This thesis focuses on developing advanced methods to infer the dynamical systems governing biological processes. Over the past century, techniques to describe the nonlinear dynamics of interacting systems in precise mathematical terms has advanced our ability to understand, predict, and control a variety of processes in physics and engineering, as well as more recently in the biological sciences. Most commonly, the resulting dynamical systems consist of differential equations derived from a mechanistic understanding of the interactions involved, which are then “fit” to dense time series of data using optimization methods to extract specific parameter values. However, this approach can be difficult to translate to systems with large numbers of interacting variables, highly stochastic dynamics, very short or long timescales, or for which the ability to experimentally intervene or monitor the system is limited. Here we consider two such systems where traditional methods fail for different reasons: inferring the genetic networks controlling aging across the human lifespan, and inferring the processes allowing latent HIV infection to persist and evade a cure with existing treatments.