Information Geometric Regularization for Simulation and Optimization of Supersonic Flow
Abstract
The compressible Euler equations describe the dynamics of an inviscid fluid or gas. Even starting with smooth initial conditions, they develop jump discontinuities in finite time. These shock waves are especially abundant in supersonic flows arising in aerospatial applications. Most existing approaches for equations with shocks adaptively add numerical viscosity. The amount of added viscosity has to be chosen carefully to avoid excessive smoothing of the solutions. This problem is magnified when using adjoint methods for computing sensitivities, an important tool for PDE-constrained optimization. The proposed work uses a geometric approach to regularize the Euler equations without introducing viscosity. Like interior point methods in optimization, it modifies the trajectories of particles to avoid collisions by replacing Euclidean geometry with the information geometry generated by a barrier function. The Euler equations can be viewed as Newton s equations on the manifold of diffeomorphisms and shocks arise when the solution leaves the manifold. From this perspective, information geometric regularization changes the geometry of the diffeomorphism manifold to restore geodesic completeness and thus avoid shock formation. The proposed work aims to establish information geometric regularization as a practical tool for the simulation of supersonic flow, with a special emphasis on applications in scientific machine learning and design optimization.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2024
- Source ID
- FA95502310668
Entities
People
- Florian Schaefer
Organizations
- Air Force Office of Scientific Research
- Georgia Tech Research Corporation
- United States Air Force