Gejadze, I.; Shutyaev, V.; Oubanas, H.; Malaterre, P.-O. A Bayesian-variational cyclic method for solving estimation problems characterized by non-uniqueness (equifinality). (English) Zbl 07696995 J. Comput. Phys. 488, Article ID 112239, 29 p. (2023). MSC: 90Cxx 65Kxx 49Mxx PDFBibTeX XMLCite \textit{I. Gejadze} et al., J. Comput. Phys. 488, Article ID 112239, 29 p. (2023; Zbl 07696995) Full Text: DOI
Gao, Wenhan; Wang, Chunmei Active learning based sampling for high-dimensional nonlinear partial differential equations. (English) Zbl 07649269 J. Comput. Phys. 475, Article ID 111848, 20 p. (2023). MSC: 68Txx 65Mxx 65Nxx PDFBibTeX XMLCite \textit{W. Gao} and \textit{C. Wang}, J. Comput. Phys. 475, Article ID 111848, 20 p. (2023; Zbl 07649269) Full Text: DOI arXiv
Wang, Yu; Liu, Fang; Schiavazzi, Daniele E. Variational inference with NoFAS: normalizing flow with adaptive surrogate for computationally expensive models. (English) Zbl 07568554 J. Comput. Phys. 467, Article ID 111454, 21 p. (2022). MSC: 65Cxx 65Nxx 60Hxx PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Comput. Phys. 467, Article ID 111454, 21 p. (2022; Zbl 07568554) Full Text: DOI arXiv
Kontolati, Katiana; Loukrezis, Dimitrios; Giovanis, Dimitrios G.; Vandanapu, Lohit; Shields, Michael D. A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems. (English) Zbl 07540357 J. Comput. Phys. 464, Article ID 111313, 30 p. (2022). MSC: 68Txx 65Cxx 62Hxx PDFBibTeX XMLCite \textit{K. Kontolati} et al., J. Comput. Phys. 464, Article ID 111313, 30 p. (2022; Zbl 07540357) Full Text: DOI arXiv
García, Constantino A.; Félix, Paulo; Presedo, Jesús M.; Otero, Abraham Stochastic embeddings of dynamical phenomena through variational autoencoders. (English) Zbl 07518058 J. Comput. Phys. 454, Article ID 110970, 22 p. (2022). MSC: 68Txx 65Cxx 62Gxx PDFBibTeX XMLCite \textit{C. A. García} et al., J. Comput. Phys. 454, Article ID 110970, 22 p. (2022; Zbl 07518058) Full Text: DOI arXiv
Sadr, Mohsen; Wang, Qian; Gorji, M. Hossein Coupling kinetic and continuum using data-driven maximum entropy distribution. (English) Zbl 07515444 J. Comput. Phys. 444, Article ID 110542, 24 p. (2021). MSC: 82Cxx 76Mxx 76Pxx PDFBibTeX XMLCite \textit{M. Sadr} et al., J. Comput. Phys. 444, Article ID 110542, 24 p. (2021; Zbl 07515444) Full Text: DOI Link
Kaltenbach, Sebastian; Koutsourelakis, Phaedon-Stelios Incorporating physical constraints in a deep probabilistic machine learning framework for coarse-graining dynamical systems. (English) Zbl 07507234 J. Comput. Phys. 419, Article ID 109673, 31 p. (2020). MSC: 68-XX 74-XX PDFBibTeX XMLCite \textit{S. Kaltenbach} and \textit{P.-S. Koutsourelakis}, J. Comput. Phys. 419, Article ID 109673, 31 p. (2020; Zbl 07507234) Full Text: DOI arXiv
Sadr, Mohsen; Torrilhon, Manuel; Gorji, M. Hossein Gaussian process regression for maximum entropy distribution. (English) Zbl 07506193 J. Comput. Phys. 418, Article ID 109644, 15 p. (2020). MSC: 62-XX 60-XX PDFBibTeX XMLCite \textit{M. Sadr} et al., J. Comput. Phys. 418, Article ID 109644, 15 p. (2020; Zbl 07506193) Full Text: DOI Link
Tipireddy, Ramakrishna; Barajas-Solano, David A.; Tartakovsky, Alexandre M. Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models. (English) Zbl 07506169 J. Comput. Phys. 418, Article ID 109604, 21 p. (2020). MSC: 76-XX 86-XX PDFBibTeX XMLCite \textit{R. Tipireddy} et al., J. Comput. Phys. 418, Article ID 109604, 21 p. (2020; Zbl 07506169) Full Text: DOI arXiv
Katsoulakis, Markos A.; Vilanova, Pedro Data-driven, variational model reduction of high-dimensional reaction networks. (English) Zbl 1453.62637 J. Comput. Phys. 401, Article ID 108997, 39 p. (2020). MSC: 62M10 37M10 60H10 92E20 68T05 PDFBibTeX XMLCite \textit{M. A. Katsoulakis} and \textit{P. Vilanova}, J. Comput. Phys. 401, Article ID 108997, 39 p. (2020; Zbl 1453.62637) Full Text: DOI arXiv
Tsilifis, Panagiotis; Papaioannou, Iason; Straub, Daniel; Nobile, Fabio Sparse polynomial chaos expansions using variational relevance vector machines. (English) Zbl 1437.62114 J. Comput. Phys. 416, Article ID 109498, 19 p. (2020). MSC: 62F15 74K20 PDFBibTeX XMLCite \textit{P. Tsilifis} et al., J. Comput. Phys. 416, Article ID 109498, 19 p. (2020; Zbl 1437.62114) Full Text: DOI arXiv
