Efficient rare event sampling with unsupervised normalizing flows

Abstract From physics and biology to seismology and economics, the behaviour of countless systems is determined by impactful yet unlikely transitions between metastable states known as rare events, the study of which is essential for understanding and controlling the properties of these systems. Classical computational methods to sample rare events remain prohibitively inefficient and are bottlenecks for enhanced samplers that require prior data. Here we introduce a physics-informed machine learning framework, normalizing Flow enhanced Rare Event Sampler (FlowRES), which uses unsupervised normalizing flow neural networks to enhance Monte Carlo sampling of rare events by generating high-quality non-local Monte Carlo proposals. We validated FlowRES by sampling the transition path ensembles of equilibrium and non-equilibrium systems of Brownian particles, exploring increasingly complex potentials. Beyond eliminating the requirements for prior data, FlowRES features key advantages over established samplers: no collective variables need to be defined, efficiency remains constant even as events become increasingly rare and systems with multiple routes between states can be straightforwardly simulated.