Connecting physics-based and data-driven approaches for predicting Earth Systems from partial observations.
Abstract
For a given Earth system (atmospheric circulation, subsurface transport, and the like), the "true physics" governing the system is captured by a set of coupled differential equations, such that the a systems future state at the next instant only depends on the current state. This imposes a Markovian closure among the degrees of freedom comprising the system state and their interactions. In practice, however, we only have access to a subset of a system's degrees of freedom, as provided by instrument measurements. Physics-based simulations utilize data assimilation and model parameterizations to provide an explicit Markov closure. Missing degrees of freedom are "filled in" explicitly and the approximated system state is evolved by explicitly computing the interactions among its components. We will show, mathematically and through examples, that history-dependent data-driven models predict the stochastic process over partial observations (the measured degrees of freedom) by doing implicitly what physics simulations do explicitly. Missing degrees of freedom are implicitly "filled in" using delay-coordinate embeddings, and their Markovian evolution is given through the action of the Koopman operator. The resulting perspective reveals that physics simulations (fully explicit) and data-driven methods (fully implicit) are two ends of a modeling spectrum. As a practical benefit, this facilitates developing hybrid approaches that combine explicit and implicit methods.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2021
- Bibcode:
- 2021AGUFMNG25B0516R