The summer school addresses young researchers from mathematics and engineering who are already working in the field of scientific machine learning or are interested in the field. It is primarily meant for PhD students, but also Master students or PostDocs are very welcome. We encourage people from both mathematics and engineering to participate.

31. July 2023 – 04. August 2023

The summer school will be on-site in Hannover, Germany. The venue is located at:

Leibniz University Hanover

Welfengarten 1

30167 Hannover

Registration fee is 50 €. More details follow once the registration has been done. The number of participants is limited on a first-come first-served basis.

Registration deadline is June 18^th. Registration can be done via the following form:

https://forms.gle/WsZvVsRN8YTcaFgi8

The available places have been filled and registrations will be placed on the waiting list.

If you want to give a presentation about your research related to the topic of the summer school on the last day, indicate so during registration. Please keep in mind that there will not be enough time for everyone to hold a presentation and therefore we might have to do a selection. We will tell you later on if you will be able to do so.

1. Mathematical Foundations of machine learning
2. Machine learning approaches to scientific and engineering computing
3. Artificial neural networks for solving partial differential equations in mechanical engineering applications

The school includes lectures as well as some programming sessions. The topics of the programming sessions include:

• Introduction to feed-forward neural networks
• Modeling of viscoelastic material behavior using neural networks
• Physics informed neural networks for solving partial differential equations

Prof. Dr. Gitta Kutyniok
Mathematical Data Science and Artificial Intelligence
Department of Mathematics
Ludwig-Maximilians-Universität München
3 Lectures on: Reliable Artificial Intelligence: Successes, Challenges, and Limitations
Summary: Artificial intelligence (AI) is currently leading to one breakthrough after the other, both in public life with, for instance, autonomous driving and speech recognition, and in the sciences in areas such as medical diagnostics or molecular dynamics. And, in fact, it is generally believed that we are at the beginning of the fourth industrial revolution through AI. However, one current major drawback is the lack of reliability of such methodologies. At the same time, reliability of AI technology is required by the EU AI Act, and also the G7 Hiroshima AI Process points in this direction. Reliability can however only be achieved by a deep understanding of the underlaying mechanisms of AI, typically in form of a mathematical framework. In these lectures we will provide an introduction into this exciting topic and a survey of some of the current main research directions, considering mainly the current work horse of AI, namely deep neural networks. We will focus in particular on the areas of expressivity, generalization, and explainability. On the application side, we will discuss the application of AI in imaging science for solving PDEs. Finally, we will also touch upon limitations of this methodology.

Prof. Dr. Oliver Weeger
Cyber-Physical Simulation Group
Department of Mechanical Engineering
Technical University of Darmstadt
3 Lectures on: Physics-enhanced machine learning and neural networks for material modeling
First, we will introduce the general concepts and approaches to enhance machine learning (ML) methods with physical model information, which is crucial to obtain accurate, reasonable and reliable ML models for engineering applications. Physical requirements such as conservation laws, invariances, symmetries, etc. can typically be formulated mathematically as algebraic or differential equations. Depending on the context, ML models such as neural networks (NNs) can be informed or augmented with these inductive biases through suitable choices of inputs and outputs, the network architecture, the loss function formulation, or augmented training data. These different approaches will be introduced and applied to model problems from mechanics and dynamics. Second, we will demonstrate the application of physics-augmented NN formulations for mechanical, multiphysics and multiscale material modeling. For this, the fundamentals of hyperelastic, electro-elastic, and inelastic material models will be briefly introduced and the basic concepts of suitable physics-augmented ML model formulations using (input-convex) feed-forward and recurrent NNs will be discussed. These approaches will be demonstrated for multiscale material modeling of composites and metamaterials.

Prof. Dr. Dennis Kochmann
Institute for Mechanical Systems
Department of Mechanical and Process Engineering
ETH Zürich
3 Lectures on: ML-enabled inverse design, shell modeling, and more
Summary: We will discuss the application of machine learning (ML) to several challenges in solid and structural mechanics. First, we introduce a physics-informed neural network (PINN) model for simulating shell structures, which combines shell theory with deep neural networks and overcomes some of the limitations of conventional shell finite elements. Next, we apply ML to the challenging inverse design of architected materials (using neural networks and variational autoencoders), which allows us to design materials with target effective mechanical properties. Finally, we survey a number of related ML applications – from graph neural networks (GNN) for efficient and accurate quadrature rules to diffusion models for the inverse design of nonlinear material properties.

• Grand Palace Hotel Hannover
• Motel One
• Ibis Budget Hauptbahnhof

The summer school will take place inthe main building (Welfenschloss) of Leibniz University Hanover. Detailed instructions on how to reach the location are given in the following link:

https://www.uni-hannover.de/de/universitaet/campus-und-stadt/wegweiser/anfahrtsbeschreibung/

For questions please write an e-mail to

gamm.juniors@gmail.com

Christoph, Böhm, Leibniz University Hannover
Margarita Chasapi, EPFL
Idoia Cortes Garcia, Eindhoven University of Technology
Alexander Henkes, TU Braunschweig
Roland Maier, Friedrich Schiller University Jena