A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference to develop a derivative-free stable method easy to implement in applications where the PDE (forward) model is only accessible as a black box. The method can be derived as an approximation of the regularizing Levenberg-Marquardt (LM) scheme [14] in which the derivative of the forward operator and its adjoint are replaced with empirical covariances from an ensemble of elements from the admissible space of solutions. The resulting ensemble method consists of an update formula that is applied to each ensemble member and that has a regularization parameter selected in a similar fashion to the one in the LM scheme. Moreover, an early termination of the scheme is proposed according to a discrepancy principle-type of criterion. The proposed method can be also viewed as a regularizing version of standard Kalman approaches which are often unstable unless ad-hoc fixes, such as covariance localization, are implemented. We provide a numerical investigation of the conditions under which the proposed method inherits the regularizing properties of the LM scheme of [14]. More concretely, we study the effect of ensemble size, number of measurements, selection of initial ensemble and tunable parameters on the performance of the method. The numerical investigation is carried out with synthetic experiments on two model inverse problems: (i) identification of conductivity on a Darcy flow model and (ii) electrical impedance tomography with the complete electrode model. We further demonstrate the potential application of the method in solving shape identification problems by means of a level-set approach for the parameterization of unknown geometries

Groupoid symmetry and constraints in general relativity

When the vacuum Einstein equations are cast in the form of hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold M\Sigma\ of riemannian metrics on a Cauchy hypersurface \Sigma. As in every lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection.Comment: 22 pages, major revisio

Filter Based Methods For Statistical Linear Inverse Problems

Ill-posed inverse problems are ubiquitous in applications. Understanding of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system. This opens up the possibility of using a range of other filtering methods, such as 3DVAR and Kalman based methods, to solve inverse problems, again by introducing an artificial dynamical system. The aim of this paper is to analyze such methods in the context of the linear inverse problem. Statistical linear inverse problems are studied in the sense that the observational noise is assumed to be derived via realization of a Gaussian random variable. We investigate the asymptotic behavior of filter based methods for these inverse problems. Rigorous convergence rates are established for 3DVAR and for the Kalman filters, including minimax rates in some instances. Blowup of 3DVAR and a variant of its basic form is also presented, and optimality of the Kalman filter is discussed. These analyses reveal a close connection between (iterated) regularization schemes in deterministic inverse problems and filter based methods in data assimilation. Numerical experiments are presented to illustrate the theory

Iterative regularization for ensemble data assimilation in reservoir models

We propose the application of iterative regularization for the development of ensemble methods for solving Bayesian inverse problems. In concrete, we construct (i) a variational iterative regularizing ensemble Levenberg-Marquardt method (IR-enLM) and (ii) a derivative-free iterative ensemble Kalman smoother (IR-ES). The aim of these methods is to provide a robust ensemble approximation of the Bayesian posterior. The proposed methods are based on fundamental ideas from iterative regularization methods that have been widely used for the solution of deterministic inverse problems [21]. In this work we are interested in the application of the proposed ensemble methods for the solution of Bayesian inverse problems that arise in reservoir modeling applications. The proposed ensemble methods use key aspects of the regularizing Levenberg-Marquardt scheme developed by Hanke [16] and that we recently applied for history matching in [18]. In the case where the forward operator is linear and the prior is Gaussian, we show that the proposed IR-enLM and IR-ES coincide with standard randomized maximum likelihood (RML) and the ensemble smoother (ES) respectively. For the general nonlinear case, we develop a numerical framework to assess the performance of the proposed ensemble methods at capturing the posterior. This framework consists of using a state-of-the art MCMC method for resolving the Bayesian posterior from synthetic experiments. The resolved posterior via MCMC then provides a gold standard against to which compare the proposed IR-enLM and IR-ES. We show that for the careful selection of regularization parameters, robust approximations of the posterior can be accomplished in terms of mean and variance. Our numerical experiments showcase the advantage of using iterative regularization for obtaining more robust and stable approximation of the posterior than standard unregularized methods

Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV

A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7 TeV is presented. The data were collected at the LHC, with the CMS detector, and correspond to an integrated luminosity of 4.6 inverse femtobarns. No significant excess is observed above the background expectation, and upper limits are set on the Higgs boson production cross section. The presence of the standard model Higgs boson with a mass in the 270-440 GeV range is excluded at 95% confidence level.Comment: Submitted to JHE

