Related papers: Structure-preserving model order reduction of Hami…
In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI)…
In this expository note, we give a self-contained introduction to some modern incarnations of Hamiltonian reduction. Particular emphasis is placed on applications to symplectic geometry and geometric representation theory. We thereby…
In the aim of reducing the computational cost of the resolution of parameter-dependent eigenvalue problems, a model order reduction (MOR) procedure is proposed. We focus on the case of non-self-adjoint generalized eigenvalue problems, such…
We demonstrate that system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
These are the notes of rather informal lectures given by the first co-author in UPMC, Paris, in January 2017. Practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows to…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…
The $\mathcal{H}_2$-optimal Model Order Reduction (MOR) is one of the most significant frameworks for reduction methodologies for linear dynamical systems. In this context, the Iterative Rational Krylov Algorithm (\IRKA) is a well…
Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is…
Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…
Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…
Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…
We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…
This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads,…
Model order reduction (MOR) is essential in integrated circuit design, particularly when dealing with large-scale electromagnetic models extracted from complex designs. The numerous passive elements introduced in these models pose…
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale…
A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of…
Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…