Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep unfitted Nitsche method for elliptic interface problems   This paper proposes a deep unfitted Nitsche method for computing elliptic
interface problems with high contrasts in high dimensions. To capture
discontinuities of the solution caused by interfaces, we reformulate the
problem as an energy minimization involving two weakly coupled components. This
enables us to train two deep neural networks to represent two components of the
solution in high-dimensional. The curse of dimensionality is alleviated by
using the Monte-Carlo method to discretize the unfitted Nitsche energy
function. We present several numerical examples to show the performance of the
proposed method.

32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin