论文标题
使用高斯工艺学习具有定性结构的ODE模型
Learning ODE Models with Qualitative Structure Using Gaussian Processes
论文作者
论文摘要
最新的学习技术进步使直接从数据中直接为科学和工程应用进行了动态系统的建模。但是，在许多情况下，明确的数据收集很昂贵，学习算法必须具有可行的数据有效。这表明使用有关系统的其他定性信息，通常可以从先前的实验或域知识中获得。我们提出了一种使用稀疏的高斯过程来学习微分方程的向量场的方法，该过程使我们能够将数据和其他结构信息（例如Lie组对称和固定点）组合在一起。我们表明，这种组合可以显着提高外推性能和长期行为，同时也降低了计算成本。
Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms must be data-efficient to be feasible. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain knowledge. We propose an approach to learning a vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points. We show that this combination improves extrapolation performance and long-term behaviour significantly, while also reducing the computational cost.
