UQ - Junior Research Group Uncertainty Quantification

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 in complex computational models. Our research focuses on theoretical and methodological aspects, as well as on interdisciplinary projects where theoretical sound methodologies are tailored to applications.


  1. 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
  2. Adaptive Stratification (ADSS)
    Krumscheid, S.; Pettersson, P.; Yuan, F.
    2023, February 21. doi:10.5281/zenodo.7660514
  3. 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
  1. 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
  2. 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
  3. 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
  4. Plateau proposal distributions for adaptive component-wise multiple-try metropolis
    Lau, F. D.-H.; Krumscheid, S.
    2022. METRON, 80, Art.Nr. 106003. doi:10.1007/s40300-022-00235-y
  5. 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
  1. 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
  2. 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
  1. 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
  2. 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/j.jcp.2020.109466
  1. 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
  2. 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
  1. 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
  2. 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
  1. 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
  2. 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/j.jcp.2015.05.002
  1. 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
  2. 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