Efficient Rare Event Sampling with Unsupervised Normalising Flows

Abstract

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 these systems’ properties. Classical computational methods to sample rare events remain prohibitively inefficient and are bottlenecks for enhanced samplers requiring prior data. Here, we introduce a novel physics-informed machine learning framework, FlowRES, that uses unsupervised normalising flow neural networks to enhance Monte Carlo sampling of rare events by generating high-quality nonlocal Monte Carlo proposals. We validate FlowRES by sampling the transition path ensembles of equilibrium and non-equilibrium systems of Brownian particles exploring increasingly complex potentials. Beyond eliminating requirements for prior data, FlowRES features key advantages over established samplers: no collective variables need defining, efficiency remains constant even as events become increasingly rare, and systems with multiple routes between states can be straightforwardly simulated.