In the Advanced Machine Learning lecture we will cover various advanced concepts, techniques, and algorithms. We will place focus both on the mathematical and theoretical aspects, as well as the practical aspects which involve implementing, training, and optimizing machine learning models using real-world datasets. The lecture is organized in four parts. In the first part we will tackle machine learning for graph data including generative models, ranking, and graph neural networks. In the second part we will cover modern generative models such as variational autoencoders, normalizing flows and generative adversarial networks. In the third part we will cover robustness including both attacks on machine learning models (evasion, poisoning) and defenses (certificates). Finally, in the last part we will cover uncertainty quantification techniques such as Bayesian neural networks, Gaussian processes and conformal prediction. Solid background in the fundamentals of machine learning is highly recommended, e.g. you should have passed our “Machine Learning“ lecture or equivalent.

Preliminary topics include:

• Introduction to data science: Overview of data science and its role in various industries.
• Data exploration and visualization: Use of libraries such as Matplotlib and Seaborn for data visualization.
• Data cleaning and preprocessing: Techniques for dealing with missing data, outliers, and duplicates.
• Introduction to machine learning: Basic algorithms and their applications, e.g., classification and regression.
• Ethics in data science: Data protection, data security, and ethical considerations in data collection and analysis.
• Project work: Application of the techniques and tools learned in a practical project.

By participating in this module, students will become familiar with the basics of data science and will be able to perform simple data analyses independently and interpret the results.

The lecture Machine Learning and Artificial Intelligence covers topics such as supervised learning (regression, classification, decision trees, boosting, support vector machines, neural networks); unsupervised learning (clustering, dimensionality reduction, kernel methods); learning theory (bias/variance tradeoffs); and reinforcement learning. 
The course will also discuss recent machine learning applications, and students will learn to set up their machine learning projects using R.

This course is about extracting useful knowledge from data. It covers the fundamental principles or concepts that underly data science and machine learning. We are going to avoid an algorithm-centered approach whenever possible, instead of focusing on the selection and application of techniques, and the interpretation of results. We will study data science in a business context, i.e., we will mostly work with examples, case studies and data that are relevant for business.

How does a pollutant spread in the soil—and how can this be reliably predicted? Based on this question, this lecture deals with the modeling of diffusion processes in porous media (e.g., soil) using partial differential equations. Partial differential equations play a central role in describing numerous physical, biological, and technical processes. In this lecture, the focus is on the numerical solution of partial differential equations that describe stationary and time-dependent diffusion processes. To this end, we use efficient spatial and temporal discretization methods. Modeling diffusion problems relevant to practice requires the determination of material parameters from measurement data. Since these are only available at discrete points, suitable data science methods must be used to predict the material parameters in areas where no data is available. For the numerical simulation of the application example of pollutant propagation in soil, we combine the finite element method, time discretization methods, and suitable data science methods. In this way, we show how numerical mathematics and data science interact in a current field of application.

The following topics will be covered in the lecture:

• Mathematical modeling of diffusion processes with partial differential equations and treatment of an application example for the spread of pollutants in soil
• Variational formulation and functional analysis fundamentals
• Numerical solution of partial differential equations with the finite element method: introduction, error estimates, implementation/programming
• Time-dependent problems and numerical methods for time discretization
• Modeling using uncertain or incomplete input data (e.g., soil measurements) with the help of suitable data science methods such as Kriging
• Combination of the finite element method with data science methods for numerical simulation of the application example

Programming is done in MATLAB; relevant prior knowledge is required.

Scientific Machine Learning is a new research area that is developing as a field of its own, in which techniques of scientific computing and machine learning are combined and further developed. This results in hybrid methods that are applied to the discretization of partial differential equations, the development of fast and robust solvers, and new modeling techniques.

Keywords are

1. Domain-aware scientific machine learning,
2. Mathematics-informed machine learning,
3. Interpretable scientific machine learning,
4. Machine learning-enhanced simulations,
5. Hybrid modeling (machine learning + first principle modeling).

The lecture “Visualization” deals with the visual representation of data and the interactive communication of data-based content. Interactive visualization enables both the exploratory analysis of complex data sets and the effective communication of analysis results, for example in reports, presentations, or web-based applications.
The lecture teaches the basics of visualization. This includes key concepts from the areas of visualization processes, interaction, human perception, color spaces, data types, and data structures, as well as techniques for transforming, processing, and presenting data. Different data forms are covered, such as 2D, 3D, and multivariate data, time-related and spatial data, as well as networks and graphs.
In addition, fundamental methods, practical examples, and current research topics will be presented. A special focus will be placed on visualization in the context of artificial intelligence and large language models (LLMs), for example in the creation of dashboards.
 

