Improved Sampling of Configuration Space of Biomolecules Using Shadow Hybrid Monte Carlo

Sampling the configuration space of complex biological molecules is an important and formidable problem. One major difficulty is the high dimensionality of this space, roughly $3N$, with the number of atoms $N$ typically in the thousands. This thesis introduces shadow hybrid Monte Carlo (SHMC), a propagator through phase space that enhances the scaling of sampling with space dimensionality. SHMC is a biased variation on the hybrid Monte Carlo algorithm (HMC) that uses an approximation to the modified Hamiltonian to sample more efficiently through phase space. The overhead introduced is modest in terms of time, involving only dot products of the history of positions and momenta generated by the integrator. We present the derivation of SHMC, along with: proof that it preserves microscopic reversibility; analysis of the asymptotic speedup of SHMC over HMC, which is shown to be $O(N^{1/4})$ when using Verlet integrators; and results evaluating correctness and efficiency.