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The optimisation of
trial wave functions is an essential part of any QMC simulation, but
is fraught with difficulties. The best available approach is the
variance-minimisation technique introduced by Cyrus
Umrigar [1]. Unfortunately, the variance is a
complicated non-convex function and conventional downhill minimisation
algorithms often become stuck in subsidiary minima far from the global
minimum. Furthermore, the noise level increases with the system size,
to the extent that optimising trial functions for large systems is a
major challenge. In this project we will investigate a new
optimisation algorithm proposed by Umrigar and Nightingale, that
cleverly combines the efficient downhill Levenburg-Marquardt method
with a stochastic element that makes it possible to escape from local
minima. The new method is quite closely related to simulated
annealing, but should be much more efficient. If it works as well as
we hope, it will also be useful in a wide variety of other
nonlinear-least-squares optimisation problems.
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