Many areas of scientific research are currently undergoing enormous change. This is due to the fact that new measurement methods are generating ever larger data sets, which can be analyzed in completely new ways using computer-based algorithms from the field of machine learning. At the same time, advances in computer science are also making it possible to describe increasingly complex systems in general.

The lecture series will therefore introduce concepts related to big data, machine learning, deep learning, artificial intelligence, and the various types of modeling complex systems. In addition to providing an overview of the methods and possibilities of using supercomputers, lecturers from a wide range of scientific applications will report on their current research in these areas. Students from all faculties and interested guests are welcome to attend!

This seminar examines the rapidly developing field of AI safety and the challenges it poses. Topics include the development of robust and reliable AI systems, threats from adversaries, certification and verification, alignment (e.g., with human values), explainability, monitoring and prevention of accidents or misuse, agentic and multimodal security, and AI and society. The goal is to provide participants with a comprehensive insight into AI security in order to gain a thorough understanding of the field. We will examine the latest research findings through student presentations on topics of their choice and panel discussions.

The seminar “Mathematics of Data Science” follows the lecture “Mathematics of Data Science - an Introduction” from the 2025 summer semester. Building on the lecture, theoretical and algorithmic aspects of current topics in data science and machine learning will be explored in greater depth and detail. The seminar topics include the following subject areas:

• Dimension reduction techniques
• Classical regression
• Clustering algorithms
• Classification using support vector machines and linear discriminant analysis
• Classification using classification trees and random forests
• Classical neural networks and deep learning
• Introduction to reinforcement learning
• Reduced order models (ROMs)

The preliminary meeting will take place on Friday, July 11, 2025, at 3:00 p.m. in the Mathematics Lecture Hall (Room 203) of the Mathematics Department, Weyertal 86 - 90.

You must register in advance by email (axel.klawonn@uni-koeln.de and martin.lanser@uni-koeln.de), and attendance at the preliminary meeting is mandatory. If you are unable to attend, please notify us in advance by email.

In this seminar, we will deal with the mathematical foundations of algorithmic language processing. The aim is to develop a solid understanding of the methods used to process natural languages. Depending on the available time, we will also look at smaller applications
from practice. In the preliminary discussion, the seminar content will be presented in detail and possible sources for the seminar presentations will be discussed. The seminar consists of presentations by the participants on pre-determined topics.

The advanced seminar "Artificial intelligence and (digital) society" deals with the technical aspects of current social and political debates. The aim is, on the one hand, to gain an overview of the influence of technology on political and social decisions and, on the other hand, to understand the technical fundamentals that need to be known in each area.

Specifically, we want to address the following topics (list still incomplete):

• Voting computers
• Chat control
• Electronic patient records
• Digital violence against women
• Artificial intelligence
• AI vs. copyright

The seminar will discuss current work on applications of optimization and data science in the life sciences. Various aspects, such as the underlying methodology, computational effort, and possible applications, will be presented and discussed. In individual cases, publicly available methods will also be applied in practice and the findings will be discussed.

The seminar will be held in German.

Topics are:

• Deep Learning (DL) applications in the Earth sciences
• Weather modeling with DL
• generative models
• transformers and diffusion models
• foundation models, AtmoRep

The module is concluded with a project work. 

This course introduces students to the fundamental concepts, techniques, and algorithms in machine learning. It covers the mathematical and theoretical foundations, supervised and unsupervised learning techniques, evaluation methods, and advanced aspects. Students will gain hands-on experience in implementing, training, and optimizing machine learning models using real-world datasets.

The tentative list of topics is as followed:

• Introduction
• Probabilistic Inference
• Trees and Forests
• Neighbor-based methods
• Linear models
• (Convex) Optimization
• Gradient-based Optimization
• SVMs
• Kernels
• Basics of Deep Learning: MLPs, CNNs, GNNs
• Dimensionality Reduction: PCA & tSNE
• SVD & Matrix Factorization
• k-Means and GMMs
• Hierarchical Clustering
• Robustness
• Uncertainty
• Privacy
• Fairness

Introduction to Data Science and Machine Learning 

• The value of data from a business perspective
• Data quality and data cleaning
• Design of a data analysis process
• Explanation vs. prediction
• Data visualization
• Use of data to support entrepreneurial action
• Introduction to machine learning
• Programming language: Python 

With the continuously growing importance and widespread use of automated simulations, decision-making processes, and AI, new challenges arise in the analysis and processing of data. In particular, the growing complexity of the tasks and the amount of data require new and more efficient approaches from the fields of data science, data mining, and machine learning in general.

