Learning stochastic closures using ensemble Kalman inversion

Abstract Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all interactions they describe. Therefore, researchers seek simpler descriptions that describe complex phenomena without resolving interacting components. Stochastic differential (SDEs) arise naturally models in this context. The growth data acquisition, both through experiment and simulations, provides an opportunity for systematic derivation SDE disciplines. However, inconsistencies between SDEs real at short time scales cause problems, standard statistical methodology applied parameter estimation. incompatibility can addressed by deriving sufficient statistics time-series learning parameters based on these. Here, we study computed averages, approach demonstrate lead a variety problems has secondary benefit obviating need match trajectories. Following approach, formulate fitting inverse problem solved using ensemble Kalman inversion. Furthermore, create framework non-parametric drift diffusion terms introducing hierarchical, refinable parameterizations unknown functions, Gaussian process regression. We proposed models, simulation with noisy Lorenz ’63 model, then other applications, including dimension reduction deterministic chaotic systems arising atmospheric sciences, large-scale pattern modeling climate dynamics simplified key observables molecular dynamics. results confirm robust data.