The Symbiosis of Deep Learning and Differential Equations II

In recent years, there has been a rapid increase of machine learning applications in computational sciences, with some of the most impressive results at the interface of deep learning (DL) and differential equations (DEs). DL techniques have been used in a variety of ways to dramatically enhance the effectiveness of DE solvers and computer simulations. These successes have widespread implications, as DEs are among the most well-understood tools for the mathematical analysis of scientific knowledge, and they are fundamental building blocks for mathematical models in engineering, finance, and the natural sciences. Conversely, DL algorithms based on DEs--such as neural differential equations and continuous-time diffusion models--have also been successfully employed as deep learning models. Moreover, theoretical tools from DE analysis have been used to glean insights into the expressivity and training dynamics of mainstream deep learning algorithms.

This workshop will aim to bring together researchers with backgrounds in computational science and deep learning to encourage intellectual exchanges, cultivate relationships and accelerate research in this area. The scope of the workshop spans topics at the intersection of DL and DEs, including theory of DL and DEs, neural differential equations, solving DEs with neural networks, and more.