Zou, Zongren; Meng, Xuhui; Psaros, Apostolos F.; Karniadakis, George E. NeuralUQ: a comprehensive library for uncertainty quantification in neural differential equations and operators. (English) Zbl 07805456 SIAM Rev. 66, No. 1, 161-190 (2024). MSC: 68T07 PDFBibTeX XMLCite \textit{Z. Zou} et al., SIAM Rev. 66, No. 1, 161--190 (2024; Zbl 07805456) Full Text: DOI arXiv
Chang, Cheng; Zeng, Tieyong A hybrid data-driven-physics-constrained Gaussian process regression framework with deep kernel for uncertainty quantification. (English) Zbl 07788134 J. Comput. Phys. 486, Article ID 112129, 14 p. (2023). MSC: 68Txx 65Cxx 60Hxx PDFBibTeX XMLCite \textit{C. Chang} and \textit{T. Zeng}, J. Comput. Phys. 486, Article ID 112129, 14 p. (2023; Zbl 07788134) Full Text: DOI arXiv
Cao, Lianghao; O’Leary-Roseberry, Thomas; Jha, Prashant K.; Oden, J. Tinsley; Ghattas, Omar Residual-based error correction for neural operator accelerated Infinite-dimensional Bayesian inverse problems. (English) Zbl 07788122 J. Comput. Phys. 486, Article ID 112104, 33 p. (2023). MSC: 65Nxx 65Cxx 35Rxx PDFBibTeX XMLCite \textit{L. Cao} et al., J. Comput. Phys. 486, Article ID 112104, 33 p. (2023; Zbl 07788122) Full Text: DOI arXiv
Thakur, Akshay; Chakraborty, Souvik Deep capsule encoder-decoder network for surrogate modeling and uncertainty quantification. (English) Zbl 07772231 Int. J. Numer. Methods Eng. 124, No. 12, 2783-2800 (2023). MSC: 65Cxx 60Hxx 35Rxx PDFBibTeX XMLCite \textit{A. Thakur} and \textit{S. Chakraborty}, Int. J. Numer. Methods Eng. 124, No. 12, 2783--2800 (2023; Zbl 07772231) Full Text: DOI arXiv
Martinez, Carianne; Bolintineanu, Dan S.; Olson, Aaron; Rodgers, Theron; Donohoe, Brendan; Potter, Kevin M.; Roberts, Scott A.; Pokharel, Reeju; Forrest, Stephanie; Moore, Nathan W. Automated segmentation of porous thermal spray material CT scans with predictive uncertainty estimation. (English) Zbl 07719586 Comput. Mech. 72, No. 3, 525-551 (2023). MSC: 74-XX PDFBibTeX XMLCite \textit{C. Martinez} et al., Comput. Mech. 72, No. 3, 525--551 (2023; Zbl 07719586) Full Text: DOI
Parekh, Jigar; Verstappen, R. W. C. P. Uncertainty quantification analysis for simulation of wakes in wind-farms using a stochastic RANS solver, compared with a deep learning approach. (English) Zbl 1521.76245 Comput. Fluids 257, Article ID 105867, 25 p. (2023). MSC: 76F65 PDFBibTeX XMLCite \textit{J. Parekh} and \textit{R. W. C. P. Verstappen}, Comput. Fluids 257, Article ID 105867, 25 p. (2023; Zbl 1521.76245) Full Text: DOI
Hoffmann, Clara; Klein, Nadja Marginally calibrated response distributions for end-to-end learning in autonomous driving. (English) Zbl 07692403 Ann. Appl. Stat. 17, No. 2, 1740-1763 (2023). MSC: 62Pxx PDFBibTeX XMLCite \textit{C. Hoffmann} and \textit{N. Klein}, Ann. Appl. Stat. 17, No. 2, 1740--1763 (2023; Zbl 07692403) Full Text: DOI arXiv
Nilsen, Geir K.; Munthe-Kaas, Antonella Z.; Skaug, Hans J.; Brun, Morten Epistemic uncertainty quantification in deep learning classification by the delta method. (English) Zbl 1521.68196 Neural Netw. 145, 164-176 (2022). MSC: 68T07 62B10 62E17 PDFBibTeX XMLCite \textit{G. K. Nilsen} et al., Neural Netw. 145, 164--176 (2022; Zbl 1521.68196) Full Text: DOI arXiv
Patel, Dhruv V.; Ray, Deep; Oberai, Assad A. Solution of physics-based Bayesian inverse problems with deep generative priors. (English) Zbl 1507.62235 Comput. Methods Appl. Mech. Eng. 400, Article ID 115428, 25 p. (2022). MSC: 62F15 68T07 PDFBibTeX XMLCite \textit{D. V. Patel} et al., Comput. Methods Appl. Mech. Eng. 400, Article ID 115428, 25 p. (2022; Zbl 1507.62235) Full Text: DOI arXiv
Povala, Jan; Kazlauskaite, Ieva; Febrianto, Eky; Cirak, Fehmi; Girolami, Mark Variational Bayesian approximation of inverse problems using sparse precision matrices. (English) Zbl 1507.35343 Comput. Methods Appl. Mech. Eng. 393, Article ID 114712, 31 p. (2022). MSC: 35R30 60H35 35-04 PDFBibTeX XMLCite \textit{J. Povala} et al., Comput. Methods Appl. Mech. Eng. 393, Article ID 114712, 31 p. (2022; Zbl 1507.35343) Full Text: DOI arXiv
Mancini, Tullio; Calvo-Pardo, Hector; Olmo, Jose Extremely randomized neural networks for constructing prediction intervals. (English) Zbl 1521.62187 Neural Netw. 144, 113-128 (2021). MSC: 62M45 68T07 PDFBibTeX XMLCite \textit{T. Mancini} et al., Neural Netw. 144, 113--128 (2021; Zbl 1521.62187) Full Text: DOI
