Efficient Active Learning for Continuous-Time Experiments

Data recorded from physical systems is often noisy, partially observable, irregularly sampled, and covers long time intervals. Neural ordinary differential equations (NODEs) are continuous-time dynamics models that have been proposed to model such complex physical systems. Real-world data is often scarce, which can make these models difficult to train. In this work, we propose an active learning approach to suggesting new experiments, based on a variance-maximizing NODE framework. We show that our objective approximates appropriate frequentist and Bayesian experimental designs in continuous time, and propose a principled weighting mechanism by which users can emphasize which states of the system are most critical. We provide an efficient, highly parallelized implementation and demonstrate performance on nonlinear synthetic systems in small-dataset regimes.