# Combined Data and Deep Learning Model Uncertainties: An Application to the Measurement of Solid Fuel Regression Rate

arXiv: https://arxiv.org/abs/2210.14287 · HTML: https://mlsanity.com/paper/2210.14287/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [The VIA Annotation Software for Images, Audio and Video](https://mlsanity.com/paper/1904.10699/) (2019)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Disentangling Human Error from the Ground Truth in Segmentation of Medical Images](https://mlsanity.com/paper/2007.15963/) (2020)
- [Leveraging Uncertainty Estimates for Predicting Segmentation Quality](https://mlsanity.com/paper/1807.00502/) (2018)
- [Quantifying the unknown impact of segmentation uncertainty on image-based simulations](https://mlsanity.com/paper/2012.09913/) (2020)
- [Measurement of Hybrid Rocket Solid Fuel Regression Rate for a Slab Burner using Deep Learning](https://mlsanity.com/paper/2108.11276/) (2021)
- [A Predictive Discrete-Continuum Multiscale Model of Plasticity With Quantified Uncertainty](https://mlsanity.com/paper/2012.10823/) (2020)

## Built on by (most cited first, 2 of 2)

- [A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty](https://mlsanity.com/paper/2403.08901/) (2024)
- [UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration](https://mlsanity.com/paper/2411.16693/) (2024)

## Abstract (arXiv)

In complex physical process characterization, such as the measurement of the regression rate for solid hybrid rocket fuels, where both the observation data and the model used have uncertainties originating from multiple sources, combining these in a systematic way for quantities of interest(QoI) remains a challenge. In this paper, we present a forward propagation uncertainty quantification (UQ) process to produce a probabilistic distribution for the observed regression rate dotr. We characterized two input data uncertainty sources from the experiment (the distortion from the camera Uc and the non-zero angle fuel placement Uγ), the prediction and model form uncertainty from the deep neural network (Um), as well as the variability from the manually segmented images used for training it (Us). We conducted seven case studies on combinations of these uncertainty sources with the model form uncertainty. The main contribution of this paper is the investigation and inclusion of the experimental image data uncertainties involved, and how to include them in a workflow when the QoI is the result of multiple sequential processes.