In this lecture, theoretical and algorithmic principles of modern data processing and analysis will be covered. The lecture focuses mainly, but not exclusively, on the literature given below. Among other topics, the following will be studied:

• Techniques for dimension reduction (singular value decomposition / PCA / robust PCA)
• Classical regression
• Clustering algorithms
• Classification with Support Vector Machines and Linear Discriminant Analysis
• Classification with Classification Trees and Random Forest
• Classical Neural Networks and an introduction to Deep Learning
• Introduction to Reinforcement Learning
• Reduced Order Models (ROM)

The focus will be on the algorithmic and mathematical feasibility of the mentioned methods, an application-oriented implementation, and less on statistical methods, which are part of Data Science as well.

Brunton, S., & Kutz, J. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (2nd ed.). Cambridge: Cambridge University Press. doi:10.1017/9781009089517

This course provides you with knowledge and skills required for assessing, managing, and deploying Artificial Intelligence (AI) for tasks of Information Management (IM). More recent advancements in data analytics and AI, e.g. Deep Learning, Natural Language Processing (NLP), Transformer models, and Convolutional Neural Networks, provide a powerful basis for data modeling, data analysis, and new services. The methodological approaches are deployable in many industries facing tasks of information management (IM). The course brings together both a technical and a managerial perspective. The technical perspective will cover (1) a general overview over Artificial Neural Networks (ANN or in short: NN) and the training process, (2) specific architectures like Convolutional Neural Networks and their application in Computer Vision (CV). (3) Natural Language Processing (NLP) including important concepts like Word Embeddings. Especially NLP-based approaches leveraging the Word Embedding concept will be of foremost interest including Transformer Models. Foundational prerequisites will be briefly revisited including types of data, feature selection, pre-processing of textual data, techniques for parameter optimization. The management perspective will cover selected topics at the interplay of AI and IM relevant for information managers including: 

•  AI Innovation: transform data into valuable information with an eye on data-based business model innovation
• Building organizational AI capability: identification, incorporation and development of necessary skillsets for managing AI and preparing an organization to become data-centric
• Ethics and AI, e.g., how to define and realize fair /un-biased use of data, algorithms and AI at large, aka Responsible AI, Explainable AI/ XAI
• AI and Automation – Future of Work: How work will be separated between man and machine in the future and how far can we get with AI in terms of automation?
• AI and Regulation: Is there need to regulate AI? How? 

Regulation and Systems Engineering The course strives for the state-of-the-art application of data analytics, AI approaches and issues in terms of information management. The course is less on mastering all theoretical underpinnings of the techniques or in the further development of the methods themselves. Rather, it is more on deploying AI and understanding the challenges of real-world problems. We will examine selected types of questions that can be treated with means of Artificial Intelligence and associated methods and tools. The emphasis is on understanding the concepts and logic behind a selected set of data analytics techniques. We will deploy a variety of flipped classroom elements, including team and lab work, small competitions and presentations. Individual and team assignments will be on provided data sets. Students will work in teams on a Kaggle-type competition.

High Performance Computing (HPC) is concerned with the efficient and fast execution of large simulations on modern supercomputers. It makes use of state-of-the-art technologies (such as GPUs, low-latency connections etc.) to efficiently solve complex scientific and data-driven problems. One of the key factors for the current success of machine learning models is the ability to perform calculations on modern computers with many model parameters and large amounts of training data. However, in their simplest form, current machine learning libraries only make limited efficient use of available HPC resources. The aim of this lecture is therefore to examine theoretical and practical aspects for the efficient training of machine learning and, in particular, deep learning models on modern HPC resources.

With this in mind, in the first part of the lecture, we will cover techniques that typically are used for the performance optimization of software on supercomputers. After a short introduction to HPC, we will deal specifically with GPUs (graphics processing units) and various memory models as well as performance optimization models and a practical introduction to CUDA, a programming interface developed by Nvidia for GPU programming.

In the second part of the lecture, the learnt techniques and concepts for the efficient training of Machine Learning and Deep Learning models will be applied. Different data- and model-parallel trainings methods for the efficient training on GPUs, algorithmic and practice-oriented, will be demonstrated using various examples from applications.

