The division’s aim is to develop methods for modelling, simulation, and optimization (MSO) of complex multiscale and multiphysics processes as well as the associated visualization and data analysis techniques.
The methodological basis lies in Numerical Mathematics, in particular adaptive numerics of differential equations including optimal control and meshless discretization of transfer operators for high-dimensional dynamical systems, and in Visual Data Analysis, such as interactive visualization techniques for spatiotemporal and higher-dimensional data from simulation or observation in combination with automated algorithms for identification, extraction, quantification, and classification of structures. Current goals in method development are
- the construction of novel uncertainty quantification (UQ) techniques for MSO and visualization, and their use for design, optimal control, parameter estimation and feature extraction under uncertainty;
- the development of seamless multiscale methods for systems exhibiting cascades of scales especially for hybrid multiphysics models;
- sparse and high dimension approximation techniques for transfer operator approximation and Bayesian inverse problems;
- data fusion techniques for multi-source large data and associated automation of data analysis;
- visualization in high dimensions; and
- utilization of data sparsity in classification.
Our application problems primarily come from the natural sciences with a focus on life and materials sciences:
- Solutions for Individualized Medicine (e.g., therapy planning, implant design, joint diseases, anatomy reconstruction, fusion of large medical data of various modalities, sparse classification/medical diagnostics
- Molecular and Biological Processes (design of functional molecules, systems biology and cellular reaction networks, reconstruction of biological and molecular structures from large microscopy image analysis, trace pollutants in water etc.
- Materials and Optical Processes (quantum optics, silicon, nonlinear systems in solar cells, new solar fuel technologies, materials micro- and nano-structure characterization, nondestructive testing, etc.)
- Large-Scale Data Management, Curation & Analysis (big research data, data sparsity, cohort analysis, high-throughput microscopy image analysis, data fusion, …)
- High Performance Computing (with applications in molecular dynamics, computational biology, and nano-optics).