This paper introduces operator surrogates, a method for creating finite-parametric maps that approximate complex operators between infinite-dimensional function spaces. It details the encoder-approximator-decoder paradigm, discussing representation systems like Banach frames, PCA, and Active Subspaces, alongside neural network architectures such as Fourier Neural Operators and transformers. The work also addresses theoretical analysis of approximation and generalization errors, highlighting how low-dimensional structures help overcome the curse of dimensionality. AI
IMPACT Introduces a novel mathematical framework for approximating complex operators, potentially impacting the efficiency and scalability of AI models dealing with high-dimensional data.
RANK_REASON The item is an academic paper published on arXiv detailing a new mathematical approach to approximating complex operators. [lever_c_demoted from research: ic=1 ai=1.0]
- active_subspaces
- arXiv
- Banach frames
- Fourier Neural Operators
- Josephine Westermann
- Operator Surrogates
- principal component analysis
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