Learning dynamics of complex systems from partial observations

Complex multi-component systems from cells and tissues to biochemical reactors often exhibit oscillatory and chaotic nonlinear dynamics that are essential to their signaling properties and functions. Despite the rapid advancement of sensor and imaging technology, many physical and biological systems can only be partially observed with practitioners in need of model-fitting tools that can account for this missing information. Here we develop an automated inference method that discovers predictive differential equation models from a few noisy partial observations of a system's state. We illustrate our method on a combination of both simulation and experimental data from a variety of physical, chemical and biological systems showing that in many cases noisy partial observations are sufficient to infer predictive multivariate dynamical systems.