A data-driven non-linear assimilation framework with neural networks
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ORIGINAL PAPER
A data-driven non-linear assimilation framework with neural networks 2 · Humberto C. Godinez1 ´ Nishant Panda1 · M. Giselle Fernandez-Godino
· Clint Dawson3
Received: 3 April 2020 / Accepted: 10 September 2020 © Springer Nature Switzerland AG 2020
Abstract Complex dynamical systems are an integral part of predictive analysis that model diverse phenomena. As these models improve, they become more complex and depend on an increasing number of model or driver inputs. Uncertainty plagues these inputs (initial conditions, boundary conditions, key model parameters, signal noise, etc.), thereby introducing errors into the forecast of the model and significantly degrading its predictability. In this paper, we develop a new data-driven assimilation framework for non-linear dynamical systems. In particular, we develop assimilation methods by building powerful surrogates that emulate the evolution of the model observables of the dynamical system to efficiently perform assimilation on the reduced model. There are two distinct advantages of this approach: (1) we build a surrogate that captures the model uncertainty propagation, and (2) we use entirely data-driven techniques. We employ the Bayesian framework for data assimilation and use neural networks to learn the evolution operator of the observables. We demonstrate on a chaotic test case that (a) uncertainty in initial condition is accurately captured by the surrogate, and (b) the reduced-order model can be effectively used to get estimates of the posterior. Keywords Data assimilation · Neural network · Bayesian inversion
1 Introduction Many geophysical phenomena are modeled mathematically using partial differential equations that describe the system dynamics. These models are solved through numerical methods and are primarily used to predict the future
Humberto C. Godinez
[email protected] Nishant Panda [email protected] M. Giselle Fern´andez-Godino [email protected] Clint Dawson [email protected] 1
T-5, Applied Mathematics and Plasma Physics, Los Alamos National Laboratory, Los Alamos, NM, USA
2
XCP-8, Computational Physics Verification, Validation, Los Alamos National Laboratory, Los Alamos, NM, USA
3
Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, USA
behavior of the system. As these models improve, they become more complex and depend on an increasing number of model or driver inputs. Uncertainty plagues these inputs (initial conditions, boundary conditions, key model parameters, signal noise, etc.), thereby introducing errors into the forecast of the model and significantly degrading its predictability. For the very large systems arising in geophysical models, data assimilation schemes [1, 2] have been developed to generate accurate state estimates. The data assimilation framework requires fusing observational data into the model in order to reduce uncertainty in the model forecast. Over the course of the last two decades, data assimilation has become an evolving research topi
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