Yu, Jian; Yan, Chao; Jiang, Zhenhua; Yuan, Wu; Chen, Shusheng Adaptive non-intrusive reduced order modeling for compressible flows. (English) Zbl 1453.76118 J. Comput. Phys. 397, Article ID 108855, 27 p. (2019). MSC: 76M12 65M08 68T05 35B30 76N15 PDFBibTeX XMLCite \textit{J. Yu} et al., J. Comput. Phys. 397, Article ID 108855, 27 p. (2019; Zbl 1453.76118) Full Text: DOI
Zhang, Dongkun; Lu, Lu; Guo, Ling; Karniadakis, George Em Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. (English) Zbl 1454.65008 J. Comput. Phys. 397, Article ID 108850, 19 p. (2019). MSC: 65C30 35R30 35K57 60H35 68T07 PDFBibTeX XMLCite \textit{D. Zhang} et al., J. Comput. Phys. 397, Article ID 108850, 19 p. (2019; Zbl 1454.65008) Full Text: DOI arXiv
Yang, Xiu; Barajas-Solano, David; Tartakovsky, Guzel; Tartakovsky, Alexandre M. Physics-informed cokriging: a Gaussian-process-regression-based multifidelity method for data-model convergence. (English) Zbl 1453.62651 J. Comput. Phys. 395, 410-431 (2019). MSC: 62M10 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Comput. Phys. 395, 410--431 (2019; Zbl 1453.62651) Full Text: DOI arXiv
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em Machine learning of linear differential equations using Gaussian processes. (English) Zbl 1380.68339 J. Comput. Phys. 348, 683-693 (2017). MSC: 68T05 34K37 35K57 45J05 60G15 92D10 PDFBibTeX XMLCite \textit{M. Raissi} et al., J. Comput. Phys. 348, 683--693 (2017; Zbl 1380.68339) Full Text: DOI arXiv
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em Inferring solutions of differential equations using noisy multi-fidelity data. (English) Zbl 1382.65229 J. Comput. Phys. 335, 736-746 (2017). MSC: 65L99 68T05 PDFBibTeX XMLCite \textit{M. Raissi} et al., J. Comput. Phys. 335, 736--746 (2017; Zbl 1382.65229) Full Text: DOI arXiv
Aldegunde, Manuel; Zabaras, Nicholas; Kristensen, Jesper Quantifying uncertainties in first-principles alloy thermodynamics using cluster expansions. (English) Zbl 1418.62031 J. Comput. Phys. 323, 17-44 (2016). MSC: 62C12 82B80 82D35 PDFBibTeX XMLCite \textit{M. Aldegunde} et al., J. Comput. Phys. 323, 17--44 (2016; Zbl 1418.62031) Full Text: DOI
Nagel, Joseph B.; Sudret, Bruno Spectral likelihood expansions for Bayesian inference. (English) Zbl 1351.62077 J. Comput. Phys. 309, 267-294 (2016). MSC: 62F15 62P30 65C05 65C60 PDFBibTeX XMLCite \textit{J. B. Nagel} and \textit{B. Sudret}, J. Comput. Phys. 309, 267--294 (2016; Zbl 1351.62077) Full Text: DOI arXiv
Koutsourelakis, P. S. Variational Bayesian strategies for high-dimensional, stochastic design problems. (English) Zbl 1351.62073 J. Comput. Phys. 308, 124-152 (2016). MSC: 62F15 62F10 65C50 PDFBibTeX XMLCite \textit{P. S. Koutsourelakis}, J. Comput. Phys. 308, 124--152 (2016; Zbl 1351.62073) Full Text: DOI arXiv
Guha, Nilabja; Wu, Xiaoqing; Efendiev, Yalchin; Jin, Bangti; Mallick, Bani K. A variational Bayesian approach for inverse problems with skew-\(t\) error distributions. (English) Zbl 1349.62079 J. Comput. Phys. 301, 377-393 (2015). MSC: 62F15 65C60 PDFBibTeX XMLCite \textit{N. Guha} et al., J. Comput. Phys. 301, 377--393 (2015; Zbl 1349.62079) Full Text: DOI
Gehre, Matthias; Jin, Bangti Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography. (English) Zbl 1349.78046 J. Comput. Phys. 259, 513-535 (2014). MSC: 78A46 35R30 PDFBibTeX XMLCite \textit{M. Gehre} and \textit{B. Jin}, J. Comput. Phys. 259, 513--535 (2014; Zbl 1349.78046) Full Text: DOI arXiv
Jin, Bangti A variational Bayesian method to inverse problems with impulsive noise. (English) Zbl 1243.65115 J. Comput. Phys. 231, No. 2, 423-435 (2012). MSC: 65M32 35J05 35K05 65M60 35R30 80A20 65M12 80M30 80A23 PDFBibTeX XMLCite \textit{B. Jin}, J. Comput. Phys. 231, No. 2, 423--435 (2012; Zbl 1243.65115) Full Text: DOI arXiv
Jin, Bangti; Zou, Jun Hierarchical Bayesian inference for ill-posed problems via variational method. (English) Zbl 1198.65189 J. Comput. Phys. 229, No. 19, 7317-7343 (2010). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 65M32 62F15 65M60 35K05 65M30 35R25 35R30 65M12 PDFBibTeX XMLCite \textit{B. Jin} and \textit{J. Zou}, J. Comput. Phys. 229, No. 19, 7317--7343 (2010; Zbl 1198.65189) Full Text: DOI