Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A comparison of combined data assimilation and machine learning methods
  for offline and online model error correction   Recent studies have shown that it is possible to combine machine learning
methods with data assimilation to reconstruct a dynamical system using only
sparse and noisy observations of that system. The same approach can be used to
correct the error of a knowledge-based model. The resulting surrogate model is
hybrid, with a statistical part supplementing a physical part. In practice, the
correction can be added as an integrated term (i.e. in the model resolvent) or
directly inside the tendencies of the physical model. The resolvent correction
is easy to implement. The tendency correction is more technical, in particular
it requires the adjoint of the physical model, but also more flexible. We use
the two-scale Lorenz model to compare the two methods. The accuracy in
long-range forecast experiments is somewhat similar between the surrogate
models using the resolvent correction and the tendency correction. By contrast,
the surrogate models using the tendency correction significantly outperform the
surrogate models using the resolvent correction in data assimilation
experiments. Finally, we show that the tendency correction opens the
possibility to make online model error correction, i.e. improving the model
progressively as new observations become available. The resulting algorithm can
be seen as a new formulation of weak-constraint 4D-Var. We compare online and
offline learning using the same framework with the two-scale Lorenz system, and
show that with online learning, it is possible to extract all the information
from sparse and noisy observations.

8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph