Uncertainty Analysis

Complex Systems

Probability

Machine Learning

Bayesian Inference

Time Series Analysis

Networks Analysis

My research interests focus on the development and implementation of methods that allow the probabilistic investigation of complex system dynamics. Basically, I am working in the following four overlapping methodological domaines, often in the context of time-consuming determinisitic simulation codes and system observations or models consisting of a large amount of data.

Combining machine learning algorithms to perform

- regression tasks to develop
**meta models**for complex system dynamics, e.g. via**Gauss Processes**, Support Vector Machines **adaptive sampling**approaches to investigate complex system behavior in the vicinity of critical state transitions

Using advanced analysis approaches to investigate complex systems with focus on system safety and risk measures

- via
**Monte Carlo Dynamic Event Trees (MCDET)**to exploratively study and probabilistically evaluate the impact of stochastic state transitions on the system dynamics - via Uncertainty Analysis methods, i.e. estimation of
**Tolerance Limits**via Wilks Approach,**Bootstrapping**or classical**Monte Carlo Simulations** - via Sensitivity Analysis methods to identify major contributors to the response uncertainty of a system, i.e. by squared multiple correlation coefficient or
**Sobol Indices**

Developping Bayesian inference approaches to

- detect and characterize multiple
**transition patterns**in complex time series, such as paleo-climate observations via**Linear Mixed Models** - localize cliff-edge effect regions via
**Gauss Processes**

Using network analysis and representation approaches to visualize, investigate and compare

- complex dependency patterns, e.g. multiple
**hazard impacts**on complex technical systems - dynamic patterns of
**probabilistic risk models**, e.g. to evaluate critical event sequences