2018/09/19 by Eric Laloy, Laloy, Eric, Diederik Jacques +1 · 2 citations
Decision Sciences · Engineering · Environmental Science · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Geophysics (physics.geo-ph) #Groundwater flow and contamination studies #Nuclear reactor physics and engineering #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1809.07305
openalex publication_date 2018/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a detailed comparison between 3 methods for emulating\nCPU-intensive reactive transport models (RTMs): Gaussian processes (GPs),\npolynomial chaos expansion (PCE) and deep neural networks (DNNs). Besides\ndirect emulation of the simulated uranium concentration time series, replacing\nthe original RTM by its emulator is also investigated for global sensitivity\nanalysis (GSA), uncertainty propagation (UP) and probabilistic calibration\nusing Markov chain Monte Carlo (MCMC) sampling. The selected DNN is found to be\nsuperior to both GPs and PCE in reproducing the input - output behavior of the\nconsidered 8-dimensional and 13-dimensional CPU-intensive RTMs. Furthermore,\nthe two used PCE variants: standard PCE and sparse PCE (sPCE) appear to always\nprovide the least accuracy while not differing much in performance. As a\nconsequence of its better emulation capabilities, the used DNN outperforms the\ntwo other methods for UP. In addition, DNNs and GPs offer equally good\napproximations to the true first-order and total-order Sobol sensitivity\nindices while PCE does somewhat less well. Most surprisingly, despite its\nsuperior emulation skills the DNN approach leads to the worst solution of the\nconsidered synthetic inverse problem which involves 1224 measurement data with\nlow noise. This apparently contradicting behavior is at least partially due to\nthe small but complicated deterministic noise that affects the DNN-based\npredictions. Indeed, this complex error structure can drive the emulated\nsolutions far away from the true posterior distribution. Overall, our findings\nindicate that when the available training set is relatively small (75 - to 500\ninput - output examples) and fixed beforehand, DNNs can well emulate RTMs but\nare not suited to emulation-based inversion. In contrast, GPs perform fairly\nwell across all considered tasks: direct emulation, GSA, UP, and inversion.\n