School of Mathematical Sciences

Uncertainty Quantification

Uncertainty Quantification (UQ) is concerned with characterising and modelling uncertainties inherent in a scientific problem, and then calculating the impact of those uncertainties on key aspects of interest.

All scientific theories and technological processes are subject to uncertainties, either through imperfect models (conceptual model uncertainty) or unknown parameters in a model (parametric uncertainty).


UQ plays an increasing role in environmental sciences, in particular in evaluating climate change and its impacts, and assessing the safety of geological disposal of radioactive wastes and carbon capture/storage schemes. UQ is an important issue in engineering science, and manufacturing in particular. The life sciences and medicine will also make increasing use of techniques from UQ as fundamental models improve.


Example projects:

  • ABC methods for calibrating stochastic simulators
  • Carbon Capture and Storage
  • Diagnosing errors for dynamical systems
  • Engineered barrier for radioactive waste repository
  • Gaussian process emulators for groundwater flow problems
  • GPEs applied to spreading of CO2 plumes in aquifers
  • Multilevel Monte Carlo for groundwater flow and radionuclide transport
  • Numerical methods for SDEs applied to UQ
  • Paleo climate reconstruction
  • Parameter estimation for ODEs and SDEs
  • UQ applied to groundwater flow
  • UQ for performance of air riding seals and bearings
  • UQ in manufacturing composites




Staff have coordinated or contributed to a number of UQ events, including:

Recent Publications:

BAILEY, N.Y., CLIFFE, K.A., HIBBERD, S. and POWER, H., 2013. On the dynamics of a high-speed coned fluid-lubricated bearing IMA Journal of Applied Mathematics. (In Press.)

IGLESIAS, MARCO A., LAW, KODY J.H. and STUART, ANDREW M., 2013. Evaluation of Gaussian approximations for data assimilation in reservoir models Computational Geosciences. 17(5), 851-885

IGLESIAS, M.A., LAW, K.J.H. and STUART, A.M., 2013. Ensemble Kalman methods for inverse problems Inverse Problems. 29(4), 045001

CHERNYAVSKY, IL, DRYDEN, IL and JENSEN, OE, 2012.  Characterizing the multiscale structure of fluctuations of transported quantities in a disordered medium  IMA Journal of Applied Mathematics. 77(5), 697-725

HAWKINS-DAARUD, A., PRUDHOMME, S., VAN DER ZEE, K.G. and TINSLEY ODEN, J., 2012.  Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth . Journal of Mathematical Biology (online).

PRESTON, S.P. and WOOD, A.T.A., 2012.  Approximation of transition densities of stochastic differential equations by saddlepoint methods applied to small-time Ito-Taylor sample-path expansions  Statistics and Computing. 22(1), 205-217

CLIFFE, K.A., GILES, M.B., SCHEICHL, R. and TECKENTRUP, A.L., 2011. Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients   Computing and Visualization in Science. 14(1), 3-15.

WILKINSON, R. D., VRETTAS, M., CORNFORD, D. and OAKLEY, J. E., 2011.  Quantifying simulator discrepancy in discrete-time dynamical simulators Journal of Agricultural, Biological, and Environmental Statistics. 16(4), 554-570 (In Press.)

HOLDEN, P.B., EDWARDS, N.R., OLIVER, K.I.C., LENTON, T.M. and WILKINSON, R.D., 2010.  A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1  Climate Dynamics. 35(5), 785-806

MITCHELL, M.J., JENSEN, O.E., CLIFFE, K.A. and MAROTO-VALER, M.M.,  2010.  A model of carbon dioxide dissolution and mineral carbonation kinetics  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.  466, 1265-1290.

WILKINSON, R.D., 2010. Bayesian calibration of expensive computer models. In: L. BIEGLER, G. BIROS, O. GHATTAS, M. HEINKENSCHLOSS, D. KEYES, B. MALLICK, L. TENORIO, B. VAN BLOEMEN WAANDERS and K. WILLCOX, eds., Large scale inverse problems and quantification of Uncertainty John Wiley and Sons. 195-216


Stone, Nicola (2011) Gaussian process emulators for uncertainty analysis in groundwater flow. PhD thesis, University of Nottingham.


Thinking of joining us?

We are keen to create an environment which supports all staff members by providing:




Professor Ian Dryden

School of Mathematical Sciences

University of Nottingham

University Park



t: +44 (0)115 84 67412 

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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