Systematic exploration of energy landscapes in stochastic simulators

In this work, we present an approach for the exploration of low-dimensional effective potential landscapes. Making use of extrapolation in a low dimensional space of automatically learned variables (i.e. Diffusion Maps - DMAPs - variables) and machine learning schemes (e.g. Geometric Harmonics - GH) for lifting the new points into the ambient space, the described method enables to escape from local potential wells towards new minima. A simple three-dimensional stochastic differential equation system with a non-linear two-dimensional attractive manifold is considered for illustration purposes.