# Case Studies Scientific Computing (MA4306)

## Organisation

Lecture | Prof. Dr. Callies, Dr. Tobias Köppl |
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Question time | by arrangement (Email) |

Supervision | Dr. Tobias Köppl, M.Sc. Gladys Gutiérrez |

Requirements | Basic courses on numerical mathematics: MA1304 Introduction to Numerical Linear Algebra MA2304 Numerical Methods for Ordinary Differential Equations MA3303 Numerical Methods for Partial Differential Equations |

Credits | 6 ECTS |

TUMonline | Link zum TUMonline Eintrag |

Moodle | To get access to the Moodle course, please register in TUMonline for the lecture. Afterwards you are automatically registered for the Moodle course. |

## News

- The application process has started.
- There will be a kick off meeting for all participants in the first lecture week. The exact date will be published on this website.
- In the first weeks after the kick off meeting, there will be some lectures on some background knowledge for the two projects.

## Basic Concept

Students participating in this module will work on a practical problem in small groups under the supervision of the lecturers (see Fig. 1). The project work typically starts with the discussion of the problem setup, an analysis of the important problem characteristics and a subsequent formulation as a mathematical model. During this phase, the students also present their challenges to a non-scientific audience, usually in the form of a poster presentation. They discuss their poster ideas with the supervisors and receive peer-feedback on their presentations. The participants then research suitable solution algorithms and receive lectures on additional skills where necessary. They discuss their solution approaches with the project supervisors and refine and implement the chosen algorithms. They assess and discuss their solutions and the practical properties of their algorithm with the supervisors and implement necessary modifications or enhancements and / or contrast the properties of different solution approaches with respect to the underlying application. During the project work the students discuss their progress with their supervisors from mathematics and from the field of application on a regular basis and give intermediate presentations of their problem, its characteristics and their solution approaches to the other participants. At the end, the results are presented in the form of conference talks to a scientific audience.## Grading

The final grade is composed of the following subtasks:- Poster presentation
- A short report about 10 to 15 pages summarizing the basic findings of the project
- Well-documented program code that has been developed during the project work
- Plan of milestones and workpackages as well as a time sheet
- Final presentation (15 minutes talk per candidate plus 5 minutes questions per candidate)

## Registration

Registration for this course is mandatory and has to be done before the**deadline: 14th April 2021.**

The registration is done by email to koeppl@ma.tum.de providing the following information:

- last name, first name, student ID
- curriculum (of your master's studies)
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects. (Example: (1) Project 3, (2) Project 1, (2) Project 4, (3) Project 2 - note that you can rate multiple projects with the same value)
- list of scientific computing related lectures (numerics, numerical engineering, computer science and engineering, etc.) that you have attended (for lectures from other faculties or universities. Please provide the grades you obtained in context of these lectures and give a short description of the topics covered so that we know about your expertise in the field)
- programming skills (programming languages and other programming related skills)
- persons you would like to work with as a team

**Please note that there is only a limited number of places for this module, since for each project we can only accept up to three students.**

## Projects

### Project 1: Machine learning methods for simulating the impact of left ventricular assistant devices (LVAD)

Cardiogenic shock is an illness that is characterized by the disability of the heart to provide enough blood and oxygen for the vital organs. Some of the most common causes for this illness are: heart attack, heart failure, chest injuries or internal bleeding. In order to compensate the lack of blood supply, the heart is equipped with assistance device such as blood pumps. Typically they are installed in the left ventricle, since the left ventricle of the heart pumps blood with high pressure into the systemic part of the cardiovascular circulation. Such devices are called left ventricle assistance devices (LVAD). Using a LVAD in an efficient way, the settings (rotations per minute (rpm), type of the pump etc.) of the LVAD have to be selected carefully. The goal of this project is to design a simple surrogate model mapping these settings to blood pressure and velocity curves reported in different arteries of the systemic circulation. By this it is intended to avoid computationally expensive simulations of blood pressure and velocity curves. This enables the test of different settings in a short time. In order to construct a surrogate model for this purpose, machine learning techniques should be considered and tested. The data for the training phase are provided by the company**Computational life**. The subtasks of this project read as follows:

- Get an understanding of the fundamentals on cardiovascular circulation and hemodynamics.
- Study literature on machine learning techniques such as neural networks, reduced basis or kernel methods.
- Apply these techniques to design a simple surrogate model, mapping the LVAD settings to blood pressure curves, velocity curves or other interesting quantities.
- Test the performance of these methods and report your findings.

