Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

This work presents two novel approaches for the symplectic model reduction of high-
dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical …

This work presents a nonintrusive physics-preserving method to learn reduced-order models
(ROMs) of canonical Hamiltonian systems. Traditional intrusive projection-based model …

We have recently proposed a data‐driven correction reduced‐order model (DDC‐ROM)
framework for the numerical simulation of fluid flows, which can be formally written as …

A method for the nonintrusive and structure-preserving model reduction of canonical and
noncanonical Hamiltonian systems is presented. Based on the idea of operator inference …

This work focuses on the conservation of quantities such as Hamiltonians, mass, and
momentum when solution fields of partial differential equations are approximated with …

This work presents a nonintrusive physics-preserving method to learn reduced-order models
(ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive …

Abstract Hamiltonian Operator Inference has been introduced in Sharma et al.(2022) to
learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This …

Abstract Galerkin and Petrov–Galerkin projection-based reduced-order models (ROMs) of
transient partial differential equations are typically obtained by performing a dimension …

2. Hyper-reduction methods 2.1 Parametrized integrals 2.2 Empirical quadrature methods
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …