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About this paper

Apostolos F Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis

Researchers from Brown University and collaborators present a unified framework for Uncertainty Quantification (UQ) in Scientific Machine Learning (SciML), focusing on Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets). The work provides a systematic comparison of over ten UQ methods across five prototype problems, demonstrating that post-training calibration significantly improves statistical consistency and that functional priors enhance accuracy in scenarios with noisy or limited data.

Key insights

• Less computationally expensive UQ methods can achieve performance comparable to more costly ones, especially when NN parameter priors are learned or hyperparameters are carefully tuned.
• Post-training calibration, even with small held-out datasets, significantly improves the statistical consistency of predictions by reducing calibration error.
• Learning neural network parameter priors reduces the burden of meticulous architecture selection and can lead to more consistent epistemic uncertainty behavior across different network expressivities.

Summary by alphaXiv.