Related papers: Fully adaptive structure-preserving hyper-reductio…
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally,…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…
We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…
This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…
We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…