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Uncertainty Quantification in Neural Differential Equations

arXiv 2111.04207 ↗First posted 8 Nov 2021cs.LGcited by 3

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Abstract (arXiv)

Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can make deep models more reliable has increased as well. Among applications that can benefit from effective handling of uncertainty are the deep learning based differential equation (DE) solvers. We adapt several state-of-the-art UQ methods to get the predictive uncertainty for DE solutions and show the results on four different DE types.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 14 of its 23 references that are in the map. First posted on arXiv 8 Nov 2021.

Builds on

14 of 23 references.

References · 14

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
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  12. 2020Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spreadcited by 8
2 more
  1. 2017Solving differential equations with unknown constitutive relations as recurrent neural networkscited by 6
  2. 2020Unsupervised Learning of Solutions to Differential Equations with Generative Adversarial Networkscited by 3

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Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 0; 2025: 1.

3 papers.

  1. 2022Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networkscited by 4
  2. 2025Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundlescited by 3
  3. 2023Continuous Time Evidential Distributions for Irregular Time Seriescited by 0