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：数据同化旨在将动力学模型与一组含噪声且不完整的观测数据相结合，以推断系统随时间变化的状态，在多数应用场景中均涉及不确定性。基于已有的确定性机器学习方法，我们提出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，并可集成到更广泛的变分数据同化流程中，从而在增长的数据同化时间窗长度下获得更大收益。代码发布于 https://github.com/anthony-frion/Stochastic_CODA。