Third DigiWell Julia Seminar with AMOC, Nov. 2 2023
Integrating Machine Learning into Differential Equations for Automated Discovery of Missing Physics and Optimal Control
In this presentation, we will introduce the SciML software ecosystem as a versatile tool that seamlessly integrates insights from physical laws and scientific models with data-driven machine learning approaches. At the heart of this ecosystem, we present a mathematical construct referred to as Universal Differential Equations (UDEs), which serves as the unifying framework binding the various elements together. Our demonstration showcases the remarkable flexibility of this software suite with top-tier solvers in handling stochasticity, time delays, and implicit events, thus streamlining a wide variety of SciML applications into a coherent set of training mechanisms. These mechanisms are compatible with distributed parallelism and GPU acceleration. To illustrate the UDE formalism, we will delve into the toy example of a predator-prey model. We'll discuss parameter inference, model selection & discovery, and stochastic optimal control for variations of this model.