Efficient Bayesian geoacoustic inversion using mixture density networks

Bayesian seabed geoacoustic inverse problems are commonly addressed using Markov chain Monte Carlo (McMC) methods or their variants, which are computationally expensive. This study proposes an efficient Bayesian geoacoustic inversion approach based on mixture density networks (MDNs). Rather than training separate networks for each parameter, this approach models the joint posterior probability distribution of all parameters. Moreover, the classical Bayesian geoacoustic inversion framework is enhanced by utilizing the MDN theory to analytically deduce essential geoacoustic statistics from the multidimensional posterior probability density (PPD). This approach not only eliminates the computationally intensive numerical integration typically required for Bayesian inversion but also provides deeper insight into the statistical characteristics of the Bayesian PPD. Comparisons of MDN and McMC inversion results across various cases reveal that the inversion using MDN (MDN inversion) produces PPD approximations that align well with the McMC method in terms of overall trends, despite some local discrepancies. Analysis of inter-parameter correlations indicates that the MDN can capture key trade-offs between parameters. This approach offers an efficient method for solving seabed geoacoustic inverse problems within the Bayesian inference framework, making it a promising technique for real-time inversion.