Monte Carlo methods for massively parallel architectures

Scientists working with computer simulations need to move away from intrinsically serial algorithms to find new approaches that can make good use of potentially millions of cores. Monte Carlo methods based on Markov chains are intrinsically serial and hence are hard to parallelize. For short-range interactions one can use domain decompositions for parallel updates. A complementary approach simulates several chains in parallel, either at different temperatures such as in replica-exchange Monte Carlo or at the same temperature by simply pooling the statistics from independent runs. I review such methods and, in particular, focus on two especially promising approaches: firstly, a parallel variant of the multicanonical simulation method that uses independent walkers to speed up the convergence and shows close to perfect scaling up to 10⁵ threads. Secondly, a sequential Monte Carlo method known as population annealing, that simulates a large population of configurations at the same temperature and then uses resampling and successive cooling. This approach is particularly suitable for parallel computing, and I disucc an efficient GPU implementation. A number of improvements turn it into a fully adaptive algorithm for the simulation of systems with complex free-energy landscapes.