Model reduction accelerates stochastic dynamical system predictions
Model reduction in time: Learning flow maps for reducing stochastic dynamical systems in time
Machine Learning
Summary
Predicting the future behavior of complex systems that involve randomness can take a long time because each step depends on the previous one. The authors developed a method called FM-FTM that learns shortcuts to jump ahead in time during simulations, greatly speeding up predictions. Their method uses a mathematical technique to capture how randomness evolves and then creates a flow map that directly predicts outcomes over long time periods. Tests show this approach can make predictions up to 100 times faster while maintaining accuracy.
What this means in practice
- •For simulation engineers: Speed up running ensemble simulations of systems influenced by random effects to obtain long-term predictions faster.
- •For financial risk modelers: Generate quicker scenario analyses of stochastic models used in finance by reducing time steps without losing key statistical details.
Authors
Shreya Jha, Benjamin Peherstorfer
Abstract
Predictions with dynamical systems can be computationally expensive---even with reduced models---because reaching future prediction times can require many sequential time integration steps. We propose Flow-Map First-Order Trajectory Matching (FM-FTM), a nonintrusive model reduction approach that accelerates ensemble predictions of stochastic dynamical systems by learning flow maps that replace multiple time-integration steps. Our method uses first-order trajectory matching (FTM) to learn a deterministic representation of the stochastic probability-current dynamics and then reduces its evolution over time into a flow map whose evaluation directly yields predictions over long time horizons. Numerical experiments on evolution problems with stochastic forcing demonstrate that FM-FTM accelerates ensemble predictions by up to two orders of magnitude while accurately predicting time marginals and ensemble statistics.