14 research outputs found
Hyperparameter optimization of hp-greedy reduced basis for gravitational wave surrogates
In a previous work we introduced, in the context of gravitational wave
science, an initial study on an automated domain-decomposition approach for
reduced basis through hp-greedy refinement. The approach constructs local
reduced bases of lower dimensionality than global ones, with the same or higher
accuracy. These ``light'' local bases should imply both faster evaluations when
predicting new waveforms and faster data analysis, in particular faster
statistical inference (the forward and inverse problems, respectively). In this
approach, however, we have previously found important dependence on several
hyperparameters, which do not appear in global reduced basis. This naturally
leads to the problem of hyperparameter optimization (HPO), which is the subject
of this paper. We tackle the problem through a Bayesian optimization, and show
its superiority when compared to grid or random searches. We find that for
gravitational waves from the collision of two spinning but non-precessing black
holes, for the same accuracy, local hp-greedy reduced bases with HPO have a
lower dimensionality of up to for the cases here studied, depending
on the desired accuracy. This factor should directly translate in a parameter
estimation speedup, for instance. Such acceleration might help in the near
real-time requirements for electromagnetic counterparts of gravitational waves
from compact binary coalescences. In addition, we find that the Bayesian
approach used in this paper for HPO is two orders of magnitude faster than, for
example, a grid search, with about a acceleration. The code
developed for this project is available as open source from public
repositories.Comment: This paper is an invited contribution to the Special Issue "Recent
Advances in Gravity: A Themed Issue in Honor of Prof. Jorge Pullin on his
60th Anniversary'
An offline/online procedure for dual norm calculations of parameterized functionals: empirical quadrature and empirical test spaces
We present an offline/online computational procedure for computing the dual
norm of parameterized linear functionals.
The key elements of the approach are
(i) an empirical test space for the manifold of Riesz elements associated
with the parameterized functional, and
(ii) an empirical quadrature procedure to efficiently deal with
parametrically non-affine terms. We present a number of theoretical results to
identify the different sources of error and to motivate the technique. Finally,
we show the effectiveness of our approach to reduce both offline and online
costs associated with the computation of the time-averaged residual indicator
proposed in [Fick, Maday, Patera, Taddei, Journal of Computational Physics,
2018 (accepted)]
Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy.Peer ReviewedPostprint (published version
Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accurac