Abstract
One of the greatest challenges in computational science and engineering today is how to combine complex data with complex models to create better predictions. This challenge cuts across every application area within CS&E, from geosciences, materials, chemical systems, biological systems, and astrophysics to engineered systems in aerospace, transportation, structures, electronics, biomedicine, and beyond. Many of these systems are characterized by complex nonlinear behavior coupling multiple physical processes over a wide range of length and time scales. Mathematical and computational models of these systems often contain numerous uncertain parameters, making high-reliability predictive modeling a challenge. Rapidly expanding volumes of observational data—along with tremendous increases in HPC capability—present opportunities to reduce these uncertainties via solution of large-scale inverse problems.
This work was supported by AFOSR grants FA9550-12-1-0484 and FA9550-09-1-0608, DARPA/ARO contract W911NF-15-2-0121, DOE grants DE-SC0010518, DE-SC0009286, DE-11018096, DE-SC0006656, DE-SC0002710, and DE-FG02-08ER25860, and NSF grants ACI-1550593, CBET-1508713, CBET-1507009, CMMI-1028889, and ARC-0941678. Computations were performed on supercomputers at TACC, ORNL, and LLNL. We gratefully acknowledge this support.
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References
Alexanderian, A., Petra, N., Stadler, G., Ghattas, O.: A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized \(\ell _0\)-sparsification. SIAM J. Sci. Comput. 36(5), A2122–A2148 (2014)
Alexanderian, A., Petra, N., Stadler, G., Ghattas, O.: A fast and scalable method for A-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems. SIAM J. Sci. Comput. 38(1), A243–A272 (2016)
Alexanderian, A., Gloor, P., Ghattas, O.: On Bayesian A- and D-optimal experimental designs in infinite dimensions. Bayesian Anal. 11(3), 671–695 (2016)
Bui-Thanh, T., Burstedde, C., Ghattas, O., Martin, J., Stadler, G., Wilcox, L.C.: Extreme-scale UQ for Bayesian inverse problems governed by PDEs. In: Proceedings of IEEE/ACM SC12 (2012)
Bui-Thanh, T., Ghattas, O., Martin, J., Stadler, G.: A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with applications to global seismic inversion. SIAM J. Sci. Comput. 35(6), A2494–A2523 (2013)
Burstedde, C., Ghattas, O., Gurnis, M., Isaac, T., Stadler, G., Warburton, T., Wilcox, L.C.: Extreme-scale AMR. In: Proceedings of ACM/IEEE SC 2010 (2010)
Burstedde, C., Wilcox, L.C., Ghattas, O.: p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees. SIAM J. Sci. Comput. 33(3), 1103–1133 (2011)
Flath, H.P., Wilcox, L.C., Akcelik, V., Hill, J., van Bloemen, B., Ghattas, O.: Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations. SIAM J. Sci. Comput. 33(1), 407–432 (2011)
Hesse, M., Stadler, G.: Joint inversion in coupled quasistatic poroelasticity. J. Geophys. Res. Solid Earth 119, 1425–1445 (2014)
Isaac, T., Burstedde, C., Ghattas, O.: Low-cost parallel algorithms for 2:1 octree balance. In: International Parallel and Distributed Processing Symposium (IPDPS 2012), pp. 426–437. IEEE Computer Society (2012)
Isaac, T., Burstedde, C., Wilcox, L.C., Ghattas, O.: Recursive algorithms for distributed forests of octrees. SIAM J. Sci. Comput. 37(5), C497–C531 (2015)
Isaac, T., Petra, N., Stadler, G., Ghattas, O.: Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet. J. Comput. Phys. 296(1), 348–368 (2015)
Isaac, T., Stadler, G., Ghattas, O.: Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics. SIAM J. Sci. Comput. 37(6), B804–B833 (2015)
Martin, J., Wilcox, L.C., Burstedde, C., Ghattas, O.: A Stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM J. Sci. Comput. 34(3), A1460–A1487 (2012)
Petra, N., Martin, J., Stadler, G., Ghattas, O.: A computational framework for infinite-dimensional Bayesian inverse problems: Part II: Stochastic Newton MCMC with application to ice sheet flow inverse problems. SIAM J. Sci. Comput. 36(4), A1525–A1555 (2014)
Petra, N., Zhu, H., Stadler, G., Hughes, T.J.R., Ghattas, O.: An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model. J. Glaciol. 58(211), 889–903 (2012)
Ratnaswamy, V., Stadler, G., Gurnis, M.: Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples. Geophys. J. Int. 202(2), 768–786 (2015)
Rudi, J., Malossi, A.C.I., Isaac, T., Stadler, G., Gurnis, M., Staar, P.W.J., Ineichen, Y., Bekas, C., Curioni, A., Ghattas, O.: An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth’s mantle. In: Proceedings of IEEE/ACM SC 2015 (2015)
Rudi, J., Stadler, G., Ghattas, O.: Weighted BFBT Preconditioner for Stokes Flow Problems with Highly Heterogeneous Viscosity (submitted) (2016)
Worthen, J., Stadler, G., Petra, N., Gurnis, M., Ghattas, O.: Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow. Phys. Earth Planet. Inter. 234, 23–34 (2014)
Zhu, H., Li, S., Fomel, S., Stadler, G., Ghattas, O.: A Bayesian approach to estimate uncertainty for full waveform inversion using a priori information from depth migration. Geophysics 81(5), R307–R323 (2016)
Zhu, H., Petra, N., Stadler, G., Isaac, T., Hughes, T.J.R., Ghattas, O.: Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model. Cryosphere 10, 1477–1494 (2016)
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Ghattas, O., Isaac, T., Petra, N., Stadler, G. (2017). Scalable Algorithms for Bayesian Inference of Large-Scale Models from Large-Scale Data. In: Dutra, I., Camacho, R., Barbosa, J., Marques, O. (eds) High Performance Computing for Computational Science – VECPAR 2016. VECPAR 2016. Lecture Notes in Computer Science(), vol 10150. Springer, Cham. https://doi.org/10.1007/978-3-319-61982-8_1
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