uncertainty quantification low-rank tensors hierarchical matrices uq uncertainty propagation kle pce subsurface flow density driven flow bayesian update parallel computing hlibpro matern covariance covariance uncertain geometry drinking water fresh water uncertainty low-rank tensor techniques bayesian update surrogate h-matrices modeling henry problem f-divergence multigrid statistics low-rank tensors in statistics mle ug4 matrix determinant tensor train schur complement data assimilation stochastic galerkin kld elliptic pdes with uncertainties parameter identification low-rank approximation mmse high-dimansional problem eigenvalue problem polynomial chaos expansion mlmc salty water porosity salinity multi level monte carlo entropy knn electro-magnetic scattering hpc prediction data analysis machine learning reservoir parallel algorithms pollution water aquifer multi-level monte carlo likelihood parameter inference kriging fourier transform uncertainty in geology data compression loglikelihood parameter estimation density random angle of attack random fields on sphere stochastic galerkin library sglib statistical moments of higher order nested dissection fast fourier transformation large data sets paralle h-matrices hlib low-rank tensor formats kullback-leibler log-likelihood level sets karhunen-loeve expansion stochastic pdes karhunen-loeve numerical aerodynamics low-rank svd sparse grids 3d kriging fft geostatistical optimal design low-rank tensor approximation surrogate fracture recharge permeability efficient numerical methods risk saltwater groundwater salt mass fraction density-driven flow exponent logarithm functions of tensors weakly supervised clustering hadamard product neural networks decision tree decision forest multi-fidelity multi-level deep neural network random forest decision trees parametric problems curse of dimensionality forecast scattering cross sections radar cross section electromagnetic scattering fast multipole method multilevel monte carlo method cem parallel elder's problem hlibcov determinant hierarchical methods covariance matrix optimization data sets cluster ensemble regression cluster analysis semi-supervised uncertain fingers generalised pce shaheen kaust parallel computations contamination ground water flow sparse matrices parameter identification in matern class spatial statistics covariance matrics parallel h-matrices low-rank tensor statistics low-rank tucker approximation spatio-temporal statistics tucker tensor format application of parallel hierarchical matrices low-rank techniques krylov and geometric/algebraic multigrids + ilu as newton for non-linearity implicit and explicit in time fv spatial discretization build-in mpi based parallelization loglikelihood surrogate. kalman lter hilbert tensor non-linear approximation of bayesian formula update of pce coefficients co2 reservoir maaden mine business velocity. pressure propagation of uncertainites from aoa and mach num low-rank compression of snapshots drag maximum loglikelihood moisture field cholesky decomposition boxplots exceedance probabilities random geometry probability density functions for lift and drag random lift and drag random perturbations in airfoil inverse coefficient problems gauss-markov theorem variance of the pressure and density management of uncertainties in numerical aerodynam mimimization of uncertainties multi-dimensional integrals uncertain mach number non-intrusive methods tau code gauss-hermite quadrature random shape geometry mach number the whole pressure unertain drag turbulence kinetic energy fields. lift and drag- coefficients velocity uncertain angle of attack uncertain angle of attack and mach number random mach number uncertain shape of the airfoil eigenvalue problems lanczos efficient postprocessing computing different statistics of high-dimensional geometrical sense of determinant definition of determinant properties of determinant history of determinants how to compute determinants fast numerical methods multi-dimensional problems bem spherical harmonics multipole method polynomial chaos update computing the mean postprocessing in tt format variance random fields karhunen loeve hierachical cholesky soil moisture environtmental statistics parallel hierarchical matrices maximum element in tensor multi-dimansional histogram levels sets in tensor tensor completion kaust maximum spdes lorenz problem with uncertain coefficients correlation length h-matrcies multilevel hierarchical domain decompostions domain decomposition jumping and strongly oscillatory coefficients application h-matrices for solving pdes with multi hierachical domain decomposition multiple right-hand side diffusion with jumping coefficients skin problem preconditioner circulant and toeplitz matrices fast techniques mean square error sylvester riccati matrix equation lyapunov application in spatial statistics partial inversion nested disection solution on interface hierarchical domain decomposition solution in a subdomain linear complexity postprocessing in low-rank tensor format h-matrix uq in aerodynamics inverse problems efficient methods tensot train approximation of bayesian update composition of two pce surrogate to bayesian update odes with uncertain coefficients frequency tensor calculus multi-parametric problem low-rank tensor methods higher-order moments spde functional approximation low-rank tensor pce-based surogate robust optimization rae2822 gradient-employing surrogate management of uncertainties toeplitz circulant
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