University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Uncertainty quantification and optimal decisions.
Proceedings. Mathematical, physical, and engineering sciences issue 2200 volume 473 page 20170115-20170115 (26 April 2017)
Wave propagation along periodic layers
SIAM Journal on Applied Mathematics issue 4 volume 78 page 2154–2175- (14 August 2018)
Numerical rivers: A synthetic streamflow generator for water resources vulnerability assessments
Water Resources Research issue 7 volume 51 page 5382-5405 (1 July 2015)
Direct calculation of distortion energies in colloidal liquid crystals from single-particle data
Molecular Physics issue 17-18 volume 113 page 2693-2698 (1 June 2015)
One-dimensional wave dispersion in layered media
SIAM Journal on Applied Mathematics issue 5 volume 75 page 2128–2146- (1 January 2015)
Defining the estimated core genome of bacterial populations using a Bayesian decision model
PLoS Computational Biology issue 8 volume 10 page e1003788- (21 August 2014)
My current main interests are: uncertainty quantification for inverse problems from a Bayesian viewpoint, data assimilation, construction of spatial priors using various types of spde, decision and control problems in the presence of uncertainty and the optimisation of expensive functions. At the moment my focus is on the inverse problem for the wave equation and for chaotic dynamical systems such as the Lorenz 96 model, generalised to include unknown and unobserved parameters.
In the recent past I was active in the adaptive management of natural resources, flow through porous media, grid generation and numerical simulation of elliptic pde with tensor coefficients. Until March 2016 I was funded by the Oxford Martin School as co-director of the programme on Modelling and Predicting Climate and as a PI on the Oxford Martin Programme on Resource Stewardship. For further information see http://www.oxfordmartin.ox.ac.uk/.
Prizes, awards, and scholarships:
Royal Society Industry Fellow 2002-2006.
Major / recent publications:
H. Ockendon, J.R. Ockendon, C.L. Farmer and D.J. Allwright. 2015. "One-dimensional wave dispersion in layered media". SIAM Journal on Applied Mathematics (SIAP), Vol. 75, No. 5, pp 2128-2146, doi:10.1137/15M101138X.
E. Borgomeo, C.L. Farmer and J.W. Hall. 2015. "Numerical rivers: A synthetic streamflow generator for water resources vulnerability assessments", Water Resources Research, 51, doi:10.1002/2014WR016827.
K.E. Klop, C.L. Farmer, R.P.A. Dullens and D.G.A.G. Aarts. 2015. "Direct calculation of distortion energies in colloidal liquid crystals from single-particle data". Molecular Physics, DOI: 10.1080/00268976.2015.1051151.
C. L. Farmer. "An ensemble variational filter for sequential inverse problems". Proceedings of 'Inverse Problems -- from Theory to Applications (IPTA 2014)', pp 164-168, Institute of Physics, 2014. http://ipta2014.iopconfs.org/IPTAProceedings
W. Lee and C. L. Farmer. 2014. "Data Assimilation by Conditioning of Driving Noise on Future Observations". IEEE Transactions on Signal Processing, 62 (15), pp 3887-3896.
J. M. Fowkes, N. I. M. Gould and C. L. Farmer. 2012. "A Branch and Bound Algorithm for the Global Optimization of Hessian Lipschitz Continuous Functions", Journal of Global Optimization, pp. 1-25. ISSN 0925-5001. http://dx.doi.org/10.1007/s10898-012-9937-9
Potsepaev, R. V. and Farmer, C. L. (2010), “Application of Stochastic Partial Differential Equations to Reservoir Property Modelling”, Paper B003, in the Proceedings of the 12th European Conference on the Mathematics of Oil Recovery, Oxford, organised by the European Association of Geoscientsts and Engineers.
Farmer, C.L., Fowkes, J.M. and Gould, N.I.M. (2010), "Optimal Well Placement", Paper B033, in the Proceedings of the 12th European Conference on the Mathematics of Oil Recovery, Oxford, organised by the European Association of Geoscientsts and Engineers.
Busby, D, Farmer C.L. and Iske, A. Hierarchical nonlinear approximation for experimental design and statistical data fitting. SIAM Journal on Scientific Computing. 29 (1), January 2007, pp 49-69.
Farmer, C.L. Bayesian Field Theory Applied to Scattered Data Interpolation and Inverse Problems. Algorithms for Approximation. Ed. A. Iske and J. Levesley, Springer-Verlag, Heidelberg, 2007, pp. 147-166.
Busby, D, Farmer C.L. and Iske, A (2006). Uncertainty Evaluation in Reservoir Forecasting by Bayes Linear Methodology. Algorithms for Approximation. Ed. A. Iske and J. Levesley, Springer-Verlag, Heidelberg, 2007, pp. 187-196.
Farmer, C.L. and Howison, S.D. (2005). The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations. Applied Mathematics Letters, 19 (4), April 2006, 356-361.
Geological modelling and reservoir simulation. Article in 'Mathematical Methods and Modeling in Hydrocarbon Exploration and Production', Editors: Armin Iske and Trygve Randen, Springer-Verlag, Heidelberg. ISBN: 3-540-22536-6, 2005, pp 119-212.
Upscaling: A Review. Numerical Methods in Fluids, 40(1-2), 63-78, September 2002.
Farmer C.L. , A.J. Fitzpatrick and R. Potsepaev. Multipoint Flux Approximation via Upscaling. Paper A19 in the Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, Bergen, September 2008.
Local Geostatistics. Paper A005 in the Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Cannes, September 2004.