# A Robust Learning Methodology for Uncertainty-aware Scientific Machine Learning models

arXiv: https://arxiv.org/abs/2209.01900 · HTML: https://mlsanity.com/paper/2209.01900/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 5 Sep 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Learning Functional Priors and Posteriors from Data and Physics](https://mlsanity.com/paper/2106.05863/) (2021)

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

- [Digital Twin Framework for Optimal and Autonomous Decision-Making in Cyber-Physical Systems: Enhancing Reliability and Adaptability in the Oil and Gas Industry](https://mlsanity.com/paper/2311.12755/) (2023)
- [Scientific machine learning in Hydrology: a unified perspective](https://mlsanity.com/paper/2506.06308/) (2025)

## Abstract (arXiv)

Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the different uncertainty components involved in SciML model identification. Hence, this work proposes a comprehensive methodology for uncertainty evaluation of the SciML that also considers several possible sources of uncertainties involved in the identification process. The uncertainties considered in the proposed method are the absence of theory and causal models, the sensitiveness to data corruption or imperfection, and the computational effort. Therefore, it was possible to provide an overall strategy for the uncertainty-aware models in the SciML field. The methodology is validated through a case study, developing a Soft Sensor for a polymerization reactor. The results demonstrated that the identified Soft Sensor are robust for uncertainties, corroborating with the consistency of the proposed approach.