Tuning Hamiltonian Monte Carlo in full waveform inversion

Jinji Li, Kristopher A. Innanen

Tuning the Hamiltonian Monte Carlo (HMC) stands as a crucial endeavor, especially within the realm of geophysical optimization and inversion where the problems are complex and high-dimensional. In the context of this report, we offer an in-depth examination of the functionalities associated with the tunable parameters, such as the integration length, time step, and mass matrix. The minimum-model sampling experiment has shown that assigning the second-order information to the mass matrix can help the sampler reach the target distribution more efficiently, and the HMC-FWI experiment has shown that an adaptive tuning strategy can significantly accelerate the convergence and thus produce more precise solutions within limited sampling attempts. This work contributes to a deeper understanding of the role of tuning in HMC applications and can serve as a valuable reference for future utilization.