Mathematical Sciences, UTD
Computationally Efficient Monte Carlo Methods for Velocity Inversion and Uncertainty Quantification
Stochastic methods for uncertainty quantification in inverse problems are powerful because fewer assumptions are imposed on the shape of the posterior distribution. However, methods like Markov chain Monte Carlo (MCMC) often require tens or hundreds of thousands of solutions of the forward problem. In geophysics applications this forward problem is computationally expensive, which can make MCMC methods infeasible for large problems. Furthermore, velocity fields often contain fine details and require hundreds or thousands of unknowns to characterize. In Metropolis-Hastings MCMC (MH-MCMC), high dimensional problems often require more samples to converge to the posterior distribution than is computationally feasible. Two-stage MCMC reduces the computational expense of MH-MCMC by introducing an inexpensive filter to quickly reject unacceptable samples. Samples that are accepted on the filter are then tested with the full forward problem, thereby ensuring the posterior distribution is accurate for the likelihood function containing the full forward problem. Hamiltonian Monte Carlo (HMC) uses gradient information to overcome the space exploration difficulty posed by high-dimensional problems. In this talk, I will discuss two-stage MCMC for the velocity inversion problem using two filters: operator upscaling, which uses an augmented coarse grid to reduce computational cost while retaining the ability to resolve sub-coarse-block details, and a neural net trained to predict the likelihood function. I will also introduce a two-stage HMC framework for the velocity inversion problem.
John Zweck , 972-883-6699
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