Rachel Cooper

Austin Chennault, Andrey A. Popov, Amit N. Subrahmanya et al.

Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data assimilation procedures used in many geoscience applications, such as numerical weather forecasting, are variants of the our-dimensional variational (4D-Var) algorithm. The cost of solving the underlying 4D-Var optimization problem is dominated by the cost of repeated forward and adjoint model runs. This motivates substituting the evaluations of the physical model and its adjoint by fast, approximate surrogate models. Neural networks offer a promising approach for the data-driven creation of surrogate models. The accuracy of the surrogate 4D-Var solution depends on the accuracy with each the surrogate captures both the forward and the adjoint model dynamics. We formulate and analyze several approaches to incorporate adjoint information into the construction of neural network surrogates. The resulting networks are tested on unseen data and in a sequential data assimilation problem using the Lorenz-63 system. Surrogates constructed using adjoint information demonstrate superior performance on the 4D-Var data assimilation problem compared to a standard neural network surrogate that uses only forward dynamics information.

Rachel Cooper, Andrey A. Popov, Adrian Sandu

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of freedom. Traditional ROM techniques such as proper orthogonal decomposition (POD) focus on linear projections of the dynamics onto a set of spectral features. In this paper we explore the construction of ROM using autoencoders (AE) that perform nonlinear projections of the system dynamics onto a low dimensional manifold learned from data. The approach uses convolutional neural networks (CNN) to learn spatial features as opposed to spectral, and utilize a physics informed (PI) cost function in order to capture temporal features as well. Our investigation using the quasi-geostrophic equations reveals that while the PI cost function helps with spatial reconstruction, spatial features are less powerful than spectral features, and that construction of ROMs through machine learning-based methods requires significant investigation into novel non-standard methodologies.