Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep transfer learning for partial differential equations under
  conditional shift with DeepONet   Traditional machine learning algorithms are designed to learn in isolation,
i.e. address single tasks. The core idea of transfer learning (TL) is that
knowledge gained in learning to perform one task (source) can be leveraged to
improve learning performance in a related, but different, task (target). TL
leverages and transfers previously acquired knowledge to address the expense of
data acquisition and labeling, potential computational power limitations, and
the dataset distribution mismatches. Although significant progress has been
made in the fields of image processing, speech recognition, and natural
language processing (for classification and regression) for TL, little work has
been done in the field of scientific machine learning for functional regression
and uncertainty quantification in partial differential equations. In this work,
we propose a novel TL framework for task-specific learning under conditional
shift with a deep operator network (DeepONet). Inspired by the conditional
embedding operator theory, we measure the statistical distance between the
source domain and the target feature domain by embedding conditional
distributions onto a reproducing kernel Hilbert space. Task-specific operator
learning is accomplished by fine-tuning task-specific layers of the target
DeepONet using a hybrid loss function that allows for the matching of
individual target samples while also preserving the global properties of the
conditional distribution of target data. We demonstrate the advantages of our
approach for various TL scenarios involving nonlinear PDEs under conditional
shift. Our results include geometry domain adaptation and show that the
proposed TL framework enables fast and efficient multi-task operator learning,
despite significant differences between the source and target domains.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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
9
The categories of this paper are: nlin