Probabilistic Modelling of Operational Design Domains, A New Approach for Testing AI Systems

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.

Large Language Models (LLMs) have transformed artificial intelligence from primarily generative systems into increasingly capable reasoning agents. Recent advances in theorem proving, autoformalization, symbolic reasoning, and tool-augmented language models demonstrate substantial progress toward machine-assisted formal reasoning. However, current reasoning systems still suffer from hidden logical inconsistencies, hallucinated symbolic transitions, unsupported theorem applications, and limited reliability guarantees. Existing approaches remain fragmented across formal verification, runtime assurance, neuro-symbolic reasoning and trustworthy Artificial Intelligence (AI) research communities. This paper introduces ReasonOps, a unified operational paradigm for trustworthy verified reasoning systems. Inspired by operational ecosystems such as DevOps and MLOps, ReasonOps treats reasoning as a continuously monitored, verifiable, reliability-aware operational process rather than an isolated inference task. The proposed paradigm integrates semantic interpretation, autoformalization, symbolic reasoning, theorem proving, runtime assurance, probabilistic reliability estimation, and adaptive correction into a unified reasoning lifecycle. The paper further presents the ReasonOps architecture, demonstrates its workflow using an autonomous braking system analysis example, and discusses its potential role in future safety-critical autonomous AI systems. We argue that operational reasoning paradigms such as ReasonOps may become foundational infrastructure for next-generation trustworthy AI ecosystems.

Enterprise AI systems, built on large language models, retrieval pipelines and autonomous agents, introduce a class of risks that traditional software quality assurance was never designed to address. These systems are probabilistic, context-sensitive and emergent: they cannot be verified to be correct in the classical sense, but only evaluated with increasing confidence. This paper presents a comprehensive assurance strategy for enterprise AI systems built around three key principles: first, that AI testing should focus on continuous risk reduction rather than strict correctness verification; second, that evaluation must be treated as a core engineering discipline alongside development; and third, that failures in AI assurance can lead to organizational impacts that are fundamentally different from those seen in traditional deterministic software systems. We introduce a structured AI Failure Taxonomy, propose a revised five-layer AI Assurance Pyramid and provide operational guidance on evaluation-driven development, RAG system testing, model lifecycle management and governance. The goal is to equip engineering leaders and practitioners with a strategy that is both philosophically grounded and operationally deployable.