Predicting rare events using neural networks and short-trajectory data

Abstract

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. We illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

arXiv comment21 pages, 12 figures

References in corpus (14)

• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• Solving high-dimensional partial differential equations using deep learning
• Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
• Using machine learning to parameterize moist convection: potential for modeling of climate, climate change and extreme events
• Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM
• Galerkin Approximation of Dynamical Quantities using Trajectory Data
• Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
• Computing Committor Functions for the Study of Rare Events Using Deep Learning
• An early warning indicator for atmospheric blocking events using transfer operators
• Learning forecasts of rare stratospheric transitions from short simulations
• Eigenvector method for umbrella sampling enables error analysis
• Committor Functions for Climate Phenomena at the Predictability Margin: The example of El Niño Southern Oscillation in the Jin and Timmerman model
• Path properties of atmospheric transitions: illustration with a low-order sudden stratospheric warming model
• Augmented Transition Path Theory for Sequences of Events

Cited by in corpus (5)

• Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction
• Variational deep learning of equilibrium transition path ensembles
• Accurate estimates of dynamical statistics using memory
• On Committor Functions in Milestoning
• From high-dimensional committors to reactive insights