Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distance-based upscaling algorithm and approximations of point process theory to develop an estimation approach for effective conductivity in two-dimensions. Estimation of effective conductivity is derived directly from knowledge of the kernel size used to create the multiGaussian field, defined as the full-width at half maximum (FWHM), the truncation threshold and conductance values of the two modes. Therefore, instantiation of the multiGaussian field is not necessary for estimation of the effective conductance. The critical component of the effective medium approximation developed here is the mean distance between high conductivity inclusions. This mean distance is characterized as a function of the FWHM, the truncation threshold and the ratio of the two modal conductivities. Sensitivity of the resulting effective conductivity to this mean distance is examined for two levels of contrast in the two modal conductances and different FWHM sizes. Results demonstrate that the FWHM is a robust measure of mean travel distance in the background medium. The resulting effective conductivities are accurate when compared to numerical results and results obtained from effective media theory, distance-based upscaling and numerical simulation.
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.
Multi-scale binary permeability field estimation from static and dynamic data is completed using Markov Chain Monte Carlo (MCMC) sampling. The binary permeability field is defined as high permeability inclusions within a lower permeability matrix. Static data are obtained as measurements of permeability with support consistent to the coarse scale discretization. Dynamic data are advective travel times along streamlines calculated through a fine-scale field and averaged for each observation point at the coarse scale. Parameters estimated at the coarse scale (30 x 20 grid) are the spatially varying proportion of the high permeability phase and the inclusion length and aspect ratio of the high permeability inclusions. From the non-parametric, posterior distributions estimated for these parameters, a recently developed sub-grid algorithm is employed to create an ensemble of realizations representing the fine-scale (3000 x 2000), binary permeability field. Each fine-scale ensemble member is instantiated by convolution of an uncorrelated multiGaussian random field with a Gaussian kernel defined by the estimated inclusion length and aspect ratio. Since the multiGaussian random field is itself a realization of a stochastic process, the procedure for generating fine-scale binary permeability field realizations is also stochastic. Two different methods are hypothesized to perform posterior predictive tests. Different mechanisms for combining multi Gaussian random fields with kernels defined from the MCMC sampling are examined. Posterior predictive accuracy of the estimated parameters is assessed against a simulated ground truth for predictions at both the coarse scale (effective permeabilities) and at the fine scale (advective travel time distributions). The two techniques for conducting posterior predictive tests are compared by their ability to recover the static and dynamic data. The skill of the inference and the method for generating fine-scale binary permeability fields are evaluated through flow calculations on the resulting fields using fine-scale realizations and comparing them against results obtained with the ground truth fine-scale and coarse-scale permeability fields.
Techniques appear promising to construct and integrate automated detect-and-characterize technique for epidemics - Working off biosurveillance data, and provides information on the particular/ongoing outbreak. Potential use - in crisis management and planning, resource allocation - Parameter estimation capability ideal for providing the input parameters into an agent-based model, Index Cases, Time of Infection, infection rate. Non-communicable diseases are easier than communicable ones - Small anthrax can be characterized well with 7-10 days of data, post-detection; plague takes longer, Large attacks are very easy.
Results show that a time-series based classification may be possible. For the test cases considered, the correct model can be selected and the number of index case can be captured within {+-} {sigma} with 5-10 days of data. The low signal-to-noise ratio makes the classification difficult for small epidemics. The problem statement is: (1) Create Bayesian techniques to classify and characterize epidemics from a time-series of ICD-9 codes (will call this time-series a 'morbidity stream'); and (2) It is assumed the morbidity stream has already set off an alarm (through a Kalman filter anomaly detector) Starting with a set of putative diseases: Identify which disease or set of diseases 'fit the data best' and, Infer associated information about it, i.e. number of index cases, start time of the epidemic, spread rate, etc.
We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.
This report presents the results of our efforts to apply high-performance computing to entity-based simulations with a multi-use plugin for parallel computing. We use the term 'Entity-based simulation' to describe a class of simulation which includes both discrete event simulation and agent based simulation. What simulations of this class share, and what differs from more traditional models, is that the result sought is emergent from a large number of contributing entities. Logistic, economic and social simulations are members of this class where things or people are organized or self-organize to produce a solution. Entity-based problems never have an a priori ergodic principle that will greatly simplify calculations. Because the results of entity-based simulations can only be realized at scale, scalable computing is de rigueur for large problems. Having said that, the absence of a spatial organizing principal makes the decomposition of the problem onto processors problematic. In addition, practitioners in this domain commonly use the Java programming language which presents its own problems in a high-performance setting. The plugin we have developed, called the Parallel Particle Data Model, overcomes both of these obstacles and is now being used by two Sandia frameworks: the Decision Analysis Center, and the Seldon social simulation facility. While the ability to engage U.S.-sized problems is now available to the Decision Analysis Center, this plugin is central to the success of Seldon. Because Seldon relies on computationally intensive cognitive sub-models, this work is necessary to achieve the scale necessary for realistic results. With the recent upheavals in the financial markets, and the inscrutability of terrorist activity, this simulation domain will likely need a capability with ever greater fidelity. High-performance computing will play an important part in enabling that greater fidelity.