  A more accurate semiclassical theory for ultracold gases is derived, in which
the occupation of high energy modes is dynamically constrained to the
Bose-Einstein distribution. This regularized version of the SGPE model
preserves the proper nonlinear energy dependence of coupling to the thermal
reservoir. As a result, inclusion of high energy modes above $k_BT$ does not
cause a UV divergence. Instead, the reservoir becomes a constraint on the high
energy tails which are included explicitly in the system. Millions of modes can
be treated because computational cost scales slowly, like in other
semiclassical methods. Implementations in 1d and 3d are presented, among them
an accurate treatment of the famous case of the quadrupole mode (Jin et al,
1997), which had so far eluded satisfactory simulations with any field theory.
Our study reveals that observed frequencies and damping of the thermal cloud
depended on the experimental signal to noise ratio.
