Abstract:
Diffusion Monte Carlo was developed forty years ago within the Quantum Monte Carlo community to compute ground state energies of the Schrodinger operator. Since then the basic birth/death strategy of DMC has found its way into a wide variety of application areas. For example efficient resampling strategies used in sequential importance sampling algorithms (e.g. particle filters) are based on DMC. As I will demonstrate, some tempting generalizations of the basic DMC framework lead to an instability in the time discretization parameter. This instability has important consequences in, for example, applications of DMC in sequential importance sampling and rare event simulation. We suggest a modification of the basic DMC algorithm that eliminates this instability. In fact, the new algorithm is more efficient than DMC under any condition (parameter regime). We show numerically and analytically that the modified algorithm is stable in unstable regimes for DMC.
