Neural Integration of Continuous Dynamics

Margaret Trautner Department of Mathematics Sai Ravela † Department of Earth, Atmospheric, and Planetary Sciences Earth Signals and Systems Group, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (Dated: November 26, 2019) Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Modeled as recurrent networks embedding a continuous neural differential equation, they achieve fully neural temporal output. Using the polynomial class of dynamical systems, we demonstrate equivalence of neural and numerical integration. I. INTRODUCTION Neural dynamical systems are dynamical systems described at least in part by neural networks. Our interest in the subject emerges in the context of Systems Dynamics and Optimization [21] (SDO), which is central to many applications such as storm prediction [19], climate-risk based decision support [22], or autonomous observatories [25]. The SDO cycle conceptually involves a forward path dynamically parameterizing, reducing, calibrating, initializing and simulating numerical models, and quantifying their uncertainties. SDO further involves a return path for adaptive observation, inversion and estimation.