  Boltzmann machines are physics informed generative models with wide
applications in machine learning. They can learn the probability distribution
from an input dataset and generate new samples accordingly. Applying them back
to physics, the Boltzmann machines are ideal recommender systems to accelerate
Monte Carlo simulation of physical systems due to their flexibility and
effectiveness. More intriguingly, we show that the generative sampling of the
Boltzmann Machines can even discover unknown cluster Monte Carlo algorithms.
The creative power comes from the latent representation of the Boltzmann
machines, which learn to mediate complex interactions and identify clusters of
the physical system. We demonstrate these findings with concrete examples of
the classical Ising model with and without four spin plaquette interactions.
Our results endorse a fresh research paradigm where intelligent machines are
designed to create or inspire human discovery of innovative algorithms.
