English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper presents a nonlinear model reduction method for systems ofequations using a structured neural network. The neural network takes the formof a "three-layer" network with the first layer constrained to lie on theGrassmann manifold and the first activation function set to identity, while theremaining network is a standard two-layer ReLU neural network. The Grassmannlayer determines the reduced basis for the input space, while the remaininglayers approximate the nonlinear input-output system. The training alternatesbetween learning the reduced basis and the nonlinear approximation, and isshown to be more effective than fixing the reduced basis and training thenetwork only. An additional benefit of this approach is, for data that lie onlow-dimensional subspaces, that the number of parameters in the network doesnot need to be large. We show that our method can be applied to scientificproblems in the data-scarce regime, which is typically not well-suited forneural network approximations. Examples include reduced order modeling fornonlinear dynamical systems and several aerospace engineering problems.

Reduced Order Modeling using Shallow ReLU Networks with Grassmann Layers