100 research outputs found
Sequential design of computer experiments for the estimation of a probability of failure
This paper deals with the problem of estimating the volume of the excursion
set of a function above a given threshold,
under a probability measure on that is assumed to be known. In
the industrial world, this corresponds to the problem of estimating a
probability of failure of a system. When only an expensive-to-simulate model of
the system is available, the budget for simulations is usually severely limited
and therefore classical Monte Carlo methods ought to be avoided. One of the
main contributions of this article is to derive SUR (stepwise uncertainty
reduction) strategies from a Bayesian-theoretic formulation of the problem of
estimating a probability of failure. These sequential strategies use a Gaussian
process model of and aim at performing evaluations of as efficiently as
possible to infer the value of the probability of failure. We compare these
strategies to other strategies also based on a Gaussian process model for
estimating a probability of failure.Comment: This is an author-generated postprint version. The published version
is available at http://www.springerlink.co
Variational method in relativistic quantum field theory without cutoff
The variational method is a powerful approach to solve many-body quantum
problems non perturbatively. However, in the context of relativistic quantum
field theory (QFT), it needs to meet 3 seemingly incompatible requirements
outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In
practice, variational methods break one of the 3, which translates into the
need to have an IR or UV cutoff. In this letter, I introduce a relativistic
modification of continuous matrix product states that satisfies the 3
requirements jointly in 1+1 dimensions. I apply it to the self-interacting
scalar field, without UV cutoff and directly in the thermodynamic limit.
Numerical evidence suggests the error decreases faster than any power law in
the number of parameters, while the cost remains only polynomial.Comment: v2 - major update on the algorithm v1 - 4 pages - see same posting
for a longer companion paper "Relativistic continuous matrix product states
for quantum fields without cutoff" containing more derivations, context, and
explanation
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