The integration of Artificial Intelligence (AI) into computational science (CS) and computational fluid dynamics (CFD) has raised profound epistemological debates concerning the nature of knowledge and its effectiveness in science. A central question in this discourse is whether AI can rival, or potentially surpass, the effectiveness of traditional mathematical methods in addressing the intricate challenges of CFD. In this work, I examine the concept of effectiveness within this context, highlighting the fundamental epistemological distinctions between AI-driven approaches and classical mathematical techniques. First, this analysis identifies four foundational pillars of effectiveness (PoEs) in scientific methods: (i) symmetries, which impose internal structure and coherence; (ii) scale separation, allowing specific treatments for the different scales and their interactions; (iii) sparsity, which simplifies complexity and enhances explicability; and (iv) semantic significance, which fosters abstraction, reasoning and interpretability. Yet, unlike mathematics where rigour ensures credibility by default, AI methods raise additional concerns of robustness and trust. Therefore, beyond the four PoEs, I also discuss credibility as a complementary pillar essential for the adoption of AI in the CFD community. The next critical step is to assess whether, and to what extent, AI can emulate or even outperform the roles and functions traditionally fulfilled by mathematical models. I therefore systematically review if, and how, these four pillar of effectiveness can be applied to AI-based algorithms. I show that those pillars are actually declined in a succession of technical advances that have shown promising results when using AI in CFD.
Michaël Bauerheim (2026) studied this question.