Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prediction of large-scale dynamics using unresolved computations   We present a theoretical framework and numerical methods for predicting the
large-scale properties of solutions of partial differential equations that are
too complex to be properly resolved. We assume that prior statistical
information about the distribution of the solutions is available, as is often
the case in practice. The quantities we can compute condition the prior
information and allow us to calculate mean properties of solutions in the
future. We derive approximate ways for computing the evolution of the
probabilities conditioned by what we can compute, and obtain ordinary
differential equations for the expected values of a set of large-scale
variables. Our methods are demonstrated on two simple but instructive examples,
where the prior information consists of invariant canonical distributions

3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin