We develop and investigate algorithms for numerical data-driven prediction. The aim here is to make useful predictions for future behavior of systems based on automatically collected current and historical data.
Data-driven predictions appear in many application domains like
- virtual product development using numerical simulations
- time series analysis for predictive maintenance
- uncertainty quantification in engineering
- technical trend prediction for foreign exchange rates and other financial products
The scientific focus is the research and development of efficient numerical
methods for high-dimensional problems and is the common ground for the different applications investigated. The developed approaches are based on the modern numerical methods of »sparse grids« and »low rank tensor decompositions« to represent non-linear functions. They can be powerful even in situations were common non-linear data analysis methods cannot cope with the amount of data.
Using dimensionality reduction, we develop software solutions, which assist the engineer in the interactive study of big data in the virtual product development process and for the purpose of predictive maintenance. The goal of these tools is to simplify and fasten the engineering decision process.