Combined search for the quarks of a sequential fourth generation

Results are presented from a search for a fourth generation of quarks produced singly or in pairs in a data set corresponding to an integrated luminosity of 5 inverse femtobarns recorded by the CMS experiment at the LHC in 2011. A novel strategy has been developed for a combined search for quarks of the up and down type in decay channels with at least one isolated muon or electron. Limits on the mass of the fourth-generation quarks and the relevant Cabibbo-Kobayashi-Maskawa matrix elements are derived in the context of a simple extension of the standard model with a sequential fourth generation of fermions. The existence of mass-degenerate fourth-generation quarks with masses below 685 GeV is excluded at 95% confidence level for minimal off-diagonal mixing between the third- and the fourth-generation quarks. With a mass difference of 25 GeV between the quark masses, the obtained limit on the masses of the fourth-generation quarks shifts by about +/- 20 GeV. These results significantly reduce the allowed parameter space for a fourth generation of fermions.Comment: Replaced with published version. Added journal reference and DO

A panchromatic study of BLAST counterparts: total star-formation rate, morphology, AGN fraction and stellar mass

We carry out a multi-wavelength study of individual galaxies detected by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) and identified at other wavelengths, using data spanning the radio to the ultraviolet (UV). We develop a Monte Carlo method to account for flux boosting, source blending, and correlations among bands, which we use to derive deboosted far-infrared (FIR) luminosities for our sample. We estimate total star-formation rates for BLAST counterparts with z < 0.9 by combining their FIR and UV luminosities. Star formation is heavily obscured at L_FIR > 10^11 L_sun, z > 0.5, but the contribution from unobscured starlight cannot be neglected at L_FIR < 10^11 L_sun, z < 0.25. We assess that about 20% of the galaxies in our sample show indication of a type-1 active galactic nucleus (AGN), but their submillimeter emission is mainly due to star formation in the host galaxy. We compute stellar masses for a subset of 92 BLAST counterparts; these are relatively massive objects, with a median mass of ~10^11 M_sun, which seem to link the 24um and SCUBA populations, in terms of both stellar mass and star-formation activity. The bulk of the BLAST counterparts at z<1 appear to be run-of-the-mill star-forming galaxies, typically spiral in shape, with intermediate stellar masses and practically constant specific star-formation rates. On the other hand, the high-z tail of the BLAST counterparts significantly overlaps with the SCUBA population, in terms of both star-formation rates and stellar masses, with observed trends of specific star-formation rate that support strong evolution and downsizing.Comment: Accepted for publication in the Astrophysical Journal. 44 pages, 11 figures. The SED template for the derivation of L_FIR has changed (added new figure) and the discussion on the stellar masses has been improved. The complete set of full-color postage-stamps can be found at http://blastexperiment.info/results_images/moncelsi

Review of current Severe Accident Management (SAM) approaches for Nuclear Power Plants in Europe

The Fukushima accidents highlighted that both the in-depth understanding of such sequences and the development or improvement of adequate Severe Accident Management (SAM) measures are essential in order to further increase the safety of the nuclear power plants operated in Europe. To support this effort, the CESAM (Code for European Severe Accident Management) R&D project, coordinated by GRS, started in April 2013 for 4 years in the 7th EC Framework Programme of research and development of the European Commission. It gathers 18 partners from 12 countries: IRSN, AREVA NP SAS and EDF (France), GRS, KIT, USTUTT and RUB (Germany), CIEMAT (Spain), ENEA (Italy), VUJE and IVS (Slovakia), LEI (Lithuania), NUBIKI (Hungary), INRNE (Bulgaria), JSI (Slovenia), VTT (Finland), PSI (Switzerland), BARC (India) plus the European Commission Joint Research Center (JRC). The CESAM project focuses on the improvement of the ASTEC (Accident Source Term Evaluation Code) computer code. ASTEC,, jointly developed by IRSN and GRS, is considered as the European reference code since it capitalizes knowledge from the European R&D on the domain. The project aims at its enhancement and extension for use in severe accident management (SAM) analysis of the nuclear power plants (NPP) of Generation II-III presently under operation or foreseen in near future in Europe, spent fuel pools included. In the frame of the CESAM project one of the tasks consisted in the preparation of a report providing an overview of the Severe Accident Management (SAM) approaches in European Nuclear Power Plants to serve as a basis for further ASTEC improvements. This report draws on the experience in several countries from introducing SAMGs and on substantial information that has become available within the EU “stress test”. To disseminate this information to a broader audience, the initial CESAM report has been revised to include only public available information. This work has been done with the agreement and in collaboration with all the CESAM project partners. The result of this work is presented here.JRC.F.5-Nuclear Reactor Safety Assessmen

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns