SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability. (arXiv:2204.12670v2 [cs.LG] UPDATED)

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 …

arxiv interpretability perspectives svd