Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational system identification of the partial differential equations
  governing pattern-forming physics: Inference under varying fidelity and noise   We present a contribution to the field of system identification of partial
differential equations (PDEs), with emphasis on discerning between competing
mathematical models of pattern-forming physics. The motivation comes from
developmental biology, where pattern formation is central to the development of
any multicellular organism, and from materials physics, where phase transitions
similarly lead to microstructure. In both these fields there is a collection of
nonlinear, parabolic PDEs that, over suitable parameter intervals and regimes
of physics, can resolve the patterns or microstructures with comparable
fidelity. This observation frames the question of which PDE best describes the
data at hand. This question is particularly compelling because identification
of the closest representation to the true PDE, while constrained by the
functional spaces considered relative to the data at hand, immediately delivers
insights to the physics underlying the systems. While building on recent work
that uses stepwise regression, we present advances that leverage the
variational framework and statistical tests. We also address the influences of
variable fidelity and noise in the data.

34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph