Abstract: Inferring the structure and dynamical interactions of complex systems is critical to understanding and controlling their behavior. I am interested in discovering models from the time-series in order to understand biological systems, material behavior, and other dynamical systems. One can frame the problem as selecting which interactions, or model terms, are most likely responsible for the observed dynamics from a library of possible terms. Several challenges make model selection and parameter estimation difficult including nonlinearities, varying parameters or equations, and unmeasured state variables. I will discuss methods for reframing these problems so that sparse model selection is possible including implicit formulation and data clustering. I will also discuss preliminary results for parameter estimation and model selection for deterministic and chaotic systems with hidden or unmeasured variables. We use a variational annealing strategy that allows us to estimate both the unknown parameters and the unmeasured state variables.