On the Deep Active-Subspace Method

The deep active-subspace method is a neural-network based tool for the propagation of uncertainty through computational models with high-dimensional input spaces. Unlike original method, it does not require access to gradient model. It relies on an orthogonal projection matrix constructed Gram–Schmidt orthogonalization reduce dimensionality. This incorporated into neural network as weight first hidden layer (acting encoder), and optimized using back identify active subspace input. We propose several theoretical extensions, starting new analytic relation derivatives vectors, which are required propagation. also study use vector-valued model outputs, difficult in case method. Additionally, we investigate alternative encoder without embedded orthonormality, shows equally good performance compared Two epidemiological considered applications, where one requires supercomputer generate training data.