Accelerating Bayesian inference in hydrological modeling with a mechanistic emulator

Abstract

As in many fields of dynamic modeling, the long runtime of hydrological models hinders Bayesian inference of model parameters from data. By replacing a model with an approximation of its output as a function of input and/or parameters, emulation allows us to complete this task by trading-off accuracy for speed. We combine (i) the use of a mechanistic emulator, (ii) low-discrepancy sampling of the parameter space, and (iii) iterative refinement of the design data set, to perform Bayesian inference with a very small design data set constructed with 128 model runs in a parameter space of up to eight dimensions. In our didactic example we use a model implemented with the hydrological simulator SWMM that allows us to compare our inference results against those derived with the full model. This comparison demonstrates that iterative improvements lead to reasonable results with a very small design data set. Keypoints • Mechanistic emulation• Design data points selection • Calibration of hydrological models

Exploratory-Phase-Free Estimation of GP Hyperparameters in Sequential Design Methods—At the Example of Bayesian Inverse Problems

“…The mean function used for all GPEs in this article is the constant zero mean: m 0 ( x ) = 0. Alternatively, the mean could also be set as unknown which is sometimes referred to as ordinary Kriging, as polynomial function (universal Kriging) or any other function like a simplified mechanistic model (e.g., Machac et al, 2018 ).…”

Surrogate‐Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error

“…For example, Zhang et al (2013) proposed to first identify the posterior region with an optimization method, then build the surrogate model and implement the surrogate-based MCMC simulation; Li & Marzouk (2014) proposed an adaptive approach to find a distribution that is close to the posterior distribution by minimizing the cross entropy, and then construct a locally accurate PCE surrogate therein. Recently, Gaussian process (GP) regression (Rasmussen & Williams, 2006) was combined with MCMC simulation to iteratively refine the surrogate over the posterior distribution (Gong & Duan, 2017;Machac et al, 2018;Zhang et al, 2016;Zhang et al, 2018a). It is shown that this approach can obtain satisfying inversion results with only a small number of high-fidelity model evaluations.…”

“…These samples can be viewed as random draws from the approximated posterior distribution. Machac et al (2018) adopted a similar approach to drawing new design points for high-fidelity model evaluations, but they intentionally stretched these samples by a factor of 1.1; that is, the new samples were actually drawn from a distribution that is 1.1 wider than the approximated posterior. Gong and Duan (2017) proposed a more elaborate method to generate representative samples from the approximated posterior, which is implemented as follows: (1) Select the sample with the largest posterior density; (2) divide the converged chain states into several quintile ranges, and select in each range a new sample that has the largest distance to its nearest neighbor.…”

“…In this paper, considering that abundant published works on adaptive surrogate modeling for inverse problems have used PCE (Conrad et al, ; Li & Marzouk, ; Yan & Zhou, ) and/or GP (Conrad et al, ; Gong & Duan, ; Machac et al, ; Wang & Li, ; Zhang et al, ; Zhang, Man, et al, ), so we decide to use these two popular surrogates for demonstration. The performances of other surrogates will not be evaluated here.…”

Flooding and Overflow Mitigation Using Deep Reinforcement Learning Based on Koopman Operator of Urban Drainage Systems

“…A relatively safe option is to use a surrogate model, or emulator, as a replacement for the UDS model in the RL training to overcome the large computational burden and the low efficiency of data usage (Chua et al, 2018;Kalweit & Boedecker, 2017). Emulators can be divided into two categories: (a) the structure-based methods, which simplify the mathematical structure of the original model for fast computing (Castelletti et al, 2012;Machac et al, 2018), and (b) the data-based methods, which establish an emulator using data generated from planned experiments conducted on the simulation model or the sensor (Bieker et al, 2020;Carbajal et al, 2017;Castelletti et al, 2012). The latter category has better adaptability to different dynamics, and is the focus of this work.…”