| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | August 2, 2017 |
| Latest Amendment Date: | July 23, 2019 |
| Award Number: | 1720222 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Leland Jameson
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | August 1, 2017 |
| End Date: | July 31, 2022 (Estimated) |
| Total Intended Award Amount: | $124,995.00 |
| Total Awarded Amount to Date: | $124,995.00 |
| Funds Obligated to Date: |
FY 2018 = $41,615.00 FY 2019 = $42,269.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
615 MCCALLIE AVE CHATTANOOGA TN US 37403-2504 (423)425-4431 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Chattanooga TN US 37403-2504 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
01001819DB NSF RESEARCH & RELATED ACTIVIT 01001920DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Nonlinear filtering problem is a mathematical model for system estimation in signal processing problems arising from various scientific and engineering fields. Examples of the nonlinear filter's applications include tracking an aircraft using radar measurements, estimating a digital communications signal using noisy measurements, and estimating the volatility of financial instruments using stock market data. The key mission of the nonlinear filtering problem is to establish a "best estimate" for the true value of a dynamic system from an incomplete, potentially noisy set of observations on that system. The goal of this project is to develop novel numerical algorithms, which are accurate and efficient for the nonlinear filtering problem, by solving a backward stochastic differential equation (SDE) system. The proposed project will engage undergraduate students at an RUI institution in computational and applied mathematics research.
The cornerstone of this proposed approach, named the backward SDE filter, is the fact that the solution of the backward SDE system is the probability density function of the signal state as required in the nonlinear filtering problem. This project will start with the construction of backward SDE filter algorithms that are high order in time and adaptive in space, which blends the strengths of well known methods from this area of research. Then, the applicability of the backward SDE filter will be enlarged to tackle the grand challenge problems. Specifically, massively parallel algorithms will be designed for the backward SDE filter so that it could be implemented to solve large scale scientific computing problems on high performance computing facilities. The backward SDE filter is a new approach to solve the nonlinear filtering problem, and it addresses the main issues in the numerical solutions for nonlinear filtering problems, such like the low regularity problem and the high dimensionality problem. As a result, the backward SDE filter will provide scientists and engineers in various disciplines an accurate, efficient, and easy to use algorithm for data assimilation.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
We developed novel numerical algorithms for solving optimal filtering problems that efficiently estimate the probable state of a stochastic dynamical system given noisy partial observational data from detectors. The optimal filtering problem is a key topic in data assimilation and has applications in numerous scientific and engineering areas. The major contributions of this project were first to develop theoretical results and numerical methods for optimal filtering problems related topics, and furthermore, to blend the strengths of well-known algorithms from this area of research to create a faster, more accurate approach, and then apply the algorithms developed in this project to solve real world scientific problems.
The mathematical tool that we used to build our optimal filtering method is a system of backward stochastic differential equations (SDE), and we name our method the “Backward SDE Filter.” Through this project, we developed the mathematical foundation of Backward SDE Filter and explored its advantages and applicability.
The other activities in this research consisted of two components, computational and experimental. Our theoretical investigations were directed at predicting flow parameters such as velocity and deposition of nanoparticles under flow through uneven surfaces. A CFD model was created to model nanoscale flow and understand the key influencing parameters such as size and concentration of the nanodrugs. The experiments consisted of designing the novel flowpaths, synthesizing the nanodrug, characterizing the size and concentration of the nanodrug, and assessing its flow through the biomimetic flow channels. Undergraduate and graduate students were mentored in theoretical studies and nanotechnology experiments and computational modeling. They also participated in preparation of journal articles and professional development activities (e.g., conference presentations). Student mentoring and dissemination of results through journal publication and conference presentations were other key components of this project.
Last Modified: 06/27/2022
Modified by: Abdollah Arabshahi
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