This seminar explores the critical limitations of Large Language Models (LLMs) through the study of:

Jailbreaking: How LLMs can be intentionally manipulated to bypass safeguards and restrictions, leading to unintended or unethical outputs. Hallucinations: The tendency of LLMs to generate confidently incorrect or fabricated information, undermining their reliability. Reasoning: Gaps in logical coherence and contextual understanding that affect the models' ability to perform consistent and accurate reasoning. Scalability: Challenges related to the increasing computational and environmental costs of training larger models, and the diminishing returns on performance improvements. We will also examine other aspects that underscore the limitations of LLMs, providing a comprehensive perspective on their current capabilities and future directions.

This course will start with learning the basics of programming in Python, so no prior programming knowledge is needed, but helpful. 
Next will be an introduction to data handling and visualization (i.e., with seaborn, matplotlib). After that, we will start with basic concepts used in machine learning (i.e., learning, prediction) and helpful methodologies (i.e., cross-validation to prevent overfitting). 
In the final part of the course, we will learn to apply several machine learning procedures (i.e., regressions, tree models, deep-learning) and to use model explainers to allow the interpretation of results from otherwise black-box models. As software tools, we will use Jupyther/Colab notebooks. Miniconda or Anaconda should be installed, but all software is freely available. Depending on student demand, this course can be held in German.

As you read these lines, millions of neurons are generating electrical signals in your brain. The exchange – sending and receiving – of electrical signals between neurons creates vibrating nerve networks that perform complex oscillations. According to the latest findings in neuroscience, oscillations in brain activity play an important role in many of our brain's functions. They influence our attention, for example. Oscillations also play an important role in artificial neural networks. Artificial neural networks, which mimic networks of natural neurons, are successfully used in artificial intelligence. In this seminar we will get to know mathematical models for networks of artificial neurons with time-delayed interaction. The corresponding models consist of coupled nonlinear differential equations with time delay. Among other things, we will examine the problem of the existence and nonexistence of periodic solutions and the significance of negative coupling parameters in the emergence of oscillations.

This seminar covers current research about the principles and for the application of information visualization in practice. Topics include the visual design of graphs, regressions, and hierarchical as well as temporal data, the connection between machine learning and visualization, interaction, perception, evaluation of visualization techniques or their application in practice.

The seminar will discuss recent work on applications of mathematical modeling in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.

This seminar deals with the mathematical basics of algorithmic language processing. The goal is to develop a solid understanding of methods used for processing natural language. If time permits, small applications from practice are demonstrated.

This seminar is targeted at student teachers who are interested in a realistic, youth-oriented teaching structure for the high-school level. It covers current algorithms used for Artificial Intelligence (AI) and Machine Learning (ML), specifically for regression and classification, different variants of neural networks, ChatGPT, Nearest Neighbor algorithm, algorithms based on decision trees, and more.

For the algorithms and mathematical models, teaching modules are supposed to be created that can supplement the current curricula. The lectures will present the required mathematical basics and a suitable didactic concept.
 

In the Advanced Machine Learning lecture we will cover various advanced concepts, techniques, and algorithms. We will place focus both on the mathematical and theoretical aspects, as well as the practical aspects which involve implementing, training, and optimizing machine learning models using real-world datasets. The lecture is organized in four parts. In the first part we will tackle machine learning for graph data including generative models, ranking, and graph neural networks. In the second part we will cover modern generative models such as variational autoencoders, normalizing flows and generative adversarial networks. In the third part we will cover robustness including both attacks on machine learning models (evasion, poisoning) and defenses (certificates). Finally, in the last part we will cover uncertainty quantification techniques such as Bayesian neural networks, Gaussian processes and conformal prediction.

Scientific Machine Learning is a new research area that is developing as a field of its own, in which techniques of scientific computing and machine learning are combined and further developed. This results in hybrid methods that are applied to the discretization of partial differential equations, the development of fast and robust solvers, and new modeling techniques.

Keywords are

1. Domain-aware scientific machine learning,
2. Mathematics-informed machine learning,
3. Interpretable scientific machine learning,
4. Machine learning-enhanced simulations,
5. Hybrid modeling (machine learning + first principle modeling).

