Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the predictive uncertainty of deep-learning models describing non-linear dynamical systems are very limited to date. This paper is aimed at filling this gap and presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs through approximate inference techniques. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime, where predictions cannot be trusted.

翻译：不确定性问题的有效量化仍是深度学习在关键任务等各应用领域中的关键缺失环节。目前，针对描述非线性动力系统的深度学习模型预测不确定性的研究极为有限。本文旨在填补这一空白，并提出了基于神经状态空间模型的系统辨识不确定性量化初步研究成果。我们将学习问题置于贝叶斯概率框架中，通过近似推断技术获取神经网络权重与输出的后验分布。基于该后验分布，我们构建了输出的可信区间，并定义了一个惊喜指数，该指数能够有效诊断模型在可能危险的分布外场景中的使用情况——即当预测结果不可信时。