Tsiligkaridis, Theodoros Information aware max-norm Dirichlet networks for predictive uncertainty estimation. (English) Zbl 1521.68204 Neural Netw. 135, 105-114 (2021). MSC: 68T07 62F15 PDFBibTeX XMLCite \textit{T. Tsiligkaridis}, Neural Netw. 135, 105--114 (2021; Zbl 1521.68204) Full Text: DOI arXiv
Jacquier, Pierre; Abdedou, Azzedine; Delmas, Vincent; Soulaïmani, Azzeddine Non-intrusive reduced-order modeling using uncertainty-aware deep neural networks and proper orthogonal decomposition: application to flood modeling. (English) Zbl 07508459 J. Comput. Phys. 424, Article ID 109854, 27 p. (2021). MSC: 68-XX 86-XX PDFBibTeX XMLCite \textit{P. Jacquier} et al., J. Comput. Phys. 424, Article ID 109854, 27 p. (2021; Zbl 07508459) Full Text: DOI arXiv
Khoo, Yuehaw; Lu, Jianfeng; Ying, Lexing Solving parametric PDE problems with artificial neural networks. (English) Zbl 1501.65154 Eur. J. Appl. Math. 32, No. 3, 421-435 (2021). MSC: 65N99 68T07 35R60 PDFBibTeX XMLCite \textit{Y. Khoo} et al., Eur. J. Appl. Math. 32, No. 3, 421--435 (2021; Zbl 1501.65154) Full Text: DOI arXiv
Henkes, Alexander; Caylak, Ismail; Mahnken, Rolf A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures. (English) Zbl 1502.74087 Comput. Methods Appl. Mech. Eng. 385, Article ID 114070, 27 p. (2021). MSC: 74Q05 65N75 PDFBibTeX XMLCite \textit{A. Henkes} et al., Comput. Methods Appl. Mech. Eng. 385, Article ID 114070, 27 p. (2021; Zbl 1502.74087) Full Text: DOI arXiv
Patel, Dhruv V.; Oberai, Assad A. GAN-based priors for quantifying uncertainty in supervised learning. (English) Zbl 1473.62092 SIAM/ASA J. Uncertain. Quantif. 9, 1314-1343 (2021). MSC: 62F15 68T37 68T07 62-04 PDFBibTeX XMLCite \textit{D. V. Patel} and \textit{A. A. Oberai}, SIAM/ASA J. Uncertain. Quantif. 9, 1314--1343 (2021; Zbl 1473.62092) Full Text: DOI
Freitas, Rodolfo S. M.; Barbosa, Carlos H. S.; Guerra, Gabriel M.; Coutinho, Alvaro L. G. A.; Rochinha, Fernando A. An encoder-decoder deep surrogate for reverse time migration in seismic imaging under uncertainty. (English) Zbl 1460.86031 Comput. Geosci. 25, No. 3, 1229-1250 (2021). MSC: 86A15 86A22 PDFBibTeX XMLCite \textit{R. S. M. Freitas} et al., Comput. Geosci. 25, No. 3, 1229--1250 (2021; Zbl 1460.86031) Full Text: DOI arXiv
Kalogeris, Ioannis; Papadopoulos, Vissarion Diffusion maps-aided neural networks for the solution of parametrized PDEs. (English) Zbl 1506.65180 Comput. Methods Appl. Mech. Eng. 376, Article ID 113568, 24 p. (2021). MSC: 65M99 68T05 PDFBibTeX XMLCite \textit{I. Kalogeris} and \textit{V. Papadopoulos}, Comput. Methods Appl. Mech. Eng. 376, Article ID 113568, 24 p. (2021; Zbl 1506.65180) Full Text: DOI
Sun, Luning; Gao, Han; Pan, Shaowu; Wang, Jian-Xun Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. (English) Zbl 1442.76096 Comput. Methods Appl. Mech. Eng. 361, Article ID 112732, 25 p. (2020). MSC: 76M99 65Z05 76Z05 PDFBibTeX XMLCite \textit{L. Sun} et al., Comput. Methods Appl. Mech. Eng. 361, Article ID 112732, 25 p. (2020; Zbl 1442.76096) Full Text: DOI arXiv
Zhang, Dongkun; Guo, Ling; Karniadakis, George Em Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks. (English) Zbl 1440.60067 SIAM J. Sci. Comput. 42, No. 2, A639-A665 (2020). MSC: 60H35 34F05 62M45 PDFBibTeX XMLCite \textit{D. Zhang} et al., SIAM J. Sci. Comput. 42, No. 2, A639--A665 (2020; Zbl 1440.60067) Full Text: DOI arXiv
Boso, Francesca; Tartakovsky, Daniel M. Data-informed method of distributions for hyperbolic conservation laws. (English) Zbl 1436.35330 SIAM J. Sci. Comput. 42, No. 1, A559-A583 (2020). MSC: 35R60 35L65 35L45 35L60 PDFBibTeX XMLCite \textit{F. Boso} and \textit{D. M. Tartakovsky}, SIAM J. Sci. Comput. 42, No. 1, A559--A583 (2020; Zbl 1436.35330) 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
Tripathy, Rohit K.; Bilionis, Ilias Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification. (English) Zbl 1419.68084 J. Comput. Phys. 375, 565-588 (2018). MSC: 68T05 35R60 65N99 PDFBibTeX XMLCite \textit{R. K. Tripathy} and \textit{I. Bilionis}, J. Comput. Phys. 375, 565--588 (2018; Zbl 1419.68084) Full Text: DOI arXiv