Bundle embeddings for learning chaotic dynamics from irregularly sampled partial observable data

A challenge in training models on experimental data is the spatial sparsity of sampling. These incomplete state measurements can be augmented with state history to recover the underlying dynamics, e.g. through time delay embedding. Often the data is also sampled at irregular time intervals, such as when a sensor fails to transmit or one sensor records at different intervals than others. We use bundle embeddings to generalize previous work on uniform time delay embeddings for learning continuous dynamics from partial observable data sampled irregularly in time. Using neural ODEs, this is essentially a simple modification of the loss function. We demonstrate the accuracy of the approach for several benchmark multivariate periodic and chaotic dynamical systems.