Data Assimilation in Chaotic Systems Using Deep Reinforcement Learning
Mohamad Abed El Rahman Hammoud Naila Raboudi Edriss S. Titi Omar Knio Ibrahim Hoteit
Data assimilation (DA) plays a pivotal role in diverse applications, ranging
from climate predictions and weather forecasts to trajectory planning for
autonomous vehicles. A prime example is the widely used ensemble Kalman filter
(EnKF), which relies on linear updates to minimize variance among the ensemble
of forecast states. Recent advancements have seen the emergence of deep
learning approaches in this domain, primarily within a supervised learning
framework. However, the adaptability of such models to untrained scenarios
remains a challenge. In this study, we introduce a novel DA strategy that
utilizes reinforcement learning (RL) to apply state corrections using full or
partial observations of the state variables. Our investigation focuses on
demonstrating this approach to the chaotic Lorenz '63 system, where the agent's
objective is to minimize the root-mean-squared error between the observations
and corresponding forecast states. Consequently, the agent develops a
correction strategy, enhancing model forecasts based on available system state
observations. Our strategy employs a stochastic action policy, enabling a Monte
Carlo-based DA framework that relies on randomly sampling the policy to
generate an ensemble of assimilated realizations. Results demonstrate that the
developed RL algorithm performs favorably when compared to the EnKF.
Additionally, we illustrate the agent's capability to assimilate non-Gaussian
data, addressing a significant limitation of the EnKF.