Hydrogeological multiple-point statistics inversion by adaptive sequential Monte Carlo

Amaya, Macarena; Linde, Niklas; Laloy, Eric

doi:10.1016/j.advwatres.2022.104252

Cited by 3 publications

(4 citation statements)

References 41 publications

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“…Finally, exploring test cases that do not rely on Gaussian assumptions would be intriguing, as previously undertaken for the posterior part in Amaya et al. (2021, 2022).…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, considering alternative approaches for the intermediate steps in both phases could be interesting, such as incorporating a method based on smoothed indicator functions and thermodynamic integration proposed by Xiao et al (2019), in the second phase. Finally, exploring test cases that do not rely on Gaussian assumptions would be intriguing, as previously undertaken for the posterior part in Amaya et al (2021Amaya et al ( , 2022.…”

Section: Water Resources Researchmentioning

confidence: 99%

“…We build our PostRisk-SMC method on an adaptive version of the SMC method by Zhou et al (2016), which automatically tunes the cooling sequence between power posteriors. Recently, adaptive SMC methods have been employed successfully for geophysical (Amaya et al, 2021;Davies et al, 2023) and hydrogeological (Amaya et al, 2022) inversion problems, demonstrating superior performance compared with state-of-the-art MCMC methods.…”

Section: Introductionmentioning

confidence: 99%

“…For high‐dimensional problems with non‐linear forward solvers, standard MCMC methods often have difficulties in approximating the posterior PDF within realistic computational constraints. This happens as the Markov chains may be trapped in local minima for long times or have insignificant probabilities of switching between posterior modes (e.g., Amaya et al., 2022; Neal, 2001). To overcome these challenges, methods based on so‐called power posteriors have been introduced.…”

Section: Introductionmentioning

confidence: 99%

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Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

Friedli,

Linde

2024

Water Resources Research

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Bayesian inversions followed by estimations of rare event probabilities are often needed to analyze groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon these parameters. To address the associated methodological challenges, we introduce a two‐stage Sequential Monte Carlo approach. In the first stage, it generates particles that approximate the posterior distribution; in the second stage, it employs subset sampling techniques to assess the probability of the rare event of interest. By considering two hydrogeological problems of increasing complexity, we showcase the efficiency and accuracy of the resulting PostRisk‐SMC method for rare event probability estimation related to groundwater hazards. We compare the performance of the PostRisk‐SMC method with a traditional Monte Carlo approach that relies on Markov chain Monte Carlo samples. We showcase that our estimates align with those of the traditional method, but the coefficients of variation are notably lower for the same computational budget when targeting more rare events. Furthermore, we highlight that the PostRisk‐SMC method allows estimating rare event probabilities approaching one in a billion using less than one hundred thousand forward simulations. Even if the presented examples are related to groundwater hazards, the methodology is well‐suited for addressing a wide range of topics in the geosciences and beyond.

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“…Finally, exploring test cases that do not rely on Gaussian assumptions would be intriguing, as previously undertaken for the posterior part in Amaya et al. (2021, 2022).…”

Section: Discussionmentioning

confidence: 99%

Section: Water Resources Researchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

Friedli,

Linde

2024

Water Resources Research

Self Cite

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A multi-scale blocking moving window algorithm for geostatistical seismic inversion

JiaGen

Yin

et al. 2023

Computers & Geosciences

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Multifidelity adaptive sequential Monte Carlo for geophysical inversion

Amaya,

Meles,

Marelli

et al. 2024

Geophysical Journal International

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Summary In the context of Bayesian inversion, we consider sequential Monte Carlo (SMC) methods that provide an approximation of the posterior probability density function and the evidence (marginal likelihood). These particle approaches build a sequence of importance sampling steps between gradually-tempered distributions evolving from the prior to the posterior PDF. To automate the definition of the tempering schedule, adaptive sequential Monte Carlo (ASMC) allows tuning the temperature increments on-the-go. One general challenge in Bayesian inversions is the computational burden associated with expensive, high-fidelity forward solvers. Lower-fidelity surrogate models are interesting in this context as they can emulate the response of expensive forward solvers at a fraction of their cost. We consider surrogate modeling within ASMC and introduce first an approach involving surrogate modeling only, in which either prior samples are used to train the surrogate, or the surrogate model is re-trained by updating the training set during the inversion. In our implementation, we rely on polynomial chaos expansions for surrogate modeling, principal component analysis for model parametrization and a ground-penetrating radar cross-hole tomography problem with either an eikonal or finite-difference time-domain solver as high-fidelity solver. We find that the method based on re-training the surrogate during the inversion outperforms the results obtained when only considering prior samples. We then introduce a computationally more expensive multifidelity approach including a transition to the high-fidelity forward solver at the end of the surrogate-based ASMC run leading to even more accurate results. Both methods result in speed-ups that are larger than one order of magnitude compared to standard high-fidelity ASMC inversion.

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Hydrogeological multiple-point statistics inversion by adaptive sequential Monte Carlo

Cited by 3 publications

References 41 publications

Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

A multi-scale blocking moving window algorithm for geostatistical seismic inversion

Multifidelity adaptive sequential Monte Carlo for geophysical inversion

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