84,904 research outputs found
Progressive construction of a parametric reduced-order model for PDE-constrained optimization
An adaptive approach to using reduced-order models as surrogates in
PDE-constrained optimization is introduced that breaks the traditional
offline-online framework of model order reduction. A sequence of optimization
problems constrained by a given Reduced-Order Model (ROM) is defined with the
goal of converging to the solution of a given PDE-constrained optimization
problem. For each reduced optimization problem, the constraining ROM is trained
from sampling the High-Dimensional Model (HDM) at the solution of some of the
previous problems in the sequence. The reduced optimization problems are
equipped with a nonlinear trust-region based on a residual error indicator to
keep the optimization trajectory in a region of the parameter space where the
ROM is accurate. A technique for incorporating sensitivities into a
Reduced-Order Basis (ROB) is also presented, along with a methodology for
computing sensitivities of the reduced-order model that minimizes the distance
to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced
optimization framework is applied to subsonic aerodynamic shape optimization
and shown to reduce the number of queries to the HDM by a factor of 4-5,
compared to the optimization problem solved using only the HDM, with errors in
the optimal solution far less than 0.1%
Stimulus-invariant processing and spectrotemporal reverse correlation in primary auditory cortex
The spectrotemporal receptive field (STRF) provides a versatile and
integrated, spectral and temporal, functional characterization of single cells
in primary auditory cortex (AI). In this paper, we explore the origin of, and
relationship between, different ways of measuring and analyzing an STRF. We
demonstrate that STRFs measured using a spectrotemporally diverse array of
broadband stimuli -- such as dynamic ripples, spectrotemporally white noise,
and temporally orthogonal ripple combinations (TORCs) -- are very similar,
confirming earlier findings that the STRF is a robust linear descriptor of the
cell. We also present a new deterministic analysis framework that employs the
Fourier series to describe the spectrotemporal modulations contained in the
stimuli and responses. Additional insights into the STRF measurements,
including the nature and interpretation of measurement errors, is presented
using the Fourier transform, coupled to singular-value decomposition (SVD), and
variability analyses including bootstrap. The results promote the utility of
the STRF as a core functional descriptor of neurons in AI.Comment: 42 pages, 8 Figures; to appear in Journal of Computational
Neuroscienc
Satisfiability Modulo Transcendental Functions via Incremental Linearization
In this paper we present an abstraction-refinement approach to Satisfiability
Modulo the theory of transcendental functions, such as exponentiation and
trigonometric functions. The transcendental functions are represented as
uninterpreted in the abstract space, which is described in terms of the
combined theory of linear arithmetic on the rationals with uninterpreted
functions, and are incrementally axiomatized by means of upper- and
lower-bounding piecewise-linear functions. Suitable numerical techniques are
used to ensure that the abstractions of the transcendental functions are sound
even in presence of irrationals. Our experimental evaluation on benchmarks from
verification and mathematics demonstrates the potential of our approach,
showing that it compares favorably with delta-satisfiability /interval
propagation and methods based on theorem proving
Guaranteed parameter estimation in nonlinear dynamic systems using improved bounding techniques
This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding - or approximating as closely as possible - the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. Exclusion tests rely on the ability to bound the solution set of the dynamic system for a given parameter subset and the tightness of these bounds is therefore paramount. Equally important is the time required to compute the bounds, thereby defining a trade-off. It is the objective of this paper to investigate this trade-off by comparing various bounding techniques based on interval arithmetic, Taylor model arithmetic and ellipsoidal calculus. When applied to a simple case study, ellipsoidal and Taylor model approaches are found to reduce the number of iterations significantly compared to interval analysis, yet the overall computational time is only reduced for tight approximation levels due to the computational overhead. © 2013 EUCA
- …