New theorem advances operator approximation for encoder-decoder neural networks

Researchers have developed a new universal operator approximation theorem specifically for encoder-decoder neural network architectures. This theorem extends existing work by considering a broader range of input and output spaces, including infinite-dimensional normed or metric spaces. A key contribution is the demonstration that approximating sequences of architectures can be chosen independently of compact sets, a property that is strictly stronger in most relevant operator learning frameworks. The framework accommodates various architectures like DeepONets, BasisONets, and MIONets, and notably includes $p$-Wasserstein spaces of probability measures and Skorohod spaces of càdlàg functions as potential input or output spaces, opening avenues for applications in optimal transport. AI

IMPACT Advances theoretical understanding of neural network capabilities in approximating complex mathematical operators.

RANK_REASON The cluster contains a research paper published on arXiv detailing a new mathematical theorem. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• BasisONets
• DeepONets
• Janek Gödeke
• MIONets
• p-Wasserstein spaces
• Skorohod spaces

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