Fetching the paper…
Reading the bibliography…
Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines.
N. Wiener, “The homogeneous chaos,” American Journal of Mathematics , vol. 60, no. 4, pp. 897–936, 1938. [Online]. Available: http://www.jstor.org/stable/2371268
1938
Earlier work this paper cites.
G. S. Fishman, “Monte carlo: Concepts, algorithms, and applications,” Technometrics , vol. 39, no. 3, pp. 338–338, 1997
1997
Earlier work this paper cites.
G. Karypis and V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” SIAM Journal on Scientific Computing , vol. 20, no. 1, pp. 359–392, 1998. [Online]. Available: https://doi.org/10.1137/S1064827595287997
1998
Earlier work this paper cites.
C. R. Cole, M. P. Bergeron, C. J. Murray, P. D. Thorne, S. K. Wurstner, and P. M. Rogers, “Uncertainty analysis framework-hanford site-wide groundwater flow and transport model,” Pacific Northwest National Lab., Richland, WA (US), Tech. Rep., 2001
2001
Earlier work this paper cites.
D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” Journal of Computational Physics , vol. 187, no. 1, pp. 137 – 167, 2003. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0021999103000925
2003
Earlier work this paper cites.
G. Evensen, “The ensemble kalman filter: Theoretical formulation and practical implementation,” Ocean dynamics , vol. 53, no. 4, pp. 343–367, 2003
2003
Earlier work this paper cites.
P. D. Thorne, M. P. Bergeron, M. D. Williams, and V. L. Freedman, “Groundwater data package for hanford assessments,” Pacific Northwest National Lab.(PNNL), Richland, WA (United States), Tech. Rep., 2006
2006
Earlier work this paper cites.
J. Foo and G. E. Karniadakis, “Multi-element probabilistic collocation method in high dimensions,” Journal of Computational Physics , vol. 229, no. 5, pp. 1536 – 1557, 2010. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0021999109006044
2010
Earlier work this paper cites.
H. C. Elman, C. W. Miller, E. T. Phipps, and R. S. Tuminaro, “Assessment of collocation and galerkin approaches to linear diffusion equations with random data,” International Journal for Uncertainty Quantification , vol. 1, no. 1, pp. 19–33, 2011
2011
Earlier work this paper cites.
Z. Zhang, M. Choi, and G. Karniadakis, “Error estimates for the anova method with polynomial chaos interpolation: Tensor product functions,” SIAM Journal on Scientific Computing , vol. 34, no. 2, pp. A1165–A1186, 2012. [Online]. Available: https://doi.org/10.1137/100788859
2012
Earlier work this paper cites.
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial nets,” in Advances in neural information processing systems (2014) , 2014, pp. 2672–2680
2014
Earlier work this paper cites.
2015
Earlier work this paper cites.
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems,” 2015, software available from tensorflow.org. [Online]. Available: https://www.tensorflow.org/
2015
Cited alongside, same era.
D. A. Barajas-Solano and D. M. Tartakovsky, “Stochastic collocation methods for nonlinear parabolic equations with random coefficients,” SIAM/ASA J. Uncert. Quantif. , vol. 4, pp. 475–494, 2016
2016
Cited alongside, same era.
K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in CVPR . IEEE Computer Society, 2016, pp. 770–778
2016
Cited alongside, same era.
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2017
Cited alongside, same era.
2017
Cited alongside, same era.
2017
Cited alongside, same era.
2017
Cited alongside, same era.
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville, “Improved training of Wasserstein GANs,” in Advances in Neural Information Processing Systems (2017) , 2017, pp. 5767–5777
2017
Cited alongside, same era.
2018
Cited alongside, same era.
M. Raissi and G. E. Karniadakis, “Hidden physics models: Machine learning of nonlinear partial differential equations,” Journal of Computational Physics , vol. 357, pp. 125 – 141, 2018. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0021999117309014
2018
Cited alongside, same era.
2018
Cited alongside, same era.
2018
Cited alongside, same era.
2018
Later among the works it cites.
2018
Later among the works it cites.
X. Jia, S. Song, W. He, Y. Wang, H. Rong, F. Zhou, L. Xie, Z. Guo, Y. Yang, L. Yu, T. Chen, G. Hu, S. Shi, and X. Chu, “Highly Scalable Deep Learning Training System with Mixed-Precision: Training ImageNet in Four Minutes,” ArXiv e-prints , Jul. 2018
2018
Later among the works it cites.
M. Raissi, P. Perdikaris, and G. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational Physics , vol. 378, pp. 686 – 707, 2019. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0021999118307125
2019
Closest in time.
Google. (2019) TensorFlow website. [Online]. Available: https://tensorflow.org
2019
Closest in time.
Nvidia, “Training with mixed precision,” April 2019. [Online]. Available: https://docs.nvidia.com/deeplearning/sdk/pdf/Training-Mixed-Precision-User-Guide.pdf
2019
Closest in time.
O. R. N. Laboratory. (2019) Summit - IBM Power System AC922, IBM POWER9 22C 3.07GHz, NVIDIA Volta GV100, Dual-rail Mellanox EDR Infiniband — TOP500 Supercomputer Sites. [Online]. Available: https://www.top500.org/system/179397
2019
Closest in time.