59 citations · 63 across the 2 of their papers we have counts for
3 papers
math.NA2020★ 59 cited
Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold
Dimitris G. Giovanis, Michael D. Shields
This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The meth…
math.ST2019★ 4 cited
3rd-order Spectral Representation Method: Part II -- Ergodic Multi-variate random processes with fast Fourier transform
Lohit Vandanapu, Michael D. Shields
The second in a two-part series, this paper extends the 3rd-order Spectral Representation Method for simulation of ergodic multi-variate stochastic processes according to a prescri…
math.ST2019
3rd-order Spectral Representation Method: Part I -- Multi-dimensional random fields with fast Fourier transform implementation
Lohit Vandanapu, Michael D. Shields
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulate…