RQs linking accuracy, precision, and resources
Large-scale simulations must balance several competing demands: high accuracy, reliable treatment of uncertainty and limited computational resources. PN 5 investigated how simulation models and numerical methods could be adapted dynamically to achieve this balance more efficiently.
The research combined scientific computing, uncertainty quantification and stochastic modelling. A particular focus was on using information from both experimental data and the simulations themselves to adjust models, numerical parameters and computational effort during a simulation.
Research Focus
The research addressed four closely connected questions:
- Accuracy and resources: How could simulations dynamically adapt to achieve defined accuracy targets within available computing, time and energy constraints?
- Uncertainty and resources: How could uncertainties be quantified and reliable predictions maintained when data, models and computational resources were limited?
- Model complexity: How could stochastic models be adapted to balance predictive precision with model accuracy and available information?
- Global adaptivity: How could these aspects be combined to minimize computational effort while meeting a prescribed overall error target?
Projects
| Fully-implicit local dynamic model adaptivity with machine-learned scale bridging | Bernd Flemisch (Ingo Steinwart) |
| Bayesian, causal, universal differential equation learner | Wolfgang Nowak (Sergey Oladyshkin, Ingo Steinwart) |
| Effective uncertainty quantification and ANN dynamics via amplitude equations | Guido Schneider (Marco Oesting) |
| Application-agnostic software for model adaptivity of two-scale coupled problems | Benjamin Uekermann (Felix Fritzen) |
| Bayesian multiscale spatio-temporal modelling of extreme events | Marco Oesting (Wolfgang Nowak) |
| Uncertainty quantification for data-limited inverse problems via efficient probabilistic ML methods | Andrea Barth (Dirk Pflueger) |
| Physics-informed ANNs for dynamic, distributed and stochastic systems (SmartANN) | Sergey Oladyshkin (Dominik Göddeke) |
| Renewable energies and Data Science: Solvers for hybrid modelling in porous media – design, implementation, analysis | Dominik Göddeke, Christian Rohde, (Florin Radu, University of Bergen) |
| Optimal multidimensional accuracy-resource trade-off | Dominik Göddeke, Miriam Schulte |
| Data-driven optimisation algorithms for local dynamic model adaptivity | Bernd Flemisch (Andreas Langer, Femke Vossepoel (lab- and field-scale experiments, TU Delft) |
| Efficiency improvements by code Intrinsic uncertainty quantification via Monte Carlo methods | Michael Resch (Claus-Dieter Munz, Ralf Schneider) |
| Processing uncertain microstructural data | Andrea Barth (Felix Fritzen) |
| Physics-informed ANNs for dynamic, distributed and stochastic systems (SmartANN) | Wolfgang Nowak (Sergey Oladyshkin, Guido Schneider) |
| Uncertainty Quantification by Physics- and Data-Based Models for Mechanical Systems | Bernard Haasdonk (Dirk Pflüger) |
| Exploiting structural knowledge in (nonlinear) PDE problems for efficient deployment of the learning abilities of ANNs | Guido Schneider (Wolfgang Nowak, Sergey Oladyshkin, Björn de Rijk) |
| Adaptive and flexible macro-micro coupling software | Benjamin Uekermann (Carina Bringedal) |
Associated projects
| Uncertainty quantification for random conservation laws with discontinuous flux functions | Andrea Barth |
| Parameter inference of non-linear subsurface flow in geological carbon dioxide storage: development of adaptive Bayesian sparse2 arbitrary multi-resolution polynomial chaos expansion | Sergey Oladyshkin |
Project Network Coordinators
Andrea Barth
Prof. Dr.Computational Methods for Uncertainty Quantification
Dominik Göddeke
Prof. Dr. rer. nat.Computational Mathematics for Complex Simulations in Science and Engineering