Gaussian Process differential equations (GPODE) have recently gained momentum due to their ability to capture dynamics behavior of systems and also represent uncertainty in predictions. Prior work has described the process of training the hyperparameters and, thereby, calibrating GPODE to data. How to design efficient algorithms to collect data for training GPODE models is still an open field of research. Nevertheless high-quality training data is key for model performance. Furthermore, data collection leads to time-cost and financial-cost and might in some areas even be safety critical to the system under test. Therefore, algorithms for safe and efficient data collection are central for building high quality GPODE models. Our novel Safe Active Learning (SAL) for GPODE algorithm addresses this challenge by suggesting a mechanism to propose efficient and non-safety-critical data to collect. SAL GPODE does so by sequentially suggesting new data, measuring it and updating the GPODE model with the new data. In this way, subsequent data points are iteratively suggested. The core of our SAL GPODE algorithm is a constrained optimization problem maximizing information of new data for GPODE model training constrained by the safety of the underlying system. We demonstrate our novel SAL GPODE's superiority compared to a standard, non-active way of measuring new data on two relevant examples.

翻译：高斯过程微分方程（GPODE）近年来因其能够捕捉系统动态行为并表征预测不确定性而受到关注。先前研究已描述了训练超参数从而将GPODE校准至数据的过程。如何设计高效算法来收集训练GPODE模型的数据仍是一个开放的研究领域。然而高质量训练数据是模型性能的关键。此外，数据收集会产生时间成本与经济成本，在某些领域甚至可能对被测系统构成安全风险。因此，安全高效的数据收集算法对于构建高质量GPODE模型至关重要。我们提出的新型GPODE安全主动学习（SAL）算法通过建立高效且非安全关键数据的推荐机制应对这一挑战。SAL GPODE通过顺序推荐新数据、测量数据并用新数据更新GPODE模型来实现这一目标，从而迭代式地推荐后续数据点。我们SAL GPODE算法的核心是一个约束优化问题，在保证底层系统安全性的约束条件下最大化新数据对GPODE模型训练的信息量。通过在两个相关示例上与标准的非主动数据测量方法进行对比，我们验证了新型SAL GPODE算法的优越性。