Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs
This addresses the problem of accurate and uncertainty-aware modeling of interacting dynamical systems for researchers in machine learning and applied fields, representing an incremental advancement with a novel hybrid method.
The paper tackles the problem of modeling continuous-time dynamics of interacting objects with time uncertainty by introducing a model that decomposes independent object dynamics from interactions using latent Gaussian process ODEs. The result shows improved reliability in long-term predictions over neural network alternatives and successful handling of missing information, with the model uniquely encapsulating independent dynamics and interactions in distinct functions.
We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian process ordinary differential equations, our model infers both independent dynamics and their interactions with reliable uncertainty estimates. In our formulation, each object is represented as a graph node and interactions are modeled by accumulating the messages coming from neighboring objects. We show that efficient inference of such a complex network of variables is possible with modern variational sparse Gaussian process inference techniques. We empirically demonstrate that our model improves the reliability of long-term predictions over neural network based alternatives and it successfully handles missing dynamic or static information. Furthermore, we observe that only our model can successfully encapsulate independent dynamics and interaction information in distinct functions and show the benefit from this disentanglement in extrapolation scenarios.