Deep Data Assimilation: Integrating Deep Learning with Data Assimilation

Abstract

In this paper, we propose Deep Data Assimilation (DDA), an integration of Data Assimilation (DA) with Machine Learning (ML). DA is the Bayesian approximation of the true state of some physical system at a given time by combining time-distributed observations with a dynamic model in an optimal way. We use a ML model in order to learn the assimilation process. In particular, a recurrent neural network, trained with the state of the dynamical system and the results of the DA process, is applied for this purpose. At each iteration, we learn a function that accumulates the misfit between the results of the forecasting model and the results of the DA. Subsequently, we compose this function with the dynamic model. This resulting composition is a dynamic model that includes the features of the DA process and that can be used for future prediction without the necessity of the DA. In fact, we prove that the DDA approach implies a reduction of the model error, which decreases at each iteration; this is achieved thanks to the use of DA in the training process. DDA is very useful in that cases when observations are not available for some time steps and DA cannot be applied to reduce the model error. The effectiveness of this method is validated by examples and a sensitivity study. In this paper, the DDA technology is applied to two different applications: the Double integral mass dot system and the Lorenz system. However, the algorithm and numerical methods that are proposed in this work can be applied to other physics problems that involve other equations and/or state variables.

Artificial Intelligence Revolutionises Weather Forecast, Climate Monitoring and Decadal Prediction

“…In the particular fields of satellite remote sensing and weather forecast as well, the high potential interest in AI techniques has been recognised [29]. The different elements in the traditional satellite remote sensing/NWP weather forecast production chain show potential to be either replaced or augmented by DL techniques [30].…”

Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation

“…We will follow simplified analysis in the same setting to demonstrate the requirement for accurate adjoint model dynamics. We note that the theory based on first-order necessary conditions predicts an increase in solution accuracy regardless of the optimization algorith used to solve (2).…”

“…Surrogate models for fast, approximate inference have enjoyed great popularity in data assimilation research [5], [21], [22], [32]- [34]. Surrogate models are most often applied in one of two ways: to replace the high fidelity model dynamics constraints in (2), or to supplement the model by estimating the model error term η i in (1) [13]. In the former approach the derivatives of the surrogate model replace the derivatives of the high fidelity model in (3) and in the 4D-Var gradient calculation in (5).…”

“…Approximate models based on neural networks in the context of numerical weather prediction have been explored. Previously studied approaches include learning of the model operator by feedforward networks [9] and learning repeated application of the model operator by recurrent neural network for use in 4D-Var [20], approaches based on learning the results of the data assimilation process [2], and online and offline approaches for model error correction [12]. While to the authors' knowledge, deep-learning based models have failed to match operational weather-prediction models in prediction skill [9], [12], [36] they nonetheless have offered comparatively inexpensive approximations of operational operators which can be applied to specific areas of interest and have thus been identified as an area of application for machine learning by organizations such as the European Centre for Medium-Range Weather Forecasts [14].…”

Composing a surrogate observation operator for sequential data assimilation

“…In recent years, there have been several studies on DA where there is partial information on the statespace model. Some studies on state estimations have proposed combining standard DA procedures and neural networks for when f f f t is unknown (see, e.g., [1,2,3,4]). In addition, as another approach that does not employ neural networks, Hamilton et al [5,6,7] proposed a new filter called the Kalman-Takens filter when f f f t or h h h is unknown.…”