Nonlinear Data-driven and Structure-preserving Hamiltonian Model Reduction
Abstract
B. Kramer, University of California San Diego (Principal Investigator)Z. Wang, University of South Carolina (co-Investigator)H. Shar,ma, University of California San Diego (Senior Personnel)Computational modeling, simulation and control of physical systems characte,rized by Hamiltonian mechanics are essential for many naval applications, such as ocean flow modeling, plasma physics, and continuum, mechanics models that follow a principle of least action. Due to high model complexity, the associated transient models are high-di,mensional and nonlinear, and pro- duce massive data through numerical simulation. Efficient reduced-order models (ROMs) for the ev,olution of these high-dimensional systems are needed for long-term prediction and model- predictive control. Model reduction has bee,n successful in many compute-intensive applications. However, when these techniques are applied to Hamiltonian systems, the surrogat,e models lose their underlying physical meaning, and violate mechanical andmathematical structures. From a mathematical perspective,, Hamiltonian systems have additional physical and geometric structures in the form of symmetries, symplecticity, first integrals, an,d energy preservation. Those properties need to be preserved in time and space discretization, and particularly in data-driven reduc,ed-order modeling which is the focus of the proposed work.This project will develop a mathematically rigorous nonlinear structure-pr,eserving data-driven reduced-order modeling (SP-DDROM) strategy for Hamiltonian systems. This will produce computationally efficient, structure-preserving ROMs through learning from high-dimensional data. First, we will develop a new structure-preserving operator l,earning framework for Hamiltonian systems that also applies to noncanonical structures. Second, we will derive certifications for ac,- curacy, mechanical and mathematical properties of the obtained ROMs. Third, we will develop a transfer learning method for data-dr,iven ROMs that addresses the need to update ROM basis functions for convective and highly transient systems. Fourth, we will develop, and test these ROMs on a variety of applications with naval relevance. For example, ocean simulation models can be formulated as a,Hamiltonian system, and since they often have to be simulated for decades to centuries of real time, ROMs play a crucial role in eff,iciently making long-term predictions.Approved for public release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 05, 2022
- Source ID
- N000142212624
Entities
People
- Boris Krämer
Organizations
- Office of Naval Research
- United States Navy
- University of California, San Diego