A data-driven non-linear assimilation framework with neural networks

摘要

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.