81,240 research outputs found
CES-479 A Linear Estimation-of-Distribution GP System
We present N-gram GP, an estimation of distribution algorithm for the evolution of linear computer programs. The algorithm learns and samples the joint probability distribution of triplets of instructions (or 3-grams) at the same time as it is learning and sampling a program length distribution. We have tested N-gram GP on symbolic regressions problems where the target function is a polynomial of up to degree 12 and lawn-mower problems with lawn sizes of up to 12 ? 12. Results show that the algorithm is e?ective and scales better on these problems than either linear GP or simple stochastic hill-climbing
Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes
Uncertainty Quantification of closure relationships integrated into
thermal-hydraulic system codes is a critical prerequisite in applying the
Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and
licensing processes.The purpose of the CIRCE method is to estimate the
(log)-Gaussian probability distribution of a multiplicative factor applied to a
reference closure relationship in order to assess its uncertainty. Even though
this method has been implemented with success in numerous physical scenarios,
it can still suffer from substantial limitations such as the linearity
assumption and the difficulty of properly taking into account the inherent
statistical uncertainty. In the paper, we will extend the CIRCE method in two
aspects. On the one hand, we adopt the Bayesian setting putting prior
probability distributions on the parameters of the (log)-Gaussian distribution.
The posterior distribution of the parameters is then computed with respect to
an experimental database by means of Markov Chain Monte Carlo (MCMC)
algorithms. On the other hand, we tackle the more general setting where the
simulations do not move linearly against the multiplicative factor(s). MCMC
algorithms then become time-prohibitive when the thermal-hydraulic simulations
exceed a few minutes. This handicap is overcome by using Gaussian process (GP)
emulators which can yield both reliable and fast predictions of the
simulations. The GP-based MCMC algorithms will be applied to quantify the
uncertainty of two condensation closure relationships at a safety injection
with respect to a database of experimental tests. The thermal-hydraulic
simulations will be run with the CATHARE 2 computer code.Comment: 37 pages, 5 figure
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
A subsystems approach for parameter estimation of ODE models of hybrid systems
We present a new method for parameter identification of ODE system
descriptions based on data measurements. Our method works by splitting the
system into a number of subsystems and working on each of them separately,
thereby being easily parallelisable, and can also deal with noise in the
observations.Comment: In Proceedings HSB 2012, arXiv:1208.315
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