# Towards certification: A complete statistical validation pipeline for supervised learning in industry

arXiv: https://arxiv.org/abs/2411.02075 · HTML: https://mlsanity.com/paper/2411.02075/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 18 of 18)

- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Data Augmentation Generative Adversarial Networks](https://mlsanity.com/paper/1711.04340/) (2017)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Machine Learning Operations (MLOps): Overview, Definition, and Architecture](https://mlsanity.com/paper/2205.02302/) (2022)
- [Learning in High Dimension Always Amounts to Extrapolation](https://mlsanity.com/paper/2110.09485/) (2021)
- [Unsupervised Domain Adaptation for Robust Speech Recognition via Variational Autoencoder-Based Data Augmentation](https://mlsanity.com/paper/1707.06265/) (2017)
- [Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning](https://mlsanity.com/paper/2008.10740/) (2020)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [When does gradient descent with logistic loss find interpolating two-layer networks?](https://mlsanity.com/paper/2012.02409/) (2020)
- [An effective theory of collective deep learning](https://mlsanity.com/paper/2310.12802/) (2023)
- [Toward Certification of Machine-Learning Systems for Low Criticality Airborne Applications](https://mlsanity.com/paper/2209.13975/) (2022)
- [Dynamical stability and chaos in artificial neural network trajectories along training](https://mlsanity.com/paper/2404.05782/) (2024)
- [Correlations of network trajectories](https://mlsanity.com/paper/2206.03334/) (2022)
- [First-order methods for the convex hull membership problem](https://mlsanity.com/paper/2111.07720/) (2021)
- [Formal and Practical Elements for the Certification of Machine Learning Systems](https://mlsanity.com/paper/2310.03217/) (2023)

## Built on by (most cited first, 4 of 4)

- [Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints](https://mlsanity.com/paper/2505.02634/) (2025)
- [FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes](https://mlsanity.com/paper/2604.08586/) (2026)
- [Reliable Statistical Guarantees for Conformal Predictors with Small Datasets](https://mlsanity.com/paper/2512.04566/) (2025)
- [Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs](https://mlsanity.com/paper/2606.27126/) (2026)

## Abstract (arXiv)

Methods of Machine and Deep Learning are gradually being integrated into industrial operations, albeit at different speeds for different types of industries. The aerospace and aeronautical industries have recently developed a roadmap for concepts of design assurance and integration of neural network-related technologies in the aeronautical sector. This paper aims to contribute to this paradigm of AI-based certification in the context of supervised learning, by outlining a complete validation pipeline that integrates deep learning, optimization and statistical methods. This pipeline is composed by a directed graphical model of ten steps. Each of these steps is addressed by a merging key concepts from different contributing disciplines (from machine learning or optimization to statistics) and adapting them to an industrial scenario, as well as by developing computationally efficient algorithmic solutions. We illustrate the application of this pipeline in a realistic supervised problem arising in aerostructural design: predicting the likelikood of different stress-related failure modes during different airflight maneuvers based on a (large) set of features characterising the aircraft internal loads and geometric parameters.