Finding characteristically rich nonlinear solution space: a statistical mechanics approach

DOI10.1002/NME.6310MaRDI QIDQ6497775

Taehyoun Kim

Publication date: 6 May 2024

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

zbMATH Keywords

nonlinear systemsLiouville equationcharacteristically rich nonlinear solution spacedegenerate transformationdynamic eigenmodesgauge modal invariance

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for ordinary differential equations (65Lxx) Linear vibration theory (70Jxx)

Cites Work

• Unnamed Item
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
• Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
• Surrogate model reduction for linear dynamic systems based on a frequency domain modal analysis
• On the statistical mechanics of non-Hamiltonian systems: the generalized Liouville equation, entropy, and time-dependent metrics
• A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems
• Nonlinear model order reduction based on local reduced-order bases
• An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models
• Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

This page was built for publication: Finding characteristically rich nonlinear solution space: a statistical mechanics approach