Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems

Donsub Rim
Donsub Rim
Luca Venturi
Luca Venturi
Benjamin Peherstorfer
Benjamin Peherstorfer
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Abstract:

Classical reduced models are low-rank approximations using a fixed basis designed to achieve dimensionality reduction of large-scale systems. In this work, we introduce reduced deep networks, a generalization of classical reduced models formulated as deep neural networks. We prove depth separation results showing that reduced deep netwo...More

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