Diffusion Monte Carlo method: Numerical Analysis in a Simple Case
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The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove the convergence of the method for a fixed number of reconfigurations when the number of walkers tends to +∞ while the timestep tends to 0. We confirm our theoretical rates of convergence by numerical experiments. Various resampling algorithms are investigated, both theoretically and numerically.
Mathematics Subject Classification: 81Q05 / 65C35 / 60K35 / 35P15
Key words: Diffusion Monte Carlo method / interacting particle systems / ground state / Schrödinger operator / Feynman-Kac formula.
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