Research Topics

Mathematical models are ubiquitous in applications across science and technology, where these models are used to describe complex processes. To systematically investigate and predict phenomena of interest using computer simulations based on these models, we need accurate, reliable, and efficient computational methods.

Many complex models of practical relevance are affected by uncertainties, for example due to a lack of knowledge of material properties, intrinsic natural variability, or by incorporating noisy data. Such uncertainties inevitably impact the considered mathematical model and consequently the quantification of the reliability of simulation outcomes.

The junior research group Uncertainty Quantification (UQ) develops advanced mathematical and numerical techniques for the treatment and quantification of uncertainties at the interface of complex computational models and data. To this end, we work on methods of modern applied mathematics, machine learning techniques in conjunction with simulation-based approaches, and aspects of high-performance computing. Overall, our research focuses on theoretical and methodological aspects, as well as on interdisciplinary projects where theoretical sound methodologies are tailored to applications.


Sensitivity of the polar boundary layer to transient phenomena
Kaiser, A.; Vercauteren, N.; Krumscheid, S.
2024. Nonlinear Processes in Geophysics, 31 (1), 45–60. doi:10.5194/npg-31-45-2024
Machine learning-based conditional mean filter: A generalization of the ensemble Kalman filter for nonlinear data assimilation
Hoang, T.-V.; Krumscheid, S.; Matthies, H. G.; Tempone, R.
2023. Foundations of Data Science, 5, 56–80. doi:10.3934/fods.2022016
Adaptive Stratification (ADSS)
Krumscheid, S.; Pettersson, P.; Yuan, F.
2023, February 21. doi:10.5281/zenodo.7660514
Global sensitivity analysis of a one-dimensional ocean biogeochemical model
Mamnun, N.; Völker, C.; Krumscheid, S.; Vrekoussis, M.; Nerger, L.
2023. Socio-Environmental Systems Modelling, 5, Art.-Nr.: 18613. doi:10.18174/sesmo.18613
Stochastic upscaling for UP with OPM and ADSS
Pettersson, P.; Keilegavlen, E.; Sandve, T. H.; Gasda, S.; Krumscheid, S.
2023. doi:10.5281/zenodo.10362253
Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures
Ayoul-Guilmard, Q.; Ganesh, S.; Krumscheid, S.; Nobile, F.
2023. International Journal for Uncertainty Quantification, 13 (5), 61–98. doi:10.1615/Int.J.UncertaintyQuantification.2023045259
Statistical Learning of Nonlinear Stochastic Differential Equations from Nonstationary Time Series using Variational Clustering
Boyko, V.; Krumscheid, S.; Vercauteren, N.
2022. Multiscale Modeling & Simulation, 20 (4), 1251–1283. doi:10.1137/21M1403989
Dynamical stability indicator based on autoregressive moving-average models: Critical transitions and the Atlantic meridional overturning circulation
Rodal, M.; Krumscheid, S.; Madan, G.; Henry LaCasce, J.; Vercauteren, N.
2022. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32 (11), Art.-Nr.: 113139. doi:10.1063/5.0089694
Practical field-scale simulation approaches for quantification of fault-related leakage under uncertainty
Gasda, S.; Keilegavlen, E.; Sandve, T. H.; Berge, R.; Pettersson, P.; Krumscheid, S.
2022. Proceedings of the 16th Greenhouse Gas Control Technologies Conference. 16th International Conference on Greenhouse Gas Control Technologies (GHGT-16) 23-27 Oct 2022. doi:10.2139/ssrn.4277020
Adaptive stratified sampling for non-smooth problems
Pettersson, P.; Krumscheid, S.
2022. International Journal for Uncertainty Quantification, 12 (6), 71–99. doi:10.1615/Int.J.UncertaintyQuantification.2022041034
Complexity Analysis of stochastic gradient methods for PDE-constrained optimal Control Problems with uncertain parameters
Martin, M.; Krumscheid, S.; Nobile, F.
2021. ESAIM: Mathematical Modelling and Numerical Analysis, 55 (4), 1599–1633. doi:10.1051/m2an/2021025
Cardiorespiratory, Metabolic and Perceived Responses to Electrical Stimulation of Upper‐Body Muscles While Performing Arm Cycling
Zinner, C.; Matzka, M.; Krumscheid, S.; Holmberg, H.-C.; Sperlich, B.
2021. Journal of Human Kinetics, 77 (1), 117–123. doi:10.2478/hukin-2021-0016
Detecting Regime Transitions of the Nocturnal and Polar Near-Surface Temperature Inversion
Kaiser, A.; Faranda, D.; Krumscheid, S.; Belušić, D.; Vercauteren, N.
2020. Journal of the Atmospheric Sciences, 77 (8), 2921–2940. doi:10.1175/JAS-D-19-0287.1
Quantifying uncertain system outputs via the multilevel Monte Carlo method. Part I: Central moment estimation
Krumscheid, S.; Nobile, F.; Pisaroni, M.
2020. Journal of Computational Physics, 414, Article no: 109466. doi:10.1016/
Central limit theorems for multilevel Monte Carlo methods
Hoel, H.; Krumscheid, S.
2019. Journal of Complexity, 54, Art.-Nr.: 101407. doi:10.1016/j.jco.2019.05.001
Quantifying uncertainties in contact mechanics of rough surfaces using the multilevel Monte Carlo method
Rey, V.; Krumscheid, S.; Nobile, F.
2019. International Journal of Engineering Science, 138, 50–64. doi:10.1016/j.ijengsci.2019.02.003
Perturbation-based inference for diffusion processes: Obtaining effective models from multiscale data
Krumscheid, S.
2018. Mathematical Models and Methods in Applied Sciences, 28 (08), 1565–1597. doi:10.1142/S0218202518500434
Multilevel Monte Carlo Approximation of Functions
Krumscheid, S.; Nobile, F.
2018. SIAM/ASA Journal on Uncertainty Quantification, 6 (3), 1256–1293. doi:10.1137/17M1135566
Data-driven coarse graining in action: Modeling and prediction of complex systems
Krumscheid, S.; Pradas, M.; Pavliotis, G. A.; Kalliadasis, S.
2015. Physical Review E, 92 (4), Article no: 042139. doi:10.1103/PhysRevE.92.042139
A new framework for extracting coarse-grained models from time series with multiscale structure
Kalliadasis, S.; Krumscheid, S.; Pavliotis, G. A.
2015. Journal of Computational Physics, 296, 314–328. doi:10.1016/
Novel series connection concept for thin film solar modules : Novel series connection concept for thin film solar modules
Haas, S.; Krumscheid, S.; Bauer, A.; Lambertz, A.; Rau, U.
2013. Progress in Photovoltaics: Research and Applications, 21 (5), 972–979. doi:10.1002/pip.2188
Semiparametric Drift and Diffusion Estimation for Multiscale Diffusions
Krumscheid, S.; Pavliotis, G. A.; Kalliadasis, S.
2013. Multiscale Modeling & Simulation, 11 (2), 442–473. doi:10.1137/110854485