SVD perspectives for augmenting DeepONet flexibility and interpretability

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering

سال: 2023

ISSN: ['0045-7825', '1879-2138']

DOI: https://doi.org/10.1016/j.cma.2022.115718