Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adjoint DSMC for nonlinear Boltzmann equation constrained optimization   Applications for kinetic equations such as optimal design and inverse
problems often involve finding unknown parameters through gradient-based
optimization algorithms. Based on the adjoint-state method, we derive two
different frameworks for approximating the gradient of an objective functional
constrained by the nonlinear Boltzmann equation. While the forward problem can
be solved by the DSMC method, it is difficult to efficiently solve the
high-dimensional continuous adjoint equation obtained by the
"optimize-then-discretize" approach. This challenge motivates us to propose an
adjoint DSMC method following the "discretize-then-optimize" approach for
Boltzmann-constrained optimization. We also analyze the properties of the two
frameworks and their connections. Several numerical examples are presented to
demonstrate their accuracy and efficiency.

18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex