Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic Numerical Method of Lines for Time-Dependent Partial
  Differential Equations   This work develops a class of probabilistic algorithms for the numerical
solution of nonlinear, time-dependent partial differential equations (PDEs).
Current state-of-the-art PDE solvers treat the space- and time-dimensions
separately, serially, and with black-box algorithms, which obscures the
interactions between spatial and temporal approximation errors and misguides
the quantification of the overall error. To fix this issue, we introduce a
probabilistic version of a technique called method of lines. The proposed
algorithm begins with a Gaussian process interpretation of finite difference
methods, which then interacts naturally with filtering-based probabilistic
ordinary differential equation (ODE) solvers because they share a common
language: Bayesian inference. Joint quantification of space- and
time-uncertainty becomes possible without losing the performance benefits of
well-tuned ODE solvers. Thereby, we extend the toolbox of probabilistic
programs for differential equation simulation to PDEs.

29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc