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.

复杂的动力学系统是对各种现象进行建模的预测分析的组成部分。随着这些模型的改进，它们变得越来越复杂，并依赖于越来越多的模型或驱动程序输入。不确定性困扰着这些输入（初始条件，边界条件，关键模型参数，信号噪声等），从而在模型的预测中引入了误差，并大大降低了其可预测性。在本文中，我们为非线性动力系统开发了一个新的数据驱动的同化框架。特别是，我们通过构建功能强大的代理来开发同化方法，这些代理可以模拟动力学系统的模型可观察值的演化过程，从而对简化模型进行有效的同化。这种方法有两个明显的优点：（1）建立一个捕获模型不确定性传播的代理，（2）我们使用完全由数据驱动的技术。我们采用贝叶斯框架进行数据同化，并使用神经网络来学习可观察物的演化算子。我们在一个混乱的测试案例中证明了（a）替代条件可以准确地捕获初始条件中的不确定性，并且（b）降阶模型可以有效地用于获取后验估计。