There is growing interest in learning nonlinear operators between function spaces from data (neural operators, DeepONet). These methods use ideas from nonlinear functional analysis (approximation theory, compactness) to prove generalization bounds.
To solve nonlinear problems, one must differentiate. This extends the concept of the derivative to operators between Banach spaces (Fréchet and Gâteaux derivatives). This allows for:
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There is growing interest in learning nonlinear operators between function spaces from data (neural operators, DeepONet). These methods use ideas from nonlinear functional analysis (approximation theory, compactness) to prove generalization bounds.
To solve nonlinear problems, one must differentiate. This extends the concept of the derivative to operators between Banach spaces (Fréchet and Gâteaux derivatives). This allows for: There is growing interest in learning nonlinear operators
Legally, many universities host PDFs of lecture notes under Creative Commons. Search for: Warning: Avoid piracy
Warning: Avoid piracy. Many official PDFs are available through legitimate channels like SpringerLink (if your institution subscribes), ResearchGate (author uploads), or arXiv (preprints). ResearchGate (author uploads)