Density Functional Theory (DFT) has over the last few years emerged as an indispensable tool for understanding the behavior of matter under extreme conditions. DFT based molecular dynamics simulations (MD) have for example confirmed experimental findings for shocked deuterium,1 enabled the first experimental evidence for a triple point in carbon above 850 GPa,2 and amended experimental data for constructing a global equation of state (EOS) for water, carrying implications for planetary physics.3 The ability to perform high-fidelity calculations is even more important for cases where experiments are impossible to perform, dangerous, and/or prohibitively expensive. For solid explosives, and other molecular crystals, similar success has been severely hampered by an inability of describing the materials at equilibrium. The binding mechanism of molecular crystals (van der Waals' forces) is not well described within traditional DFT.4 Among widely used exchange-correlation functionals, neither LDA nor PBE balances the strong intra-molecular chemical bonding and the weak inter-molecular attraction, resulting in incorrect equilibrium density, negatively affecting the construction of EOS for undetonated high explosives. We are exploring a way of bypassing this problem by using the new Armiento-Mattsson 2005 (AM05) exchange-correlation functional.5, 6 The AM05 functional is highly accurate for a wide range of solids,4, 7 in particular in compression.8 In addition, AM05 does not include any van der Waals' attraction,4 which can be advantageous compared to other functionals: Correcting for a fictitious van der Waals' like attraction with unknown origin can be harder than correcting for a complete absence of all types of van der Waals' attraction. We will show examples from other materials systems where van der Waals' attraction plays a key role, where this scheme has worked well,9 and discuss preliminary results for molecular crystals and explosives.
Climate models have a large number of inputs and outputs. In addition, diverse parameters sets can match observations similarly well. These factors make calibrating the models difficult. But as the Earth enters a new climate regime, parameters sets may cease to match observations. History matching is necessary but not sufficient for good predictions. We seek a 'Pareto optimal' ensemble of calibrated parameter sets for the CCSM climate model, in which no individual criteria can be improved without worsening another. One Multi Objective Genetic Algorithm (MOGA) optimization typically requires thousands of simulations but produces an ensemble of Pareto optimal solutions. Our simulation budget of 500-1000 runs allows us to perform the MOGA optimization once, but with far fewer evaluations than normal. We devised an analytic test problem to aid in the selection MOGA settings. The test problem's Pareto set is the surface of a 6 dimensional hypersphere with radius 1 centered at the origin, or rather the portion of it in the [0,1] octant. We also explore starting MOGA from a space-filling Latin Hypercube sample design, specifically Binning Optimal Symmetric Latin Hypercube Sampling (BOSLHS), instead of Monte Carlo (MC). We compare the Pareto sets based on: their number of points, N, larger is better; their RMS distance, d, to the ensemble's center, 0.5553 is optimal; their average radius, {mu}(r), 1 is optimal; their radius standard deviation, {sigma}(r), 0 is optimal. The estimated distributions for these metrics when starting from MC and BOSLHS are shown in Figs. 1 and 2.
Arctic sea ice is an important component of the global climate system and, due to feedback effects, the Arctic ice cover is changing rapidly. Predictive mathematical models are of paramount importance for accurate estimates of the future ice trajectory. However, the sea ice components of Global Climate Models (GCMs) vary significantly in their prediction of the future state of Arctic sea ice and have generally underestimated the rate of decline in minimum sea ice extent seen over the past thirty years. One of the contributing factors to this variability is the sensitivity of the sea ice state to internal model parameters. A new sea ice model that holds some promise for improving sea ice predictions incorporates an anisotropic elastic-decohesive rheology and dynamics solved using the material-point method (MPM), which combines Lagrangian particles for advection with a background grid for gradient computations. We evaluate the variability of this MPM sea ice code and compare it with the Los Alamos National Laboratory CICE code for a single year simulation of the Arctic basin using consistent ocean and atmospheric forcing. Sensitivities of ice volume, ice area, ice extent, root mean square (RMS) ice speed, central Arctic ice thickness,and central Arctic ice speed with respect to ten different dynamic and thermodynamic parameters are evaluated both individually and in combination using the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA). We find similar responses for the two codes and some interesting seasonal variability in the strength of the parameters on the solution.
