I am just wondering where the term Umbrella Sampling came from. Is there another meaning of literal "umbrella" in physics or mathematics?
The idea is to favor parts of phase space that would not be accessible within a normal Monte Carlo run. To do so, one uses a biasing potential around each of the unfavored regions. Basically, the biasing potential has a "U" shape in the region of interest which yields an "umbrella" shape for the biased probability to be there. When the region of interest is transition path, the idea is to subdivide the path in small regions each covered by an umbrella. The results once unbiased for each umbrella are then "stiched" together
That's the origin of the name I would say