Scientific Machine Learning

For many years, the fields of scientific computing and machine learning have developed in parallel and mostly independent of each other. Recently,

1. the increasing demands of modern scientific computing to manage high-dimensional problems and integrate data with computational science and engineering (CSE) models and

2. the recent successes of machine learning (ML) in solving previously intractable tasks across various domains such as computer vision and natural language processing

have resulted in the emergence of the field of scientific machine learning (SciML).

SciML deals with the combination of techniques from scientific computing and machine learning. SciML algorithms can be categorized roughly into

• ML-enhanced scientific computing

• scientific computing-enhanced ML, and

• novel methods resulting from the combination of the two fields.

In this course you will learn some of the main topics of SciML with a focus on problems from CSE, which can be described using differential equations. The topics include

• function approximation with neural networks,

• training of neural networks,

• physics-informed machine learning,

• operator learning, and

• neural differential equations.

SciML being an emerging field, the course will also address the latest research in the field as well as the use of state-of-the-art computational tools and software libraries.