Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing deterministic machine learning approach, we propose a variational inference-based extension in which the predicted state follows a multivariate Gaussian distribution. Using the chaotic Lorenz-96 dynamics as a testing ground, we show that our new model enables to obtain nearly perfectly calibrated predictions, and can be integrated in a wider variational data assimilation pipeline in order to achieve greater benefit from increasing lengths of data assimilation windows. Our code is available at https://github.com/anthony-frion/Stochastic_CODA.

翻译：数据同化旨在结合动力学模型与一组含噪声且不完整的观测数据，以推断系统随时间变化的状态，在大多数应用场景中均涉及不确定性。基于现有的确定性机器学习方法，我们提出了一种基于变分推断的扩展模型，其中预测状态服从多元高斯分布。以混沌Lorenz-96动力学系统为测试平台，我们证明新模型能够获得近乎完美校准的预测结果，并可集成至更广泛的变分数据同化流程中，从而通过延长数据同化窗口长度获得更大效益。我们的代码公开于https://github.com/anthony-frion/Stochastic_CODA。