Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequential Monte Carlo Methods for High-Dimensional Inverse Problems: A
  case study for the Navier-Stokes equations   We consider the inverse problem of estimating the initial condition of a
partial differential equation, which is only observed through noisy
measurements at discrete time intervals. In particular, we focus on the case
where Eulerian measurements are obtained from the time and space evolving
vector field, whose evolution obeys the two-dimensional Navier-Stokes equations
defined on a torus. This context is particularly relevant to the area of
numerical weather forecasting and data assimilation. We will adopt a Bayesian
formulation resulting from a particular regularization that ensures the problem
is well posed. In the context of Monte Carlo based inference, it is a
challenging task to obtain samples from the resulting high dimensional
posterior on the initial condition. In real data assimilation applications it
is common for computational methods to invoke the use of heuristics and
Gaussian approximations. The resulting inferences are biased and not
well-justified in the presence of non-linear dynamics and observations. On the
other hand, Monte Carlo methods can be used to assimilate data in a principled
manner, but are often perceived as inefficient in this context due to the
high-dimensionality of the problem. In this work we will propose a generic
Sequential Monte Carlo (SMC) sampling approach for high dimensional inverse
problems that overcomes these difficulties. The method builds upon Markov chain
Monte Carlo (MCMC) techniques, which are currently considered as benchmarks for
evaluating data assimilation algorithms used in practice. In our numerical
examples, the proposed SMC approach achieves the same accuracy as MCMC but in a
much more efficient manner.

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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin