1887

Abstract

Summary

Knowledge of the sensitivity of a solution to small changes in the model parameters is exploited in many areas in computational physics and used to perform mesh adaptivity, or to correct errors based on discretisation and sub-grid-scale modelling errors, to perform the assimilation of data based on adjusting the most sensitive parameters to the model-observation misfit, and similarly to form optimised sub-grid-scale models. We present a goal-based approach for forming sensitivity (or importance) maps using ensembles. These maps are defined as regions in space and time of high relevance for a given goal, for example, the solution at an observation point within the domain. The presented approach relies solely on ensembles obtained from the forward model and thus can be used with complex models for which calculating an adjoint is not a practical option. This provides a simple approach for optimisation of sensor placement, goal based mesh adaptivity, assessment of goals and data assimilation. We investigate methods which reduce the number of ensembles used to construct the maps yet which retain reasonable fidelity of the maps.

The fidelity comes from an integrated method including a goal-based approach, in which the most up-to-date importance maps are fed back into the perturbations to focus the algorithm on the key variables and domain areas. Also within the method smoothing is applied to the perturbations to obtain a multi-scale, global picture of the sensitivities; the perturbations are orthogonalised in order to generate a well-posed system which can be inverted; and time windows are applied (for time dependent problems) where we work backwards in time to obtain greater accuracy of the sensitivity maps.

The approach is demonstrated on a multi-phase flow problem.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201802218
2018-09-03
2024-04-19
Loading full text...

Full text loading...

References

  1. Attia, A.
    [2016] Advanced Sampling Methods for Solving Large-Scale Inverse Problems. Ph.D. thesis, Department of Computer Science, Virginia Polytechnic Institute and State University.
    [Google Scholar]
  2. Blum, J., Le Dimet, F.X. and Navon, I.M.
    [2009] Data Assimilation for Geophysical Fluids. In: Temam, R.M. and Tribbia, J.J. (Eds.) Special Volume: Computational Methods for the Atmosphere and the Oceans, Handbook of Numerical Analysis, 14, Elsevier, 385–441.
    [Google Scholar]
  3. Brooks, R.H. and Corey, A.T.
    [1964] Hydraulic properties of porous media. In: Hydrology Papers.
    [Google Scholar]
  4. Cacuci, D.G.
    [2015] Second-order adjoint sensitivity analysis methodology (2nd-ASAM) for computing exactly and efficiently first- and second-order sensitivities in large-scale linear systems: I. Computational methodology.Journal of Computational Physics, 284, 687–699.
    [Google Scholar]
  5. Cacuci, D.G., Ionescu-Bujor, M. and Navon, I.M.
    [2005] Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems.CRC Press.
    [Google Scholar]
  6. Che, Z., Fang, F., Percival, J., Pain, C.C., Matar, O. and Navon, I.M.
    [2014] An ensemble method for sensor optimisation applied to falling liquid films.International Journal of Multiphase Flow, 67, 153–161.
    [Google Scholar]
  7. Gomes, J.L.M.A., Pavlidis, D., Salinas, P., Xie, Z., Percival, J.R., Melnikova, Y., Pain, C.C. and Jackson, M.D.
    [2017] A Force-Balanced Control Volume Finite Element Method for Multiphase Porous Media Flow Modelling.International Journal for Numerical Methods in Fluids, 83, 431–445.
    [Google Scholar]
  8. Heaney, C.E., Salinas, P., Fang, F., Pain, C.C. and Navon, I.M.
    [2018] Goal-based sensitivity maps using time windows and ensemble perturbations.ArXiv e-prints.
    [Google Scholar]
  9. Hossen, M.J., Navon, I.M. and Daescu, D.N.
    [2012] Effect of random perturbations on adaptive observation techniques.International Journal for Numerical Methods in Fluids, 69(1), 110–123.
    [Google Scholar]
  10. Ionescu-Bujor, M. and Cacuci, D.G.
    [2004] A Comparative Review of Sensitivity and Uncertainty Analysis of Large-Scale Systems-I: Deterministic Methods.Nuclear Science and Engineering, 147(3), 189–203.
    [Google Scholar]
  11. Jackson, M.D., Percival, J.R., Mostaghimi, P., Tollit, B.S., Pavlidis, D., Pain, C.C., Gomes, J.L.M.A., El-Sheikh, A.H., Salinas, P., Muggeridge, A.H. and Blunt, M.J.
    [2015] Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method.SPE Reservoir Evaluation & Engineering, 18.
    [Google Scholar]
  12. Keller, J.D., Hense, A., Kornblueh, L. and Rhodin, A.
    [2010] On the Orthogonalization of Bred Vectors.Weather and Forecasting, 25, 1219–1234.
    [Google Scholar]
  13. Leroux, R., Chatellier, L. and David, L.
    [2018] Time-resolved flow reconstruction with indirect measurements using regression models and Kalman filtered POD ROM.Experiments in Fluids, 59, 1–27.
    [Google Scholar]
  14. Liu, J. and Kalnay, E.
    [2008] Estimating observation impact without adjoint model in an ensemble Kalman filter.Quarterly Journal of the Royal Meteorological Society, 134(634), 1327–1335.
    [Google Scholar]
  15. Maday, Y. and Taddei, T.
    [2017] Adaptive PBDW approach to state estimation: noisy observations; user-defined update spaces.ArXiv e-prints.
    [Google Scholar]
  16. Merton, S.R., Buchan, A.G., Pain, C.C. and Smedley-Stevenson, R.P.
    [2013] An adjoint-based method for improving computational estimates of a functional obtained from the solution of the Boltzmann Transport Equation.Annals of Nuclear Energy, 54, 1–10.
    [Google Scholar]
  17. Merton, S.R., Smedley-Stevenson, R.P., Pain, C.C. and Buchan, A.G.
    [2014] Adjoint eigenvalue correction for elliptic and hyperbolic neutron transport problems.Progress in Nuclear Energy, 76, 1–16.
    [Google Scholar]
  18. Nerger, L., Schulte, S. and Bunse-Gerstner, A.
    [2014] On the influence of model nonlinearity and localization on ensemble Kalman smoothing.Quarterly Journal of the Royal Meteorological Society, 140, 2249–2259.
    [Google Scholar]
  19. Power, P.W., Piggott, M.D., Fang, F., Gorman, G.J., Pain, C.C., Marshall, D.P., Goddard, A.J.H. and Navon, I.M.
    [2006] Adjoint goal-based error norms for adaptive mesh ocean modelling.Ocean Modelling, 15(1), 3–38.
    [Google Scholar]
  20. Salinas, P., Pavlidis, D., Xie, Z., Jacquemyn, C., Melnikova, Y., Pain, C.C. and Jackson, M.D.
    [2017] Improving the Robustness of the Control Volume Finite Element Method with Application to Multiphase Porous Media Flow.International Journal for Numerical Methods in Fluids, 85, 235–246.
    [Google Scholar]
  21. Shah, A.J.
    [2017] Methods for Data Assimilation for the Purpose of Forecasting in the Gulf of Cambay (Khambhat).IJSRSET, 3, 224–228.
    [Google Scholar]
  22. Shapiro, R.
    [1970] Smoothing, Filtering and Boundary Effects.Review of Geophysics and Space Physics, 8, 359–387.
    [Google Scholar]
  23. Wang, Z., Navon, I.M., Le Dimet, F.X. and Zou, X.
    [1992] The second order adjoint analysis: Theory and applications.Meteorology and Atmospheric Physics, 50(1), 3–20.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201802218
Loading
/content/papers/10.3997/2214-4609.201802218
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error