Optimal Physics-Informed Bases for High-Dimensional Evolutionary Systems

Abstract

The overarching objective of this proposal is to develop a mathematical framework to extract and exploit the multi-dimensional correlations on-the-fly from the PDE. The correlated structures are expressed as a set of orthonormal bases, for which closed-from evolution equations will be derived. This amounts to a real-time model-driven tensor decomposition of the PDE and has the potential to mitigate the curse of dimensionality. We will develop this framework for high-dimensional problems encountered in fluid dynamics and combustion.

Document Details

Document Type
DoD Grant Award
Publication Date
Mar 07, 2023
Source ID
FA95502110247

Entities

People

  • Hessameddin Babaee

Organizations

  • Air Force Office of Scientific Research
  • United States Air Force
  • University of Pittsburgh

Tags

Fields of Study

  • Computer science

Readers

  • Distributed Systems and Data Platform Development
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Neural Network Machine Learning.