  We present a method for optimizing the location of the fermion ground-state
nodes using a combination of diffusion Monte Carlo (DMC) and projected gradient
descent (PGD). A PGD iteration shifts the parameters of an arbitrary
node-fixing trial function in the opposite direction of the DMC energy
gradient, while maintaining the cusp condition for atomic electrons. The energy
gradient is calculated from DMC walker distributions by one of three methods we
derive from an exact analytical expression. We combine our energy gradient
calculation methods with different gradient descent algorithms and a projection
operator that maintains the cusp condition. We apply this stochastic PGD method
to trial functions of Be, Li$_2$, and Ne, all consisting of a single Slater
determinant with randomized parameters, and find that the nodes dramatically
improve to the same DMC energy as nodes optimized by variational Monte Carlo.
Our method, therefore, departs from the standard procedure of optimizing the
nodes with a non-DMC scheme such as variational Monte Carlo, Density function
theory, or configuration interaction based calculation, which do not directly
minimize the DMC energy.
