order total-order Sobol’ indices does less well. Most surprisingly, despite skills, approach leads worst solution synthetic inverse problem which involves 1224 measurement data with low noise. apparently contradicting at partially due small but complicated deterministic noise that affects DNN-based predictions. Indeed, this complex error structure can drive emulated solutions far away posterior distribution case high-quality data. Among methods, only allows retrieving jointly (1) fit appropriate level (log-likelihood value) (2) most closely model parameter values. Overall, our findings indicate when available set relatively (75 input-output examples) fixed beforehand, best choice Instead, or DNNs should preferred. However, deliver overly biased results. In contrast, performs fairly well across all tasks: emulation, analysis, calibration.