mlsanityData to 14 Oct 2026

Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networks

arXiv 2212.06965 ↗First posted 14 Dec 2022cs.LGcited by 4

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Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for that can be found in Uncertainty Quantification (UQ) which is just beginning to emerge in the context of PINNs. Assessing how well the trained PINN complies with imposed differential equation is the key to tackling uncertainty, yet there is lack of comprehensive methodology for this task. We propose a framework for UQ in Bayesian PINNs (B-PINNs) that incorporates the discrepancy between the B-PINN solution and the unknown true solution. We exploit recent results on error bounds for PINNs on linear dynamical systems and demonstrate the predictive uncertainty on a class of linear ODEs.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 15 of its 22 references that are in the map. First posted on arXiv 14 Dec 2022.

Builds on

15 of 22 references.

References · 15

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  2. 2015Weight Uncertainty in Neural Networkscited by 554
  3. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  4. 2015Scalable Bayesian Optimization Using Deep Neural Networkscited by 284
  5. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  6. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  7. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 140
  8. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  9. 2018Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equationscited by 55
  10. 2019Physical Symmetries Embedded in Neural Networkscited by 40
  11. 2021Learning Functional Priors and Posteriors from Data and Physicscited by 37
  12. 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
3 more
  1. 2017Solving differential equations with unknown constitutive relations as recurrent neural networkscited by 6
  2. 2021Uncertainty Quantification in Neural Differential Equationscited by 3
  3. 2022Evaluating Error Bound for Physics-Informed Neural Networks on Linear Dynamical Systemscited by 3

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 0; 2025: 3.

4 papers.

  1. 2025Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networkscited by 42
  2. 2023One-Shot Transfer Learning for Nonlinear ODEscited by 3
  3. 2025Damper-B-PINN: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Vehicle State Estimationcited by 1
  4. 2025Quantifying constraint hierarchies in Bayesian PINNs via per-constraint Hessian decompositioncited by 0