Related papers: On the order reduction
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,…
Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…
Although design optimization has shown its great power of automatizing the whole design process and providing an optimal design, using sophisticated computational models, its process can be formidable due to a computationally expensive…
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…
The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. For a given system, these methods produce a reduced-order system…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…
Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…
This paper continues the examination of inventory control in which the inventory is modelled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration have general…
Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of inflationary dynamics. It automatically includes information from sub-leading terms in slow roll, and facilitatesthe inclusion of priors based on the duration on…
We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…