Iterative variational learning of committor-consistent transition pathways using artificial neural networks.

Discovering transition pathways that are physically meaningful and committor-consistent has long been a challenge in studying rare events in complex systems. Here we introduce a neural network-based strategy that learns simultaneously the committor function and the associated committor-consistent string, offering an unprecedented view of transition processes. Built on the committor time-correlation function, this method operates across diverse dynamical regimes, and extends beyond traditional approaches relying on infinitesimal time-lag approximations, valid only in the overdamped diffusive limit. It also distinguishes multiple competing pathways, crucial for understanding complex biomolecular transformations. Demonstrated on benchmark potentials and biological systems such as peptide isomerization and protein-model folding, this approach robustly reproduces established dynamics, rate constants and transition mechanisms. Its adaptability to collective variables and resilience across neural architectures make it a powerful and versatile tool for enhanced-sampling simulations of rare events, enabling insights into the intricate landscapes of biomolecular systems.