From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach
This addresses a bottleneck in molecular dynamics simulations where transitions between metastable states are rare, enabling more efficient analysis from biased data, though it appears incremental as an improvement over existing generator-based approaches.
The paper tackles the problem of learning eigenfunctions of evolution operators for time-reversal invariant stochastic processes, such as the Langevin equation in molecular dynamics, from biased simulation data, and demonstrates that their method can provably recover spectral properties of the unbiased system, showing effectiveness in experiments with datasets containing few transitions.
We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by this equation involve transitions between metastable states separated by high potential barriers that can hardly be crossed during a simulation. To overcome this bottleneck, data are collected via biased simulations that explore the state space more rapidly. We propose a framework for learning from biased simulations rooted in the infinitesimal generator of the process and the associated resolvent operator. We contrast our approach to more common ones based on the transfer operator, showing that it can provably learn the spectral properties of the unbiased system from biased data. In experiments, we highlight the advantages of our method over transfer operator approaches and recent developments based on generator learning, demonstrating its effectiveness in estimating eigenfunctions and eigenvalues. Importantly, we show that even with datasets containing only a few relevant transitions due to sub-optimal biasing, our approach recovers relevant information about the transition mechanism.