Realistic event reconstruction problems require PDE-based models, and incorporating sensor data into them must be efficient for emergency response purposes. The investigator and her colleagues will efficiently solve this problem using techniques from numerical linear algebra that do not require multiple simulations of the forward model. These techniques can be viewed from the Bayesian perspective as finding first and second moments for point and uncertainty estimates, respectively. Least squares estimates will be weighted with inverse covariance matrices found by a new technique developed as part of this work that does not require normally distributed errors. These weights make least squares estimates more accurate, and the approach is computationally more efficient than full Bayesian methods. The investigator and her colleagues will quantify uncertainty in the PDE based forward model, while accounting for both data and parameter uncertainty. These PDE-based models will adopt a multi-GPU computing paradigm for overall acceleration of the algorithms for threat detection, and it is expected that near real-time inversions of the three-dimensional contaminant dispersion model will be produced.
This problem is motivated by the fact that in their June 2008 report (GAO-08-180) to Congressional requesters, the Government Accountability Office (GAO) has found that ?While the Department of Homeland Security (DHS) and other agencies have taken steps to improve homeland defense, local first responders still do not have tools to accurately identify right away what, when, where, and how much chemical, biological, radiological, or nuclear materials are released in U.S. urban areas, accidentally or by terrorists?. DHS has deployed the BioWatch program in several major cities to monitor the air for biothreat agents. The number of sensors in urban areas is limited, and a reliable account of the chemical-biological dispersion event and its impact on the population cannot be created purely from measurements. The PI and her colleagues will develop computationally fast mathematical algorithms to reconstruct the dispersion of a chemical or biological agent that is detected by a sensor network. This will allow first responders to identify and quantify the location and amount of chemical-biological agent release. Once the dispersion event is backtracked in time it can then be projected forward using high-fidelity atmospheric transport and dispersion models to predict the hazard zone for emergency response and hazard mitigation. The problem under consideration is equally significant in defense operations on the battlefield, where estimates on the location, strength and time of chemical-biological agent release can support tactical decisions such as areas to avoid, protective gear usage and medical response.
We have developed computational algorithms for mathematical models that simulate contaminant and dispersion of chemical or biological agents in complex urban terrains. The unfortunate Fukushima Nuclear Reactor disaster is a sobering example of why these tools are necessary for emergency responders to make better decisions in the face of a crisis. Evacuation orders for this event sent people in the direction of high dosage because it was not clear how many reactors were involved, nor the direction of contamination. To address these issues, we have developed inverse methods that reconstruct the source of contaminations using measurements with large uncertainties, emphasizing computational efficiency so that information can be given to emergency responders as quickly as possible. These algorithms utilize the expertise of PIs Mead and Senocak in inverse methods and computational fluid dynamics codes running on GPU computer clusters. For this project a Bayesian inference approach was implemented through a parallel workflow to locate multiple source releases and also time-dependent puff releases. The approach is novel in that the parallel workflow enables temporal reconstruction of puff releases within minutes. A composite ranking formula was proposed to reconstruct contaminant dispersions from multiple sources through a combined method that estimates the number of sources involved in a contaminant dispersion event along with their location and emission rates. The method was validated using extensive field data from Fusion Field Trial 2007 conducted at the U.S. Army’s Dugway Proving Grounds in Utah. The field study was supported by the Defense Threat Reduction Agency. Bayesian inference requires prior information so another aspect of this project was to develop computationally efficient methods for estimating unknown information, given large uncertainties in measurements. Chi-squared statistical tests were extended to general statistical tests to estimate model parameters and their uncertainty. Statistical tests for uncertainty estimation is effective for computationally large problems because it takes the guesswork out of choosing unknowns by solving an efficient optimization problem. This methodology allows estimation of unknown uncertainties in complex problems, such as those that are nonlinear, and those that use alternative optimization approaches such as Total Variation and Compressed Sensing. Additionally, high fidelity wind models have been developed for urban and complex terrain environments. A new procedure has been formulated using computational geometry algorithms to embed arbitrarily complex geometry within a Cartesian wind solver. The embedded approach enables the calculation of wind fields with 10-20 times faster than conventional approaches. The interdisciplinary project included mathematicians, engineers and computer scientists. Three graduate students and three undergraduate students in these disciplines were trained under the project and have obtained positions in local industry, or are currently in Ph.D. programs at University of Utah, Oregon State and University of Idaho. As part of the project, these students presented three posters and gave three oral presentations at international conferences such as the Society of Industrial and Applied Mathematics conference on Uncertainty, and the 93rd and 94th American Meteorological Society Annual meetings. Together with the students, the PIs published eight papers, gave twelve conference presentations, organized two minisymposium and hosted one regional conference. The PIs also developed and taught the following interdisciplinary courses, cross-listed in math, engineering, computer science and geoscience: Parallel Scientific Computing, Applied Mathematics for Scientists and Engineers, and Inverse Methods. The following institutional efforts can directly be attributed to the collaboration between PIs Mead and Senocak on this project: A pre-proposal for a new Ph.D. in computational science was submitted to the State Board of Education by faculty in math, statistics and engineering; A Graduate Certificate in Computational Geosciences will be implemented Fall 2015; An undergraduate minor in Computational Science and Engineering was approved in Fall 2014 and will be available to students starting in Fall 2015. Software infrastructure developed under this project includes a Bayesian inference engine for continuous and puff releases from single and multiple sources, massively parallel wind solver for GPU clusters, and Matlab GUIs for inverse methods. All of these research efforts related to chemical and biological defense puts a thrust behind the above mentioned technologies and serves as a successful demonstration to encourage future users to adopt these new technologies, and create an economy around the technologies. .
