Zhu, Yinhao; Zabaras, Nicholas; Koutsourelakis, Phaedon-Stelios; Perdikaris, Paris Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. (English) Zbl 1452.68172 J. Comput. Phys. 394, 56-81 (2019). MSC: 68T07 35B30 65N75 76S05 PDFBibTeX XMLCite \textit{Y. Zhu} et al., J. Comput. Phys. 394, 56--81 (2019; Zbl 1452.68172) Full Text: DOI arXiv
Atkinson, Steven; Zabaras, Nicholas Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion. (English) Zbl 1451.62095 J. Comput. Phys. 383, 166-195 (2019). MSC: 62M10 60G15 62F15 35R60 35R30 PDFBibTeX XMLCite \textit{S. Atkinson} and \textit{N. Zabaras}, J. Comput. Phys. 383, 166--195 (2019; Zbl 1451.62095) Full Text: DOI arXiv
Xing, W. W.; Triantafyllidis, V.; Shah, A. A.; Nair, P. B.; Zabaras, N. Manifold learning for the emulation of spatial fields from computational models. (English) Zbl 1373.68340 J. Comput. Phys. 326, 666-690 (2016). MSC: 68T05 35B30 60G15 62H25 68U20 PDFBibTeX XMLCite \textit{W. W. Xing} et al., J. Comput. Phys. 326, 666--690 (2016; Zbl 1373.68340) Full Text: DOI Link
Chen, Peng; Zabaras, Nicholas; Bilionis, Ilias Uncertainty propagation using infinite mixture of gaussian processes and variational Bayesian inference. (English) Zbl 1351.76277 J. Comput. Phys. 284, 291-333 (2015). MSC: 76S05 62F15 PDFBibTeX XMLCite \textit{P. Chen} et al., J. Comput. Phys. 284, 291--333 (2015; Zbl 1351.76277) Full Text: DOI
Bilionis, Ilias; Zabaras, Nicholas; Konomi, Bledar A.; Lin, Guang Multi-output separable Gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification. (English) Zbl 1349.76760 J. Comput. Phys. 241, 212-239 (2013). MSC: 76M35 PDFBibTeX XMLCite \textit{I. Bilionis} et al., J. Comput. Phys. 241, 212--239 (2013; Zbl 1349.76760) Full Text: DOI
Bilionis, Ilias; Zabaras, Nicholas Multi-output local Gaussian process regression: applications to uncertainty quantification. (English) Zbl 1277.60066 J. Comput. Phys. 231, No. 17, 5718-5746 (2012). MSC: 60G15 60H35 60H10 PDFBibTeX XMLCite \textit{I. Bilionis} and \textit{N. Zabaras}, J. Comput. Phys. 231, No. 17, 5718--5746 (2012; Zbl 1277.60066) Full Text: DOI