[Q] intrinsic difficulty when solving MBAR for large number of similar thermodynamic states

[svandenhaute]

This is a general question rather than an actual issue.

I'm doing umbrella sampling on a variety of systems, and with a variety of collective variables. I make sure that the individual trajectories in the umbrellas are long enough, are equilibrated, and are decorrelated. I verify that this is the case by subsampling different portions of the trajectories, and verifying that the final free energies do not change.
However, I noticed that I was largely exaggerating the number of umbrellas, to the point where neighboring umbrellas were to a large extent overlapping with each other and with many other umbrellas -- see added screenshot for a simple histogram plot.
When removing a fraction of the umbrellas and re-evaluating MBAR, I did notice a significant change in the relative free energies.
Is this intrinsic to the system of equations that needs to be solved in MBAR (for example, that overlap of a given distribution with a large number of other distributions makes it intrinsically ill-conditioned, or small energy differences between hamiltonians of the different states as is the case when centering umbrellas close to each other)? I'm using the robust solver protocol, and JAX is running in 64-bit mode. He does not give me any warnings about the numerical accuracy.