We consider the problem of learning Neural Ordinary Differential Equations (neural ODEs) within the context of Linear Parameter-Varying (LPV) systems in continuous-time. LPV systems contain bilinear systems which are known to be universal approximators for non-linear systems. Moreover, a large class of neural ODEs can be embedded into LPV systems. As our main contribution we provide Probably Approximately Correct (PAC) bounds under stability for LPV systems related to neural ODEs. The resulting bounds have the advantage that they do not depend on the integration interval.

翻译：我们研究在连续时间线性参数变化（LPV）系统背景下学习神经常微分方程（neural ODEs）的问题。LPV系统包含双线性系统，已知这类系统是非线性系统的通用逼近器。此外，大量神经常微分方程可以嵌入LPV系统中。作为主要贡献，我们在稳定性条件下给出了与神经常微分方程相关的LPV系统的可能近似正确（PAC）界。所得界具有不依赖于积分区间的优势。