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Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Inverse Problems

Hartland, Tucker; Stadler, Georg; Perego, Mauro P.; Liegeois, Kim A.; Petra, Noemi

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. We demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss-Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

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TYPE Journal Article YEAR 2023
DOIOSTIScopus

Defect graph neural networks for materials discovery in high-temperature clean-energy applications

Nature Computational Science

Witman, Matthew; Goyal, Anuj; Ogitsu, Tadashi; McDaniel, Anthony H.; Lany, Stephan

We present a graph neural network approach that fully automates the prediction of defect formation enthalpies for any crystallographic site from the ideal crystal structure, without the need to create defected atomic structure models as input. Here we used density functional theory reference data for vacancy defects in oxides, to train a defect graph neural network (dGNN) model that replaces the density functional theory supercell relaxations otherwise required for each symmetrically unique crystal site. Interfaced with thermodynamic calculations of reduction entropies and associated free energies, the dGNN model is applied to the screening of oxides in the Materials Project database, connecting the zero-kelvin defect enthalpies to high-temperature process conditions relevant for solar thermochemical hydrogen production and other energy applications. The dGNN approach is applicable to arbitrary structures with an accuracy limited principally by the amount and diversity of the training data, and it is generalizable to other defect types and advanced graph convolution architectures. It will help to tackle future materials discovery problems in clean energy and beyond.

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TYPE Journal Article YEAR 2023
DOIOSTIScopus

The Effects of Gamma Ray Integrated Dose on a Commercial 65-nm SRAM Device

IEEE Transactions on Nuclear Science

Stirk, Wesley; Black, Dolores A.; Black, Jeffrey B.; Breeding, Matthew L.; Laros, James H.; Wirthlin, Mike; Goeders, Jeffrey

This work shows that the static random access memory (SRAM) error rate for a commercial 65-nm device in a dose rate environment can be highly dependent upon the integrated dose (dose rate × pulse duration). While the typical metric for such testing is dose rate upset (DRU) level in rad(Si)/s, a series of dose rate experiments at Little Mountain Test Facility (LMTF) shows dependence on the integrated dose. The error rate is also found to be dependent on the core voltage, and the preradiation value of the bits. We believe that these effects are explained by a well charge depletion caused by gamma ray photocurrent.

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TYPE Journal Article YEAR 2023
DOIOSTIScopus
Results 751–775 of 96,771
Results 751–775 of 96,771