In the Adversarial Machine Learning seminar, we will explore the robustness of machine learning models. This seminar will have a practical focus where the students will be split into two sets of teams. One set of teams will focus on developing various attacks to break or manipulate machine learning models, e.g. given an image of a cat design algorithms to add impercetible adversarial noise to the input to cause the model to misclassify it as a dog. The other set of teams will focus on defending against such attacks. The attacks and defenses will be carried out in multiple rounds allowing the attackers and defenders to learn from each other to improve their approach.

This course will start with learning the basics of programming in Python, so no prior programming knowledge is needed, but helpful. Next will be an introduction to data handling and visualization (i.e., with Seaborn, matplotlib). After that, we will start with basic concepts used in machine learning (i.e., learning, prediction) and helpful methodologies (i.e., cross-validation to prevent overfitting). In the final part of the course, we will learn to apply several machine-learning procedures (i.e., regressions, tree models, deep-learning) and to use model explainers to allow the interpretation of results from otherwise black-box models. As software tools, we will use Jupyther/Colab notebooks. Miniconda or Anaconda should be installed, but all software is freely available. Depending on student demand, this course can be held in German.

The seminar will discuss recent work on applications of mathematical modeling in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.

In this seminar, the theoretical and algorithmic basics of machine learning are covered. Individual chapters from the book Shai Shalev-Shwartz, Shai Ben-David, Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, are discussed.

In this module you take part in a programming competition about the modeling of risks of climate change. A regression function fed with public weather data needs to be implemented. Likely, the output will be publicly available mortality data. If other reliable data is available, it will be used as well.

The participants can additionally take part with their contribution in a competition sponsored by a business consultancy. The details will be made available at the beginning of the semester; the participation in the competition is voluntary, and it does not require an additional programming effort. The participants' works for the seminar are scored independently of the competition.

Expected skills:
• Good programming skills in Python, Java, or R. (There won't be enough time to acquire these skills during the semester.)
• Interest in the topic of the programming competition
• Work independently to process public data and experiment with various Machine Learning models
• Interest in Data Science
• Helpful are first experiences with Machine Learning models such as neural networks and decision trees.

The goal is to model the impact of climate changes (particularly the temperature) on human health and mortality.
 

Potential topics include convex optimization for computer-assisted proofs and algorithms, as well as machine learning techniques for quantifier elimination in real closed fields. Prerequisites for this seminar are the lectures "Polynomial Optimization" or "Convex Optimization".

The seminar is targeted at student teachers who are interested in a realistic, youth-oriented teaching structure for the high school level through algorithms in the context of different applications like MP3, JPEG, RSA, GPS, the computation of the Page Rank by search engines etc.

In line with the topic of the Year of Science 2019 (an initiative of the Federal Ministry of Education and Research in Germany), algorithms from the area of artificial intelligence (AI) and machine learning (ML) are treated. Quantum computing and quantum algorithms are another possible focus for the seminar.

For the algorithms and mathematical models, teaching modules are supposed to be created that can supplement the current curricula. The lectures will present the corresponding mathematical basics and a suitable didactic concept.
 

This seminar shall give an introduction to modern methods of data analysis and machine learning for scientific research. We will focus on methods beyond “black box models” that allow for scientific insight and discoveries.

Contents of the course:
• Fundamentals of Data Analysis and Machine Learning
• Bayesian Statistics and Data Analysis
• Interpretable Machine Learning
• Causal Inference and Modelling
• Inference of Nonlinear Dynamic Systems and Networks

This course introduces students to the fundamental concepts, techniques, and algorithms in machine learning. It covers the mathematical and theoretical foundations, supervised and unsupervised learning techniques, evaluation methods, and advanced aspects. Students will gain hands-on experience in implementing, training, and optimizing machine learning models using real-world datasets.

The tentative list of topics is as followed:

• Introduction
• Probabilistic Inference
• Trees and Forests
• Neighbor-based methods
• Linear models
• (Convex) Optimization
• Gradient-based Optimization
• SVMs
• Kernels
• Basics of Deep Learning: MLPs, CNNs, GNNs
• Dimensionality Reduction: PCA & tSNE
• SVD & Matrix Factorization
• k-Means and GMMs
• Hierarchical Clustering
• Robustness
• Uncertainty
• Privacy
• Fairness

As the importance and widespread use of automated simulations, decision-making processes and AI continues to grow, new challenges arise in the analysis and processing of data. In particular, the growing complexity of tasks and the available size of the data sets used for the above-mentioned areas require new and more efficient approaches from the fields of data science, data mining, and machine learning in general.

