Midpoint projection algorithm for stochastic differential equations on manifolds.

Stochastic differential equations projected onto manifolds occur in physics, chemistry, biology, engineering, nanotechnology, and optimization, with interdisciplinary applications. Intrinsic coordinate stochastic equations on the manifold are sometimes computationally impractical, and numerical projections are therefore useful in many cases. In this paper a combined midpoint projection algorithm is proposed that uses a midpoint projection onto a tangent space, combined with a subsequent normal projection to satisfy the constraints.

Energy Derivatives in Real-Space Diffusion Monte Carlo.

We present unbiased, finite-variance estimators of energy derivatives for real-space diffusion Monte Carlo calculations within the fixed-node approximation. The derivative d is fully consistent with the dependence (λ) of the energy computed with the same time step. We address the issue of the divergent variance of derivatives related to variations of the nodes of the wave function both by using a regularization for wave function parameter gradients recently proposed in variational Monte Carlo and by introducing a regularization based on a coordinate transformation.