Related papers: Structure Preserving Model Reduction of Parametric…
Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
This paper studies the problem of modifying the input matrix of a structured system to make the system strongly structurally controllable. We focus on the generalized structured systems that rely on zero/nonzero/arbitrary structure, i.e.,…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…
Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…
Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…
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,…
We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations.…
Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM for control captures critical task-relevant aspects of the full dynamics while remaining low dimensional. However, planning within the…
Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide…
A multi-fidelity framework is established and demonstrated for prediction of combustion instabilities in rocket engines. The major idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to…
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)…
In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy…
How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for linear parabolic PDEs. We prove that our new method can be…
The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…
Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…
Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…