Structure-Preserving and Discovery in Scientific Machine Learning
Abstract
Computational modeling of physical and engineering systems has played a pivotal role in advancing science and technology. However, simulating complex physical systems, such as unsteady fluid flows, poses significant computational challenges. Traditional approaches struggle with non-linearities, uncertainties, and varying scales, resulting in costly and resource-intensive simulations. Machine Learning (ML) offers an exciting avenue to refine these models by leveraging observational data. However, the collection of accurate data for complex systems can be both intrusive and costly. In the burgeoning field of Scientific Machine Learning (SciML), the effective use of limited data is vital. This proposal targets the relationship between physical structures (e.g., symmetry, constraint, conservation laws) and data in SciML. The goal is to robustly preserve these inherent structures in SciML models, enhancing data efficiency while adhering to physical laws. The research also extends to uncovering hidden structures within high-dimensional data like video sequences, opening doors for new insights in physics and structure discovery. The projected implications of this research span both theoretical and practical domains. It could lead to improvements in areas such as turbulence modeling, system coarse-graining, uncertainty quantification, and physical structure identification from data, including high-dimensional video sequences.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502510079
Entities
People
- Wei Zhu
Organizations
- Air Force Office of Scientific Research
- United States Air Force