Data Assimilation and Parameter Estimation for Parametric Partial Differential Equations
Abstract
Statement of Work:The PI will develop mathematical tools to address the grant challenge in Big Data, namely, the "curse ofdimensionality" in the numerical approximation of multivariable functions.Objective:While the PI s viewpoint and interests are broad and of generic value, this proposal is centered on numerical methods for solving partial differential equations (PDEs), whose solution depends on many variables or parameters. The main interest will be the ubiquitous family of parametric and stochastic PDEs. These equations arise in various applications such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even infinite and the development of numerical methods for these parametric problems is faced with the above mentioned curse of dimensionality.Approach:There are several directions and several application areas in which reduced modeling is not sufficiently wellunderstood. These will be some of the topics of our proposed research. The PI s main interest is in parameter estimation and the assimilation of data. These are the main components of what is commonly called uncertainty quantification. Our proposed research in this direction is explained in the last two sections. The PI will specifically the following areas:1) Parametric and Stochastic PDEs and the numerical computation of the solution map of such PDEs,2) investigate for which parametric PDEs the reduced modeling works, and 3) develop nonlinear methods for solution manifolds when the manifold is not smooth.Overall Merit and ONR Mission/Relevance:Overall Merits: The PI will be developing state-of-the art analytical tools to assist with computations in one of the most critical areas of numerical analysis today, namely, in the realm of Big Data.ONR Relevance: The PI s effort will impact solving deterministic and stocastic partial differential equations, areas of critical importance to a multitude of applications of interest to the Navy and the DoD.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141612706
Entities
People
- Ronald DeVore
Organizations
- Office of Naval Research
- Texas A&M University
- United States Navy