## Ph.D. Course on Scientific Machine Learning

We offer a Ph.D. course on Scientific Machine Learning.

The course is offered with support from the DTU Compute Graduate School (ITMAN) and the Danish Center for Applied Mathematics and Mechanics (DCAMM) at Technical University of Denmark.

The aim of the course is to introduce the students to some of the modern methods and algorithms used in Scientific Machine Learning (SciML), and let the students experience these methods on elementary computer experiments.

The PhD course covers several topics in SciML: neural differential equations, universal differential equations, physics-informed neural networks (PINN),automatic differentiation (AD) / differentiable programming, neural operators, symbolic regression, and more. The objective is to give the student an overview of the "tools" available and how they can be modified for particular SciML applications. The course is partly based on the lecture notes from MIT's 18.337 Parallel Computing and Scientific Machine Learning.

## Learning objectives:

A student who has met the objectives of the course will be able to:

- Understand problems and questions addressed by SciML methods.
- Understand how methods are used as building blocks to address SciML questions.
- Be able to choose a suitable method depending on the situation and problem.
- Implement some of these methods in Julia.
- Skillfully perform numerical experiments and interpret the results.
- Setup and train neural differential equations and physics-informed neural networks.
- Identify and exploit the properties and structure of scientific knowledge within machine learning applications.
- Independently solve a special topics problem offered in the course.
- Written presentation of results in a report or a poster.

## Requirements:

Couses in numerical algorithms / numerical analysis (e.g. 02686/02687) and in machine learning (e.g. 02450) and deep learning (02456). It is considered an advantage to have background in in advanced numerical methods course (e.g. 02689) and functional analysis.

The students must have a fundamental knowledge of programming and scientific computing, linear algebra, and must be able to program in some high level language (R, MATLAB, Python, Julia, C++, C, etc.).

## Responsible:

The course will be given by:

- Dr. Christopher Rackauckas, Massachusetts Institute of Technology (MIT), Boston, United States, meREMOVEMEchrisrackauckas.com