Related papers: On the order reduction
We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1%…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
We investigate the accuracy of slow-roll inflation in light of current observational constraints, which do not allow for a large deviation from scale invariance. We investigate the applicability of the first and second order slow-roll…
We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization,…
We study the equivalence of two - order-by-order Einstein's equation and Reduced action - approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we…
We extend the WKB method for the computation of cosmological perturbations during inflation beyond leading order and provide the power spectra of scalar and tensor perturbations to second order in the slow-roll parameters. Our method does…
The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…
We study constant roll inflation systematically. This is a regime, in which the slow roll approximation can be violated. It has long been thought that this approximation is necessary for agreement with observations. However, recently it was…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
The meaning of the inflationary slow-roll approximation is formalised. Comparisons are made between an approach based on the Hamilton-Jacobi equations, governing the evolution of the Hubble parameter, and the usual scenario based on the…
In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…
The slow roll approximation is studied for cosmological models in Hyperextended Scalar-Tensor Theories of Gravity. A procedure to obtain slow roll solutions in non-minimally coupled gravity is outlined and some examples are provided. An…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical…
In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…