Reproduce “Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference” on OpenResearch

About this paper

Frank Shih, Zhenghao Jiang, Faming Liang

An Extended Fiducial Inference (EFI) framework quantifies uncertainty in Physics-Informed Neural Networks (PINNs), addressing the limitations of subjective prior distributions and arbitrary hyperparameters in existing methods. The framework delivers well-calibrated confidence intervals for both solution and model parameters across various forward and inverse problems, even for high-dimensional models.

Key insights

• The EFI framework overcomes the subjectivity of prior distributions or dropout rates by framing uncertainty quantification as solving data-generating equations, leading to objective confidence sets.
• The "narrow-neck" w-network effectively reduces the dimensionality of parameter estimation by leveraging the correlation among individual parameter estimates, making EFI applicable to large-scale deep learning models without sparse priors.
• Built-in self-diagnosis capabilities, such as QQ-plots for imputed errors and energy function convergence checks, provide data-driven validation of the inference process.

Summary by alphaXiv.