Najafi, HosseinMortensen Steagall, Marcos2025-11-032025-11-032025-06-17LINK PRAXIS, ISSN: 3021-1131 (Online), Auckland University of Technology (AUT) Library, 3(1), 222-247. doi: 10.24135/link-praxis.v3i1.493021-1131http://hdl.handle.net/10292/20042Heuristic inquiry, rooted in experiential and iterative exploration, plays a central role for both artistic research and artificial intelligence (AI) research. This article provides a guide for supervising PhD projects that incorporate heuristic inquiry in their creative and computational transdisciplinary contexts. Drawing on transdisciplinary literature and research examples, it addresses how supervisors can support students through to approach AI for their creative projects with an informed approach. Key topics include embracing uncertainty, heuristic iteration, intuitive problem-solving, supporting interdisciplinary learning, and navigating the epistemological challenges using heuristic methods. By mapping structural and methodological convergences between artistic and AI domains, this article aims to equip supervisors with adaptable tools to nurture complex, innovative, and practice-led doctoral projects.Copyright (c) 2025 Hossein Najafi; Marcos Mortensen Steagall (Translator). This work is licensed under a Creative Commons Attribution 4.0 International License.Artificial intelligenceartistic researchheuristic inquiryPhD supervisionpractice-led researchJournal ArticleOpenAccess10.24135/link-praxis.v3i1.49