PhD Position in the IAS Focus Group Scientific Machine Learning on Dynamic Neural Networks

11.01.2022, Wissenschaftliches Personal

We are looking for a researcher (PhD candidate) to join our team at the Institute for Advanced Study, in the Focus Group "Scientific Machine Learning" involving Hans Fischer Senior Fellow Prof. Wil Schilders (Eindhoven University of Technology) and his host Prof. Hans-Joachim Bungartz (Chair of Scientific Computing in Computer Science–SCCS, TUM Department of Informatics). Pivotal to the PhD project is the challenge of embedding prior knowledge into the design of dynamic neural networks.

About Us
Located in the prosperous capital of Bavaria and home to over 39000 students, the Technical University of Munich (TUM) is one of the world’s top universities. It is committed to excellence in research and teaching, interdisciplinary education, and the active promotion of promising young scientists. TUM benefits from the healthy mix of companies and startups of all sizes headquartered in the region and is tightly connected to regional research hospitals. The university also forges strong links with companies and scientific institutions across the world.

The focus of the chair of Scientific Computing in Computer Science is on the algorithmics of scientific and high-performance computing as well as applications of numerical simulation. The spectrum extends from efficient numerical algorithms via parallel and distributed computing as well as the embedding of simulation tasks up to simulation scenarios from various fields (fluid dynamics, fluid-structure interaction, chemical engineering, traffic, finance, or quantum chemistry). Our research projects, due to the tasks' complexity, are typically tackled in multi-disciplinary cooperation and, thus, cover almost the entire simulation pipeline.

We are looking for a researcher (PhD candidate) to join our team at the Institute for Advanced Study, in the Focus Group "Scientific Machine Learning" involving Hans Fischer Senior Fellow Prof. Wil Schilders (Eindhoven University of Technology) and his host Prof. Hans-Joachim Bungartz (Chair of Scientific Computing in Computer Science –SCCS, TUM Department of Informatics).

Description
Our understanding of processes and phenomena in nature, industry and society is being radically transformed by machine learning and the availability of data. This is evident also from the large numbers of researchers embracing deep learning as a tool. At the same time, obstacles and challenges are becoming apparent: most deep-learning approaches require large amounts of data, but in many domains such massive datasets are not available. Furthermore, the emergent behaviour of deep neural networks is usually difficult to interpret. To overcome these drawbacks, the effective use of prior knowledge is key. Furthermore, efficiency of scientific computations is of prime importance, hence the size of neural networks, especially those used in combination with traditional physical models, must be kept minimal in size. This holds especially when constructing digital twins of industrial products and processes. The main objective of the Focus Group Scientific Machine Learning: revealing how dynamic neural networks can be made much more effective by incorporating mathematical and physical understanding in their design and reducing their size by means of model order reduction. The latter also implies mathematically based predictions of the topology of the network based on related state space formulations. The Focus Group aims to build a mimetic theory of neural networks that will enable their data-efficient and understandable use for industrial simulations and scientific discovery in physics, astronomy and beyond, as well as building a theory of model order reduction methodologies tailored to dynamic neural networks. Stated in a slightly different way, the goal of this research is to better understand neural networks to enable the design of highly efficient, tailor-made neural networks built on top of and interwoven with structure-preserving properties of underlying scientific and industrial challenges. This is unexplored terrain and will lead to novel types of machine learning that are much more effective and have a much lower need for abundant sets of data.

Pivotal to the PhD project is the challenge of embedding prior knowledge into the design of dynamic neural networks. On the one hand, this will be done by incorporating known properties and structures, thereby avoiding physically unrealistic solutions. On the other hand, relations between dynamic neural networks and state space representations of the underlying problem can be used to extract information that will lead to mathematically correct topologies (number of hidden layers, number of neurons) of the network to be used. In addition, suitable neuron actions will be developed and researched, including the solution of second-order ODEs, corresponding to neurons that act as high or low pass filters.

Requirements for the PhD candidate

• Mathematics, Informatics, or related Masters degree.
• Knowledge in Model Order Reduction, machine learning (neural networks), and numerical methods is preferred.
• Experience in MATLAB, Python, Julia or related software is preferred.
• Interest in industrial challenges and international collaboration (especially TU Eindhoven).
• Soft skills: analytical thinking, structured and organized work, high intrinsic motivation.

The PhD candidate associated to the project is expected to work on:

• Revealing/unraveling the relation between dynamic neural networks and state-space models, and building robust and efficient model reduction methods for neural networks on this.
• Developing a theory for dynamic neural networks with different neuron actions, suitable for different applications, and corresponding model reduction techniques.
• Research on methods suitable for weakly and strongly nonlinear situations.

Your application should comprise at least the following:

• An application letter pointing out why you are interested in the project and why you would like to pursue a PhD.
• A detailed curriculum vitae.
• The transcripts of records, including courses and grades.
• Names of one or two contact persons (we will ask them for letters of reference).

Please send your application

to:

. The position can start any time, the early the better.

Note that TUM has been pursuing the strategic goal of substantially increasing the diversity of its staff. As an equal opportunity and affirmative action employer, TUM explicitly encourages nominations of and applications from women as well as from all others who would bring additional diversity dimensions to the university’s research and teaching strategies. Preference will be given to disabled candidates with equal qualifications. International candidates are also highly encouraged to apply.

Contact
For questions on the project in general:

Hans Fischer Senior Fellow
Prof. Wil Schilders (Eindhoven University of Technology)
[email protected]
IAS profile page

For questions on the application process:

Dr. Felix Dietrich
[email protected]
Link to the chair homepage
www.fd-research.com/contact

Data Protection Information:
When you apply for a position with the Technical University of Munich (TUM), you are submitting personal information. With regard to personal information, please take note of the Datenschutzhinweise gemäß Art. 13 Datenschutz-Grundverordnung (DSGVO) zur Erhebung und Verarbeitung von personenbezogenen Daten im Rahmen Ihrer Bewerbung. (data protection information on collecting and processing personal data contained in your application in accordance with Art. 13 of the General Data Protection Regulation (GDPR)). By submitting your application, you confirm that you have acknowledged the above data protection information of TUM.

Kontakt: Dr. Felix Dietrich, [email protected]