Learning Biological Dynamics From Spatio-Temporal Data by Gaussian Processes

Model discovery methods offer a promising way to understand biology from data. We propose a method to learn biological dynamics from spatio-temporal data by Gaussian processes. This approach is essentially "equation free" and hence avoids model derivation, which is often difficult due to high complexity of biological processes. By exploiting the local nature of biological processes, dynamics can be learned with data sparse in time. When the length scales (hyperparameters) of the squared exponential covariance function are tuned, they reveal key insights of the underlying process. The squared exponential covariance function also simplifies propagation of uncertainty in multi-step forecasting. After evaluating the performance of the method on synthetic data, we demonstrate a case study on real image data of E. coli colony.