Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference

arXiv:2402.18512v1 Announce Type: new
Abstract: The vector field of a controlled differential equation (CDE) describes the relationship between a control path and the evolution of a solution path. Neural CDEs (NCDEs) treat time series data as observations from a control path, parameterise a CDE's vector field using a neural network, and use the solution path as a continuously evolving hidden state. As their formulation makes them robust to irregular sampling rates, NCDEs are a powerful approach for modelling real-world data. …

abstract arxiv control cs.lg data difference differential differential equation equation evolution path relationship series solution time series type vector