Neural Differential Equations for Irregularly Sampled Time Series

Sammanfattning

Irregularly sampled time series appear in many sectors, including healthcare, finance, and climate modeling. Traditional machine learning models based on fixedtime grids are often ill-suited to handle irregular observation patterns. Neural differential equations offer a continuous-time framework that naturally handles such data. In this thesis, a synthetic dataset of irregularly sampled Archimedean spirals generated using seven different point processes is introduced to study the effect of sampling mechanisms on model performance. Two neural differential equation models are evaluated alongside their time-discrete analogues on tasks of parameter prediction and point process classification. The results show that neural differential equations, particularly Neural controlled differential equations (Neural CDEs), perform well when provided with informative control paths, but their performance depends on the structure of the underlying sampling process. In the parameter prediction task, mark-dependent Cox, mark-dependent Hawkes,and Hawkes processes are the most challenging, while in the process classification task, Poisson and Hawkes-based processes are consistently harder to distinguish than other processes. These results suggest that model performance is influenced not only by architecture, but also by the properties of the data-generating process.