Learn quasi-stationarity diagnostics using neural networks on low-dimensional data
Learning on-the-fly quasi-stationarity diagnostics from low-dimensional surrogates
Machine Learning
Summary
Certain simulations need to know when a system has settled into a stable behavior, called quasi-stationarity. The authors develop a way to use simpler, lower-dimensional models and neural networks to detect this stabilization more efficiently than previous methods. Their approach works even for complex systems that don’t have certain mathematical properties, and it performs well in various tests, sometimes better than older techniques. This helps speed up simulations that rely on detecting these stable phases.
What this means in practice
- •For computational chemists: Accelerate molecular simulations by improving detection of quasi-stationary phases during complex system dynamics.
- •For statistical physicists: Employ learned diagnostics to better identify metastable states in high-dimensional stochastic systems from collective variable data.
Authors
Noé Blassel
Abstract
Accelerated dynamics methods, such as parallel replica dynamics, require estimates of the decorrelation time, after which a process trapped in one of its metastable states is distributed according to the quasi-stationary distribution (QSD). In a method proposed by Binder, Lelièvre and Simpson, decorrelation times are defined by coupling a particle approximation of the non-linear conditioned probability flow of the process with MCMC-inspired diagnostics. We explore an alternative to MCMC diagnostics, based on coarse-graining of non-linear probability flows and simulation-based inference. We first develop a coarse-graining framework for killed Markov jump processes conditioned on survival, proving uniform-in-time, non-asymptotic estimates approximating the non-linear probability flow of the true process by the non-linear flow of a surrogate process, defined with a collective variable. The framework does not assume reversibility of the true process, and also gives bounds which scale explicitly in an adiabatic regime. Motivated by these results, we then construct a quasi-stationarity diagnostic using simulation-based inference: a recurrent neural network (RNN), trained on particle approximations of non-linear effective flows, estimates posterior probabilities of decorrelation. The learned diagnostic is then transferred to collective-variable traces of high-dimensional particle approximations. We investigate the behavior and robustness of this diagnostic on a set of numerical experiments, comparing it to the MCMC diagnostic of Binder et al.\ on both synthetic examples and a molecular system, in and out of its training prior distribution. When its prior assumptions hold, the RNN diagnostic outperforms the MCMC diagnostic in ROC analysis, is less conservative, fails less often, and has an interpretable decision threshold.