AIEADA 1.0: Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

Abstract

Abstract. Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior, and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by four orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIAEDA (Artificial Intelligence Emulator Assisted Data Assimilation).

Equation‐Free Surrogate Modeling of Geophysical Flows at the Intersection of Machine Learning and Data Assimilation

“…However, in this study, the forward model is replaced with the surrogate model, and therefore, we perform the DA in the latent space. The similar ideas have also been used in other studies that deals with the DA for reduced-order models (Amendola et al, 2020;Maulik et al, 2022;Peyron et al, 2021). Once the LSTM network is trained, it is used to forecast the future state of the POD modal coefficients in an auto-regressive manner .…”

“…DA could benefit a lot from ML, where a forecast model is replaced with a hybrid model that incorporates a neural network as a component of the physical model (Hsieh & Tang, 1998; Pawar & San, 2021) or as a complete replacement with a data‐driven model for forecasting and state estimation (Chattopadhyay et al., 2022; Penny et al., 2022). Another advantage of an ML‐based emulator is the quick computation of backpropagation gradient with automatic differentiation that can be used as a replacement for expensive adjoint solvers within variational DA (Chennault et al., 2021; Maulik et al., 2022). Similarly, some of the challenges with ML such as handling uncertain and sparsely sampled data can be mitigated with DA.…”

Deep Learning-Enhanced Ensemble-Based Data Assimilation for High-Dimensional Nonlinear Dynamical Systems

“…Tsuyuki et al [30] integrated ML with an EnKF to perform state estimation in a nonlinear dynamical system using a small number of ensemble members. Maulik et al [31] used 4D-Var-based DA with ML for forecasting in high-dimensional dynamical systems. Penny et al [32] used a recurrent neural network and 4D-Var for scalable state estimation.…”