# Defining Operational Conditions for Safety-Critical AI-Based Systems from Data

arXiv: https://arxiv.org/abs/2601.22118 · HTML: https://mlsanity.com/paper/2601.22118/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 82 references that are in the map.
- First posted on arXiv 29 Jan 2026.

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

- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Guaranteeing Safety for Neural Network-Based Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1912.07084/) (2019)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [White Paper Machine Learning in Certified Systems](https://mlsanity.com/paper/2103.10529/) (2021)
- [Autonomous Vehicles Meet the Physical World: RSS, Variability, Uncertainty, and Proving Safety (Expanded Version)](https://mlsanity.com/paper/1911.01207/) (2019)
- [How to design a dataset compliant with an ML-based system ODD?](https://mlsanity.com/paper/2406.14027/) (2024)
- [Generating Probabilistic Safety Guarantees for Neural Network Controllers](https://mlsanity.com/paper/2103.01203/) (2021)
- [Data-centric Operational Design Domain Characterization for Machine Learning-based Aeronautical Products](https://mlsanity.com/paper/2307.07681/) (2023)
- [Safe and Reliable Training of Learning-Based Aerospace Controllers](https://mlsanity.com/paper/2407.07088/) (2024)
- [LeRAAT: LLM-Enabled Real-Time Aviation Advisory Tool](https://mlsanity.com/paper/2503.16477/) (2025)
- [Formalization of Operational Domain and Operational Design Domain for Automated Vehicles](https://mlsanity.com/paper/2408.14481/) (2024)
- [Fast Kernel Density Estimation with Density Matrices and Random Fourier Features](https://mlsanity.com/paper/2208.01206/) (2022)
- [Towards certifiable AI in aviation: landscape, challenges, and opportunities](https://mlsanity.com/paper/2409.08666/) (2024)
- [One Stack, Diverse Vehicles: Checking Safe Portability of Automated Driving Software](https://mlsanity.com/paper/2501.18769/) (2025)

## Built on by (most cited first, 1 of 1)

- [On the Applicability of Safety Nets: A Safety-By-Design Solution for Certifying Neural Networks](https://mlsanity.com/paper/2608.20053/) (2026)

## Abstract (arXiv)

Artificial Intelligence (AI) has been on the rise in many domains, including numerous safety-critical applications. However, for complex systems in the real world, defining the underlying environmental conditions in which the AI-based system must operate---the Operational Design Domain (ODD)---is extremely challenging. This often results in an incomplete description of the ODD, which contrasts with the requirements of many domains for certifying AI-based systems. Traditionally, the ODD is created in the early stages of the development process, drawing on sophisticated expert knowledge and related standards. This paper presents a novel method for defining the ODD a posteriori from previously collected data using a multidimensional kernel-based representation. This approach is validated through both synthetic benchmarks and a real-world aviation use case. Moreover, the paper defines similarity of two ODDs if they generate the same outputs up to Lebesgue-null input sets and proves convergence in volume of the calibrated representation under the stated assumptions. The novel, safety-by-design, deterministic kernel-based ODD representation is derived fully automatically, given documented assurance inputs, permutation-stable, bounded by construction, and, under affine-equivariant per-dimension normalization, invariant to the choice of units. Utilizing the proposed ODD representation supports future certification of data-driven, safety-critical AI-based systems.