Methods
Developing scientific computing methods is a central aim for research activities at IWR. We employ mathematical and computational techniques and combine them in innovative ways. Our principal investigators construct tools and libraries for use in interdisciplinary projects. The two central pillars in designing methods are the classical branch of modeling, simulation and optimization (MSO), and the data-centric approach using machine learning and artificial intelligence (ML & AI). Both are complemented with scientific visualization to improve the understanding of results and the analysis of correlations.
Methods @ IWR
The methods that our research groups develop are influenced by the applications we are working on. The interplay of appropriate algorithms for specific applications makes up a lot of the efficiency of the scientific computing approach. Five key areas are defined as focus points for our scientific approach:
Mathematical and Numerical Analysis is the background for models based on first principles or differentiable heuristics. Our optimization portfolio ranges from gradient-based Newton-type methods to approximation algorithms using evaluations of the cost function and constraints.
Numerical Algorithms and Software are the basis of numerical experiments. The implementation and usability of algorithms in software is an important factor in the acceptance of the scientific computing paradigm.
Data Analysis and Visualization faclititate the understanding and creation of insights from the data produced by simulations, statistical tests, and collected research data. Specifically, graphical representation allows for a major speedup in understanding data.
Machine Learning and Computer Vision are two closely related fields in modern scientific computing. Shaping structures to learn statistical evidence from large data sets brings artificial intelligence approaches to immediate use in science.
Arithmetic, Geometry and Topology provide the methodological background for understanding structures and connections in models as well as data. The influence of these mathematical fields on both numerical models and aritificial intelligence cannot be overestimated.