Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: SVD Perspectives for Augmenting DeepONet Flexibility and
  Interpretability   Deep operator networks (DeepONets) are powerful architectures for fast and
accurate emulation of complex dynamics. As their remarkable generalization
capabilities are primarily enabled by their projection-based attribute, we
investigate connections with low-rank techniques derived from the singular
value decomposition (SVD). We demonstrate that some of the concepts behind
proper orthogonal decomposition (POD)-neural networks can improve DeepONet's
design and training phases. These ideas lead us to a methodology extension that
we name SVD-DeepONet. Moreover, through multiple SVD analyses, we find that
DeepONet inherits from its projection-based attribute strong inefficiencies in
representing dynamics characterized by symmetries. Inspired by the work on
shifted-POD, we develop flexDeepONet, an architecture enhancement that relies
on a pre-transformation network for generating a moving reference frame and
isolating the rigid components of the dynamics. In this way, the physics can be
represented on a latent space free from rotations, translations, and stretches,
and an accurate projection can be performed to a low-dimensional basis. In
addition to flexibility and interpretability, the proposed perspectives
increase DeepONet's generalization capabilities and computational efficiencies.
For instance, we show flexDeepONet can accurately surrogate the dynamics of 19
variables in a combustion chemistry application by relying on 95% less
trainable parameters than the ones of the vanilla architecture. We argue that
DeepONet and SVD-based methods can reciprocally benefit from each other. In
particular, the flexibility of the former in leveraging multiple data sources
and multifidelity knowledge in the form of both unstructured data and
physics-informed constraints has the potential to greatly extend the
applicability of methodologies such as POD and PCA.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con