<ul><li>The study focuses on the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks.</li><li>The approximation accuracy of the operator's derivatives can significantly impact the performance of the surrogate model for various outer-loop tasks in science and engineering.</li><li>The study analyzes the approximation errors of neural operators in Sobolev norms over infinite-dimensional Gaussian input measures.</li><li>The analysis is validated on numerical experiments with elliptic PDEs, demonstrating the accuracy of bases informed by the map.</li></ul>

Dimension reduction for derivative-informed operator learning: An analysis of approximation errors

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