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Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons. (arXiv:2201.07766v1 [cs.LG])
Jan. 20, 2022, 2:10 a.m. | Apostolos F Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis
cs.LG updates on arXiv.org arxiv.org
Neural networks (NNs) are currently changing the computational paradigm on
how to combine data with mathematical laws in physics and engineering in a
profound way, tackling challenging inverse and ill-posed problems not solvable
with traditional methods. However, quantifying errors and uncertainties in
NN-based inference is more complicated than in traditional methods. This is
because in addition to aleatoric uncertainty associated with noisy data, there
is also uncertainty due to limited data, but also due to NN hyperparameters,
overparametrization, optimization and …
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