Data-Driven Statistical-Stochastic Model for Effective Ensemble Forecast of Complex Systems
Abstract
The capability of using imperfect statistical reduced-order models to capture crucial statistics in turbulent geophysical systems is investigated. The proposed modeling framework extends the purely statistical modeling approach that is practically limited to the homogeneous statistical regime for high-dimensional state variables. The new closure system allows one to overcome several practical issues that emerge in the non-homogeneous statistical regimes. First, the proposed ensemble modeling that couples the mean statistics and stochastic fluctuations naturally produces positive-definite covariance matrix estimation, which is a challenging issue that hampers the purely statistical modeling approaches. Second, the proposed closure model, which embeds a non-Markovian neural-network model for the unresolved fluxes such that the variance of the dynamics is consistent, overcomes the inherent stability of the stochastic fluctuation dynamics. Effectively, the proposed framework extends the classical stochastic parametric modeling paradigm for the unresolved dynamics to a semi-parametric parameterization with a residual Long-Short-Term-Memory neural network architecture. Third, based on empirical information theory, we provide an efficient and effective training procedure by fitting a loss function that measures the differences between response statistics. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the reduced-order model in various dynamical regimes of the flow field with distinct statistical structures.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2022
- Bibcode:
- 2022AGUFMNG35B0471Q