A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

Wu, Keyi; Li, Jinglai

doi:10.1016/j.jcp.2016.06.020

Cited by 15 publications

(11 citation statements)

References 18 publications

(13 reference statements)

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“…The latter study also introduces a method which refines the surrogate continually as MCMC proceeds (and thus reduces the number of training points required), while the asymptotic exactness is ensured. We also mention, 49‐52 in which a similar approach is taken. For example, the approach in Reference 50 uses forward simulations from the PDEs for incrementally refining a local approximation of the (unnormalised) log posterior.…”

Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

Păun

Husmeier

2020

Numer Methods Biomed Eng

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The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid‐dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient‐specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed‐form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state‐of‐the‐art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long‐term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

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Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

Păun

Husmeier

2020

Numer Methods Biomed Eng

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“…[17,16,12]). To this end, surrogates have been used to accelerate the simulations in both the SS [20] and the MMC [26] methods. Thus we hope to develop surrogate based methods to reduce the computational cost of the SMMC algorithm.…”

Section: Discussionmentioning

confidence: 99%

A subset multicanonical Monte Carlo method for simulating rare failure events

Chen

2017

Journal of Computational Physics

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Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g ≤ 10 −10 ). In this case, standard Monte Carlo methods are not feasible due to the extraordinarily large number of samples required. To address these problems, we propose an algorithm that combines the main ideas of two very powerful failure probability estimation approaches: the subset simulation (SS) and the multicanonical Monte Carlo (MMC) methods. Unlike the standard MMC which samples in the entire domain of the input parameter in each iteration, the proposed subset MMC algorithm adaptively performs MMC simulations in a subset of the state space and thus improves the sampling efficiency.With numerical examples we demonstrate that the proposed method is significantly more efficient than both of the SS and the MMC methods. Moreover, the proposed algorithm can reconstruct the complete distribution function of the parameter of interest and thus can provide more information than just the failure probabilities of the systems.

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“…The popularity of MC simulations is illustrated by their continuous development. This development has led to various stratified sampling methods [28,29] that reduce the computational burden of MC, for example, Latin Hypercube Sampling [30][31][32]. Another improvement was the combination of MC with the Markov Chain process [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis of Spatiotemporal Models with Point Estimate Methods (PEMs)—The Case of the ANUGA Hydrodynamic Model

Issermann

Chang

2020

Water

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Practitioners often neglect the uncertainty inherent to models and their inputs. Point Estimate Methods (PEMs) offer an alternative to the common, but computationally demanding, method for assessing model uncertainty, Monte Carlo (MC) simulation. PEMs rerun the model with representative values of the probability distribution of the uncertain variable. The results can estimate the statistical moments of the output distribution. Hong’s method is the specific PEM implemented here for a case study that simulates water runoff using the ANUGA model for an area in Glasgow, UK. Elevation is the source of uncertainty. Three realizations of the Sequential Gaussian Simulation, which produces the random error fields that can be used as inputs for any spatial model, are scaled according to representative values of the distribution and their weights. The output from a MC simulation is used for validation. A comparison of the first two statistical moments indicates that Hong’s method tends to underestimate the first moment and overestimate the second moment. Model efficiency performance measures validate the usefulness of Hong’s method for the approximation of the first two moments, despite the method suffering from outliers. Estimation was less accurate for higher moments but the moment estimates were sufficient to use the Grams-Charlier Expansion to fit a distribution to them. Regarding probabilistic flood-inundation maps, Hong’s method shows very similar probabilities in the same areas as the MC simulation. However, the former requires just three 11-minute simulation runs, rather than the 500 required for the MC simulation. Hong’s method therefore appears attractive for approximating the uncertainty of spatiotemporal models.

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A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

Cited by 15 publications

References 18 publications

Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

A subset multicanonical Monte Carlo method for simulating rare failure events

Uncertainty Analysis of Spatiotemporal Models with Point Estimate Methods (PEMs)—The Case of the ANUGA Hydrodynamic Model

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