Priors, Posteriors, and Approximations: Perspectives on Massively Parallel Cloud Computing as a Road Forward for Hydrogeophysical Inverse Problems

Past limits on computational power produced an emphasis on fast and efficient methods for searching the model parameter space with a minimum number of calculations of the forward model. As computational resources have grown over the past few decades interest has grown in applying stochastic sampling methods, such as Markov chain Monte Carlo, to estimate posterior uncertainty of model parameters. In both cases, however, a key challenge for hydrogeophysical imaging problems is that many of these search approaches require a sequential updating of the model parameters to move toward an overall best-fit of the observed data in a high dimensional parameter space. Methodologies have emerged in hydrogeophysics to reduce the dimensionality of the parameter space, such as coupled and basis constrained inversion. These approaches can be considered broadly as examples of subspace methods that that reduce the dimensionality of the geophysical parameter space to improve the search efficiency for an optimal solution. The search of this space, however, still occurs in a sequential fashion that requires successive calculations of the forward model, which may be computationally intensive.

Cloud computing is providing increasingly cheap and available capacity for high-throughput computation, i.e., thousands (or even millions) of models may be run in parallel. In other words, many samples of the likelihood can be generated at the same time. As a result, if sufficient samples are obtained to accurately approximate the posterior distribution in a single massive deployment on cloud resources, the shortest possible time required to solve an inverse problem would in theory be equivalent to the computational time for a single run of the forward model. Given that we have finite computational resources available, we have implemented an approach where we iteratively improve the approximation of the posterior as new samples are obtained. To achieve a good approximately of the posterior while guiding the sampling toward regions of high probability, we use space filling methods with genetic algorithms and other search techniques. The approach also allows us to frame the problem as a multi-objective optimization without any additional computation, thereby allowing decision makes to investigate consequences of fitting different types of data.