Surrogate-assisted Bayesian inversion for landscape and basin evolution models

Rohitash Chandra,Arpit Kapoor,Danial Azam,R Dietmar Müller

doi:10.5194/gmd-13-2959-2020

Abstract

Abstract. The complex and computationally expensive nature of landscape evolution models poses significant challenges to the inference and optimization of unknown model parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed parallel tempering Bayeslands as a framework for parameter estimation and uncertainty quantification for the Badlands landscape evolution model. Parallel tempering Bayeslands features high-performance computing that can feature dozens of processing cores running in parallel to enhance computational efficiency. Nevertheless, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape evolution problems, a single model evaluation can take from several minutes to hours and in some instances, even days or weeks. Surrogate-assisted optimization has been used for several computationally expensive engineering problems which motivate its use in optimization and inference of complex geoscientific models. The use of surrogate models can speed up parallel tempering Bayeslands by developing computationally inexpensive models to mimic expensive ones. In this paper, we apply surrogate-assisted parallel tempering where the surrogate mimics a landscape evolution model by estimating the likelihood function from the model. We employ a neural-network-based surrogate model that learns from the history of samples generated. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelism. The results show that the proposed methodology is effective in lowering the computational cost significantly while retaining the quality of model predictions.

Highlights

The Bayesian methodology provides a probabilistic approach for the estimation of unknown parameters in complex models (Sambridge, 1999; Neal, 1996; Chandra et al, 2019b)
We can view a deterministic geophysical forward model as a probabilistic model via Bayesian inference, which is known as Bayesian inversion, which has been used for landscape evolution (Chandra et al, 2019a, c), geological reef evolution models (Pall et al, 2020), and other geoscientific models (Sambridge, 1999, 2013; Scalzo et al, 2019; Olierook et al, 2020)
We evaluate the trade-off between quality of estimation by pseudo-likelihood and overall cost of computation for the true likelihood function for different types of problems

Summary

Introduction

The Bayesian methodology provides a probabilistic approach for the estimation of unknown parameters in complex models (Sambridge, 1999; Neal, 1996; Chandra et al, 2019b). Markov chain Monte Carlo (MCMC) sampling is typically used to implement Bayesian inference that involves the estimation and uncertainty quantification of unknown parameters (Hastings, 1970; Metropolis et al, 1953; Neal, 2012, 1996). Our previous work presented parallel tempering Bayeslands for parameter estimation and uncertainty quantification for landscape evolution models (LEMs) (Chandra et al, 2019c). MCMC methods provide a probabilistic approach for estimation of free parameters in a wide range of models (Kass et al, 1998; van Ravenzwaaij et al, 2016). Convergence is defined by a predefined number of samples or until the likelihood function has reached a specific value

Methods

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Discussion

Conclusion