The most challenging problems in academia and industry are characterized by increasing complexity. New scientific breakthroughs, as well as new industrial developments, often require international collaboration and interdisciplinary interaction. Both of these components are strongly represented in this research program. This IRTG is therefore ideally suited to train the next-generation workforce in research-driven environments. The proposed projects span both fundamental and more applied research questions, leading to future career paths as scientists or
research engineers.

The IRTG qualification program is designed to prepare doctoral researchers for these career paths by providing high-quality research training and education in relevant areas, while also providing sufficient structure and supervision so as to facilitate completion within three years.

Research Program

Computational Approach to Modern Inverse Problems

Computational techniques are an indispensable component of every engineer’s toolset and every scientist’s laboratory. By now, the field of Computational Engineering (and) Science (CES) had significant impact on the world and can be considered a discipline on its own. However, the computational approach is often viewed strictly as a replacement for experimental analysis or merely as a prediction tool; by contrast, its full potential may only be realized by adopting new analysis and design processes.

For nearly two decades, CES has been a major research field both at RWTH Aachen and at UT Austin: Computational approaches are used as a new tool to discover, identify, and discriminate previously unknown
models that govern and describe complex phenomena, and also to yield innovative and optimized products and processes. In all these approaches we single out one comprehensive methodology that the IRTG labels modern inverse problems. The IRTG uses this term to describe this wide range of recent problems in engineering and science, where CES is able to lead to unprecedented breakthroughs in design quality, efficiency of operation, and understanding of systems and materials.

The International Research Training Group of RWTH and UT Austin builds upon their successful research experience and goes beyond it in the following ways:

  • Research focus is on crucial and emerging aspects of inverse problems, in particular, data analysis, model hybridization, advanced geometric modeling, quantification of uncertainties, and transfer to applications.
  • By enhancing the interaction between the Center for Simulation and Data Science (JARA-CSD) at RWTH and the Oden Institute for Computational Engineering and Sciences at UT, doctoral researchers benefit from a holistic and interdisciplinary perspective on modern inverse problems, which is integrated in the training at both institutions.

Alliance of Geometry, Data, Models, and Applications

From the wide range of aspects in modern inverse problems, the IRTG identified four themes that encompass the research directions pursued within the IRTG. The themes do not stand alone, but instead their interaction plays an essential role in the projects described below.

  1. Geometry. A digital representation of the geometric shape or domain is the basis of most engineering applications. A proper and flexible problem-specific geometric representation is crucial for computation. Generally, there are two classes of problems: In the first case, the geometry is an ingredient of the forward model and must be known, possibly in a rough way. It must be thoroughly coupled to the model to achieve performance and accuracy. In the second case, the geometry is unknown and is to be retrieved via an inverse problem. A typical example is image processing.
  2. Data. The combination of observations and measurements with models is a fundamental aspect of inverse problems in CES. Often, practical physical models of a process cannot be derived from first principles alone. At the same time, significant data about the process in the form of observations or measurements are available but typically affected by uncertainty. Conversely, a large amount of data may be available from first principles computation but remain difficult to handle. All this should be taken into account when estimating parameters of a model or deriving the model itself.
  3. Models. Increasingly, engineering problems involve a variety of physical effects, and consequently, multiple scales and interacting models. This poses challenges to both model formulation and numerical methods, in particular when considered in the context of an inverse problem. Additionally, modeling is of great importance when interpreting and processing data, and representing the geometry. Here, the concept of a model goes beyond a differential equation, and increasingly involves data-driven relations.
  4. Applications. Modern inverse problems must respect and be tailored to the specific application. At the same time, industrial applications are showing growing demand for individualization, and a steady rise in complexity of processes. Combined, these factors represent significant challenges for both the classic production industry and the development of simulation technology. This requires a change in paradigm towards automated yet specialized design approaches which fit the framework of inverse problems