Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient descent globally solves average-case non-resonant physical
  design problems   Optimization problems occurring in a wide variety of physical design
problems, including but not limited to optical engineering, quantum control,
structural engineering, involve minimization of a simple cost function of the
state of the system (e.g. the optical fields, the quantum state) while being
constrained by the physics of the system. The physics constraints often makes
such problems non-convex and thus only locally solvable, leaving open the
question of finding the globally optimal design. In this paper, I consider
design problems whose physics is described by bi-affine equality constraints,
and show that under assumptions on the stability of these constraints and the
physical system being non-resonant, gradient descent globally solves a typical
physical design problem. The key technical contributions of this paper are (i)
outline a criteria that ensure the convergence of gradient descent to an
approximate global optima in the limit of large problem sizes, and (ii) use
random matrix theory to outline ensembles of physically motivated problems
which, on an average, satisfy this convergence criteria.

14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas