Using Knowledge-based Neural Ordinary Differential Equations to Learn Complex Dynamics and Chaos*

Robots and autonomous systems give us unprecedented access to landscapes and habitats both big and small.  They provide in-situ monitoring of the environments they are immersed in and adapt their strategies to respond to various external stimuli.  These systems enable us to more richly and extensively interact with the world we live in, better our understanding of the complexities of the world, and assist in the discovery of new processes and phenomena.  Nevertheless, the ability to robustly operate in natural unstructured environments often requires robots to have or acquire a model or estimate the environment, often with limited sensing and communication resources.  In this talk, I will present some of our recent efforts in developing knowledge embedded machine learning strategies for modeling and predicting complex spatiotemporal phenomena.

In this work, I will present a universal learning framework for extracting predictive models of  nonlinear systems based on observations. A key challenge is how to embed first principles domain knowledge into modern machine learning strategies.  I will show how our Knowledge-based Nerual Ordinary Differential Equation (K-NODE) framework can explicitly model nonlinear systems as continuous-time systems, thus more easily incorporate first principle knowledge.   The ability to incorporate first principles knowledge into the learning framework improves the extracted models' extrapolation power and reduces the amount of data needed for training.   I will demonstrate the effectiveness of our scheme by learning predictive models for a wide variety of nonlinear dynamical systems.  I will also show how the framework can be used to extract single agent control strategies for swarming and to develop robust feedback control strategies for autonomous vehicles.