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<p>Limited observational data and the challenge of obtaining direct measurements contribute to the prevalence of inverse problems in earth system modeling. Bayesian framework is an approach for making informed inferences in inverse problems. Solving high-dimensional Bayesian inverse problems poses challenges due to the curse of dimensionality, necessitating the development of effective methods for Markov Chain Monte Carlo (MCMC) sampling. Due to the vast parameter space, traditional random walk methods suffer from poor convergence rates in such problems. In contrast, gradient-based approaches leverage the geometry of the target distribution to navigate from low to high-density regions. The availability of automatic differentiation further facilitates the widespread adoption of gradient-based methods. This study employs the No U-Turn sampler (NUTS) to sample from the posterior distribution of a high-dimensional geophysical inverse problem. NUTS offers a tuning-free solution to the step-size and integration time dilemma inherent in Hamiltonian Monte Carlo (HMC). Augmented with online learning of the mass matrix, NUTS emerges as an effective tool for addressing high-dimensional sampling challenges. However, this enhancement comes with the cost of increased computational overhead compared to optimally tuned HMC. We demonstrate the effectiveness of NUTS for high-dimensional sampling with intercorrelated dimension problems through real-case field experiments in non-linear Bayesian seismic amplitude versus offset (AVO) inversion and synthetic benchmark problems. Our findings underscore the value of NUTS as a tuning-free approach for Bayesian inference in a complex model.</p>

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Geophysical bayesian inverse problem solving with tuning-free adaptive MCMC sampler

  • 期刊论文

  • 发表日期：

    2025年1月17日

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  • Amin Arabpour,
  • Rasoul Hamidzadeh Moghadam,
  • Mohammad Emami Niri

摘要

Limited observational data and the challenge of obtaining direct measurements contribute to the prevalence of inverse problems in earth system modeling. Bayesian framework is an approach for making informed inferences in inverse problems. Solving high-dimensional Bayesian inverse problems poses challenges due to the curse of dimensionality, necessitating the development of effective methods for Markov Chain Monte Carlo (MCMC) sampling. Due to the vast parameter space, traditional random walk methods suffer from poor convergence rates in such problems. In contrast, gradient-based approaches leverage the geometry of the target distribution to navigate from low to high-density regions. The availability of automatic differentiation further facilitates the widespread adoption of gradient-based methods. This study employs the No U-Turn sampler (NUTS) to sample from the posterior distribution of a high-dimensional geophysical inverse problem. NUTS offers a tuning-free solution to the step-size and integration time dilemma inherent in Hamiltonian Monte Carlo (HMC). Augmented with online learning of the mass matrix, NUTS emerges as an effective tool for addressing high-dimensional sampling challenges. However, this enhancement comes with the cost of increased computational overhead compared to optimally tuned HMC. We demonstrate the effectiveness of NUTS for high-dimensional sampling with intercorrelated dimension problems through real-case field experiments in non-linear Bayesian seismic amplitude versus offset (AVO) inversion and synthetic benchmark problems. Our findings underscore the value of NUTS as a tuning-free approach for Bayesian inference in a complex model.