This lecture will cover theoretical and algorithmic foundations of modern data processing and analysis. The lecture is strongly, but not exclusively, based on the literature listed below and covers the following topics, among others:

• Techniques for dimension reduction (singular value decomposition/PCA/robust PCA)
• Classical regression
• Clustering algorithmsClassification using Support Vector Machines and Linear Discriminant Analysis
• Classification using Classification Trees and Random Forest
• Classical neural networks or introduction to deep learning
• Introduction to Reinforcement Learning (optional)
• Reduced Order Models (ROMs) (optional)

The lecture will have a strong focus on the algorithmics and mathematical computability of the methods mentioned as well as the application-oriented implementation and less on statistical methods, which are also a component of data science.

Brunton, S., & Kutz, J. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (2nd ed.). Cambridge: Cambridge University Press. doi:10.1017/9781009089517

Machine learning models are increasingly used in safety-critical applications and to make automated decisions about humans. Beyond accuracy and efficiency, we expect such models to also be robust to noise and adversaries, to faithfully represent their (aleatoric and epistemic) uncertainty, to preserve privacy, to be fair w.r.t. different demographic groups, and to be interpretable. In this seminar, we will cover the latest research on these trustworthiness aspects, as well as the (fundamental) trade-offs between them. We will study the shortcomings and failures of traditional machine learning models and how to improve them.

The seminar will discuss recent work on applications of mathematical modeling in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.

In this seminar, we will discuss machine learning methods currently used in various application areas. We will focus on concrete methods, for example:
• mathematical basics,
• model-selection algorithms,
• regularization,
• dimension reduction,
• decision trees,
• support vector machines,
• neural networks.
The basis for the seminar is the book “The Elements of Statistical Learning”.

This seminar uses current research for practical applications of information visualization. The topics cover the areas of visual design, using machine learning in visualization, interaction, evaluation of visualization techniques or their application. The goal of the seminar is to learn to work through and understand scientific works and use them for own practical applications.

In the lecture we will cover various advanced machine learning concepts, techniques, and algorithms. We will place focus both on the mathematical and theoretical aspects, as well as the practical aspects which involve implementing, training, and optimizing machine learning models using real-world datasets. Some of the topics that we will cover include: semi-supervised learning, machine learning for graph data, machine learning for sequential data, Gaussian processes, temporal point processes, trustworthy machine learning, advanced topics in optimization, machine learning theory, and generative models.

New developments in the field of deep neural networks have enabled a large amount of applications in recent years that were previously unthinkable to achieve in high quality: From image recognition, speech recognition, simulation of protein folding, automatic playing of computer games to image generation or speech generation with systems like ChatGPT. In this lecture we will cover the concepts behind deep neural networks, in particular Convolutional Neural Networks, attention mechanisms, modern transformer architectures, and their extensions. We focus on supervised deep learning and unsupervised deep learning, where many training examples are available for a given task, and the network learns independently from this data. In this lecture, a mathematical understanding of the mechanisms and the design of neural networks is conveyed. At the same time, examples are given on how to efficiently implement and use neural networks with the help of modern Deep Learning frameworks such as PyTorch.

Scientific Machine Learning is a new research area that is developing as a field of its own, in which techniques of scientific computing and machine learning are combined and further developed. This results in hybrid methods that are applied to the discretization of partial differential equations, the development of fast and robust solvers, and new modeling techniques.

Keywords are

1. Domain-aware scientific machine learning,
2. Mathematics-informed machine learning,
3. Interpretable scientific machine learning,
4. Machine learning-enhanced simulations,
5. Hybrid modeling (machine learning + first principle modeling).

The seminar will discuss recent work on applications of mathematical methods in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.

In this seminar, we will discuss machine learning methods currently used in various application areas. We will focus on concrete methods, for example:
• mathematical basics,
• model-selection algorithms,
• regularization,
• dimension reduction,
• decision trees,
• support vector machines,
• neural networks.
The basis for the seminar is the book “The Elements of Statistical Learning”.

In this seminar the theoretical and algorithmic basics of machine learning will be treated. Individual chapters from the book “Understanding Machine Learning: From Theory to Algorithms” are discussed.

The practical training deals with the design, implementation and evaluation of visual analysis of large and complex data sets: Visualization, interaction, human perception, data analysis and their combination to solve application-oriented problems. Problems from current research and application topics in the field of visual analytics will be addressed and implemented. Application areas are for example finance, economics, geosciences, meteorology, medicine, biology, transportation, or sports. In addition to deepening technical knowledge, the course can also be used to acquire communication and presentation skills.