Simulated tempering with non-equal occupancy of states

GROMACS version: 2021
GROMACS modification: No
Hi Gromacs team and users,

we run simulated tempering with the Wang-Landau algorithm. Since collecting many frames at the base temperature is critical for us, we do not want equal occupancy among all temperature states, but instead we want to spend more time at the base temperature. For example, we want to spend 50% of the simulation at 300K and the other 50% equally distributed among all higher temperatures.

We understand that this is in principle possible by first burning in the weights, and then modifying the free energy of the base temperature by hand. However, this does not work since we get poor coverage of the states as soon as we stop updating the weights; hence, we keep on updating the weights throughout the simulation.

Is there a way to force increased occupancy (increased probability) of certain states with the current code?

Many thanks for any input,