Steal this research idea
Automatic control of Monte Carlo simulations - I want to know how to do it, but I don't necessarily want to figure it out myself. :)
- Determining equilibrium and phase transitions.
Typically the particles are started in a lattice or random configuration and let run a whlie to equilibrate. I want automatic detection of equilibrium, which is especially tricky near phase boundaries. Also near phase transitions, the system can suddenly change phases. - Adjustment of parameters for optimum efficiency
The key quantity affecting the efficiency is the correlation time, but it's very noisy. Is there some other quantity that we could use that would behave similarly, but with less noise? Since this will only affect the efficiency, approximations are quite okay. Like assuming some analytic form for the autocorrelation function with a small number of parameters and fitting to it?
Also note that SGA-like algorithms can be used for control as well as optimization. The decay parameter reaches a constant to follow the system, rather than continuing to decrease, as in optimization. - Better control of DMC population
Occasionally, I have trouble with the number of walkers increasing rapidly. In my codes, this means it exceeds some maximum value and stops the program. Sometimes the number of walkers jumps to a large but stable value, and the energy becomes far too low and clearly wrong. The hard part is that population control introduces a bias, and can't be too intrusive.
For these items, are there any concepts from control theory or signal processing that would be useful?
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