Neural Controlled Differential Equations

Neural controlled differential equations (NCDEs) evolve a hidden state continuously as it is driven by an input path, making them useful when time-series observations are irregular, sparse, or asynchronous. Common approaches encode observations with interpolated or smoothed paths, use log-signatures to retain temporal information, or add structured vector fields and graph knowledge; latent NCDEs also support probabilistic forecasting and generation. They are evaluated on tasks such as time-series forecasting and synthesis, including settings with missing data, irregular observation grids, and changing dynamics. A central tension is balancing faithful representations and expressive dynamics against training and inference cost, while maintaining reliable forecasts and calibrated uncertainty.