# Uncertainty Quantification in Neural Differential Equations

arXiv: https://arxiv.org/abs/2111.04207 · HTML: https://mlsanity.com/paper/2111.04207/

## 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 (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [Benchmarking the Neural Linear Model for Regression](https://mlsanity.com/paper/1912.08416/) (2019)
- [Multivariate Deep Evidential Regression](https://mlsanity.com/paper/2104.06135/) (2021)
- [Solving Differential Equations Using Neural Network Solution Bundles](https://mlsanity.com/paper/2006.14372/) (2020)
- [Unsupervised Reservoir Computing for Solving Ordinary Differential Equations](https://mlsanity.com/paper/2108.11417/) (2021)
- [Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread](https://mlsanity.com/paper/2010.05074/) (2020)
- [Solving differential equations with unknown constitutive relations as recurrent neural networks](https://mlsanity.com/paper/1710.02242/) (2017)
- [Unsupervised Learning of Solutions to Differential Equations with Generative Adversarial Networks](https://mlsanity.com/paper/2007.11133/) (2020)

## Built on by (most cited first, 3 of 3)

- [Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networks](https://mlsanity.com/paper/2212.06965/) (2022)
- [Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles](https://mlsanity.com/paper/2505.06459/) (2025)
- [Continuous Time Evidential Distributions for Irregular Time Series](https://mlsanity.com/paper/2307.13503/) (2023)

## 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.