Mathematical Foundations of Complex System Science
Research
The beauty and fascinating enigmatic nature that complex systems embody might be the driving force behind the ambitions of many scientists in their realm of scientific research. As it turns out, resolving the computational bottleneck of scientific questions being addressed today often appears as the central issue. Our research mission is to accumulate valuable insights in applied and numerical mathematics, especially in their practical applications to these real-world challenges. Hereby, a fulfilling aspect of our work is the ability to construct a bridge between the abstract, theoretical world of pure mathematics and the practical, empirical world of the sciences. This connection serves as a source of immense satisfaction and a driving force behind our ambitions in the realm of scientific research.
Team
- Visiting Professor Dr. Michael Hecht
- Azita Hajizade
- Phil-Alexander Hofmann
- Alexander Benedix Robles
- Janina Schreiber
- Dr. Damar Wicaksono
- Gentian Zavalani
Research Topics
- High-Dimensional Interpolation and Fast Spectral Methods
Polynomial interpolation goes back to Newton, Lagrange, and others, and its fundamental importance in mathematics and computing is undisputed. We have extended Newton and Lagrange interpolation to a multivariate interpolation algorithm (MIP), maintaining their numerical stability and computational efficiency.
- Numerical Differential Geometry
We have developed a computational scheme that derives a global polynomial level set parametrisation (GPLS) for smooth closed surfaces from a regular surface-point set. The GPLS enables to approximate a broad class of smooth surfaces by affine algebraic varieties. Posterior, differential-geometric quantities like mean and Gauss curvature can be efficiently and accurately computed. Even 4th-order terms such as the Laplacian of mean curvature are approximated with high precision.
- Black-Box Optimization
We have developed a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian optimization steps, using Gaussian processes to model the error between the objective and its polynomial fit. PMBO is demonstrated to outperform the classic Bayesian optimization and is robust with respect to the choice of its correlation function family and its hyper-parameter setting.
Events
Has no events.