Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adversarial Multi-task Learning Enhanced Physics-informed Neural
  Networks for Solving Partial Differential Equations   Recently, researchers have utilized neural networks to accurately solve
partial differential equations (PDEs), enabling the mesh-free method for
scientific computation. Unfortunately, the network performance drops when
encountering a high nonlinearity domain. To improve the generalizability, we
introduce the novel approach of employing multi-task learning techniques, the
uncertainty-weighting loss and the gradients surgery, in the context of
learning PDE solutions. The multi-task scheme exploits the benefits of learning
shared representations, controlled by cross-stitch modules, between multiple
related PDEs, which are obtainable by varying the PDE parameterization
coefficients, to generalize better on the original PDE. Encouraging the network
pay closer attention to the high nonlinearity domain regions that are more
challenging to learn, we also propose adversarial training for generating
supplementary high-loss samples, similarly distributed to the original training
distribution. In the experiments, our proposed methods are found to be
effective and reduce the error on the unseen data points as compared to the
previous approaches in various PDE examples, including high-dimensional
stochastic PDEs.

25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph