  We develop a method for multidimensional optimisation using flow equations.
This method is based on homotopy continuation in combination with a maximum
entropy approach. Extrema of the optimising functional correspond to fixed
points of the flow equation. While ideas based on Bayesian inference such as
the maximum entropy method always depend on a prior probability, the crucial
step in our approach is to perform a continuous update of the prior during the
homotopy flow. The prior probability thus enters the flow equation only as an
initial condition. We demonstrate the applicability of our optimisation method
for two paradigmatic problems in theoretical condensed matter physics:
numerical analytic continuation from imaginary to real frequencies and finding
(variational) ground-states of frustrated (quantum) Ising models with random or
long-range antiferromagnetic interactions.
