The arrival of mass amounts of data from imaging, sensors, business transactions and social media has brought with it significant challenges for data science. Traditional parametric models are not flexible enough to capture the complexity of these datasets, and non-parametric approaches are prone to overfitting them. Methods that produce flexible parsimonious models from partially observed noisy data are both rare and desirable.
We propose two smoothing methods called Data2LD and Data2PDE, for developing and estimating linear dynamical systems from data. These build on the collocation inference approach of Ramsay et al. (2007), by taking advantage of the linearity of the system and developing a new iterative scheme to achieve fast and stable computation. Data2LD and Data2PDE are used to attain dynamical systems that adequately represent real data from medicine, climatology and biomechanics.