Because the potential effects of climate change are more severe than had previously been thought, increasing focus on uncertainty quantification is required for risk assessment needed by policy makers. Current scientific efforts focus almost exclusively on establishing best estimates of future climate change. However, the greatest consequences occur in the extreme tail of the probability density functions for climate sensitivity (the 'high-sensitivity tail'). To this end, we are exploring the impacts of newly postulated, highly uncertain, but high-consequence physical mechanisms to better establish the climate change risk. We define consequence in terms of dramatic change in physical conditions and in the resulting socioeconomic impact (hence, risk) on populations. Although we are developing generally applicable risk assessment methods, we have focused our initial efforts on uncertainty and risk analyses for the Arctic region. Instead of focusing on best estimates, requiring many years of model parameterization development and evaluation, we are focusing on robust emergent phenomena (those that are not necessarily intuitive and are insensitive to assumptions, subgrid-parameterizations, and tunings). For many physical systems, under-resolved models fail to generate such phenomena, which only develop when model resolution is sufficiently high. Our ultimate goal is to discover the patterns of emergent climate precursors (those that cannot be predicted with lower-resolution models) that can be used as a 'sensitivity fingerprint' and make recommendations for a climate early warning system that would use satellites and sensor arrays to look for the various predicted high-sensitivity signatures. Our initial simulations are focused on the Arctic region, where underpredicted phenomena such as rapid loss of sea ice are already emerging, and because of major geopolitical implications associated with increasing Arctic accessibility to natural resources, shipping routes, and strategic locations. We anticipate that regional climate will be strongly influenced by feedbacks associated with a seasonally ice-free Arctic, but with unknown emergent phenomena.
We present results from a recently developed multiscale inversion technique for binary media, with emphasis on the effect of subgrid model errors on the inversion. Binary media are a useful fine-scale representation of heterogeneous porous media. Averaged properties of the binary field representations can be used to characterize flow through the porous medium at the macroscale. Both direct measurements of the averaged properties and upscaling are complicated and may not provide accurate results. However, it may be possible to infer upscaled properties of the binary medium from indirect measurements at the coarse scale. Multiscale inversion, performed with a subgrid model to connect disparate scales together, can also yield information on the fine-scale properties. We model the binary medium using truncated Gaussian fields, and develop a subgrid model for the upscaled permeability based on excursion sets of those fields. The subgrid model requires an estimate of the proportion of inclusions at the block scale as well as some geometrical parameters of the inclusions as inputs, and predicts the effective permeability. The inclusion proportion is assumed to be spatially varying, modeled using Gaussian processes and represented using a truncated Karhunen-Louve (KL) expansion. This expansion is used, along with the subgrid model, to pose as a Bayesian inverse problem for the KL weights and the geometrical parameters of the inclusions. The model error is represented in two different ways: (1) as a homoscedastic error and (2) as a heteroscedastic error, dependent on inclusion proportionality and geometry. The error models impact the form of the likelihood function in the expression for the posterior density of the objects of inference. The problem is solved using an adaptive Markov Chain Monte Carlo method, and joint posterior distributions are developed for the KL weights and inclusion geometry. Effective permeabilities and tracer breakthrough times at a few 'sensor' locations (obtained by simulating a pump test) form the observables used in the inversion. The inferred quantities can be used to generate an ensemble of permeability fields, both upscaled and fine-scale, which are consistent with the observations. We compare the inferences developed using the two error models, in terms of the KL weights and fine-scale realizations that could be supported by the coarse-scale inferences. Permeability differences are observed mainly in regions where the inclusions proportion is near the percolation threshold, and the subgrid model incurs its largest approximation. These differences also reflected in the tracer breakthrough times and the geometry of flow streamlines, as obtained from a permeameter simulation. The uncertainty due to subgrid model error is also compared to the uncertainty in the inversion due to incomplete data.
Exascale systems will have hundred thousands of compute nodes and millions of components which increases the likelihood of faults. Today, applications use checkpoint/restart to recover from these faults. Even under ideal conditions, applications running on more than 50,000 nodes will spend more than half of their total running time saving checkpoints, restarting, and redoing work that was lost. Redundant computing is a method that allows an application to continue working even when failures occur. Instead of each failure causing an application interrupt, multiple failures can be absorbed by the application until redundancy is exhausted. In this paper we present a method to analyze the benefits of redundant computing, present simulation results of the cost, and compare it to other proposed methods for fault resilience.
We consider the problem of placing a limited number of sensors in a municipal water distribution network to minimize the impact over a given suite of contamination incidents. In its simplest form, the sensor placement problem is a p-median problem that has structure extremely amenable to exact and heuristic solution methods. We describe the solution of real-world instances using integer programming or local search or a Lagrangian method. The Lagrangian method is necessary for solution of large problems on small PCs. We summarize a number of other heuristic methods for effectively addressing issues such as sensor failures, tuning sensors based on local water quality variability, and problem size/approximation quality tradeoffs. These algorithms are incorporated into the TEVA-SPOT toolkit, a software suite that the US Environmental Protection Agency has used and is using to design contamination warning systems for US municipal water systems.