**Contact:**

**Computational life**, USA, 251 Little Falls Drive, Wilmington, New Castle County. Delaware 19808-1674, https://www.computational-life.com

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**Literature:**

- H. Liu, S. Liu, X. Ma, and Y. Zhang.
**A numerical model applied to the simulation of cardiovascular hemodynamics and operating condition of continuous-flow left ventricular assist device.**Mathematical Biosciences and Engineering 17, no. 6 (2020): 7519-7543. - G. Santin and B. Haasdonk.
**Kernel methods for surrogate modeling.**, (2019), arXiv preprint arXiv:1907.10556.

### Project 2: Neural network based calibration of five hole probes

In order to enable safe operation of ships and planes (see Figure 1), it is necessary to have an accurate knowledge on flows around them. In case of planes, probes are placed at certain distances on their wings. These probes contain several sensors that measure static and dynamic pressures as well as velocities and angles of attack. An accurate measurement of these units is achieved by calibrating each probe before it is used. The necessity for this arises from the fact that the dependence of the measured pressures on the angle of attack varies from probe to probe. This is mainly due to the manufacturing tolerances. The goal of this project is to understand and program calibration algorithms for multi-hole probes. The subtasks of this project read as follows:- Get an understanding of the fundamentals from fluid mechanics.
- Study literature on the calibration of multi-hole probes.
- Choose suitable neural networks methods to determine the calibration parameters.
- Implement a calibration algorithm in MATLAB/C++ for a multi-hole probe.
- Develop strategies based on neural networks for recognizing wrong measurements.
- Test the MATLAB/C++ programs by means of some measurements.

**Vectoflow GmbH**. Vectoflow provides measurements taken in wind tunnels. These measurements should be used to test the MATLAB/C++ programs mentioned above. Furthermore, you are assisted by vectoflow to get a better understanding of the different issues related to the project.

**Contact:**

**Vectoflow GmbH**, Friedrichshafener Straße 1, 82205 Gilching, Dr. Christian Haigermoser, https://www.vectoflow.de

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**Literature:**

- K. Rediniotis and R. Vijayagopal.
**Miniature multihole pressure probes and their neural-network-based calibration.**AIAA journal 37, no. 6 (1999): 666-674. - A. Ghosh, D. Birch and O. Marxen.
**Neural-Network-Based Sensor Data Fusion for Multi-Hole Fluid Velocity Probes.**IEEE Sensors Journal 20, no. 10 (2020): 5398-5405.

### Project 3: Optimization of artificial neural networks (ANN)

An ANN is a system of nodes which are referred to as artificial neurons, since they can be compared to neurons in a brain. A connection or edge between two nodes, like the synapses in a biological brain, can send a signal to other nodes. A node receiving a signal can send it to other nodes which are connected to it. Within an ANN the signal is a real number, and the output of each node is provided by a combination of non-linear functions and its inputs. To each node (neuron) and edge one assigns a weight that is adjusted during a training process. According to the weight the strength of the signal at a connection can be strengthened or weakened. Nodes typically have also a threshold such that signals received by the node such that they are only transmitted if they exceed this threshold. Typically, nodes are grouped together in form of layers. The different layers typically connect by edges linking the different nodes of the layers. Signals enter the network at the first layer (input layer) and leave the last layer (output layer) corresponding to quantities of interest. ANNs have successfully been used as simple surrogate models for complex relationships. For a learning process a sufficient amount of training data is required to determine the different weights. However, it is in general not quite clear how many nodes or neurons and layers have to be chosen to obtain an accurate ANN. The goal of this project is to find algorithms and estimates that can help to design an optimal structure for ANNs. In this context, the term**optimal**indicates that an ANN contains a minimal number of layers and neurons. The subtasks of this project read as follows:

- Study the literature on optimization algorithms for ANNs.
- Implement some algorithms in MATLAB or C++.
- Apply your ANNs to data sets describing the temperature in electrical engines (provided by
**Vitesco Technologies**). - Compare your results with PyTorch.

**Contact:**

**Vitesco Technologies GmbH**, Siemensstraße 12, 93055 Regensburg, MSc. Michael Wutz, (Vitesco Technologies

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**Literature:**

- J. He, L. Lin Li, J. Xu, and C. Zheng.
**ReLU deep neural networks and linear finite elements.**arXiv preprint arXiv:1807.03973 (2018). - A. Baldominos, Y. Saez, and P. Isasi.
**On the automated, evolutionary design of neural networks: past, present, and future.**Neural Computing and Applications 32, no. 2 (2020): 519-545. - https://www.adagos.com/projects/