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.

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