Sparse, active learning of stochastic differential equations from data

Automatic machine learning of empirical models from experimental data is becoming feasible as a result of the increased availability of computational power and dedicated algorithms. I will discuss different approaches for the inference of governing equations from data. A robust method is proposed for the sparse solution of the inverse problem related to the inference of differential equations governing deterministic and stochastic systems. Next, I present a method that we call active learning of stochastic differential equations. In active learning, an inference of the stochastic dynamics is combined with perturbations to the measured system in a feedback loop. This procedure can significantly improve the inference of global models for systems with multiple energetic minima. If time remains, I will also discuss the use of deep convolutional networks and deep attention models for the automated analysis of biological cells.