Deep active subspaces - a scalable method for high-dimensional uncertainty propagation
This work addresses the challenge of efficient surrogate modeling in high-dimensional systems for uncertainty quantification, offering a scalable solution that is incremental by building on active subspaces with deep learning.
The authors tackled the problem of constructing accurate surrogate models for high-dimensional uncertainty quantification without requiring gradient information, by developing a scalable method that combines deep neural networks with a reparameterized active subspace projection, showing favorable predictive performance compared to classical active subspaces on synthetic and real-world datasets.
A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accurate surrogate modeling in such systems, is further compounded by data scarcity brought about by the large cost of forward model evaluations. Traditional response surface techniques, such as Gaussian process regression (or Kriging) and polynomial chaos are difficult to scale to high dimensions. To make surrogate modeling tractable in expensive high-dimensional systems, one must resort to dimensionality reduction of the stochastic parameter space. A recent dimensionality reduction technique that has shown great promise is the method of `active subspaces'. The classical formulation of active subspaces, unfortunately, requires gradient information from the forward model - often impossible to obtain. In this work, we present a simple, scalable method for recovering active subspaces in high-dimensional stochastic systems, without gradient-information that relies on a reparameterization of the orthogonal active subspace projection matrix, and couple this formulation with deep neural networks. We demonstrate our approach on synthetic and real world datasets and show favorable predictive comparison to classical active subspaces.