AI models of unstable flow exhibit hallucination.

We identify hallucination in AI models of fluid dynamics using the canonical problem of hydrodynamically unstable transport known as viscous fingering. AI-based modeling of flow with instabilities remains challenging because rapidly evolving, multiscale fingering patterns are difficult to resolve accurately. We define hallucination in physics-based AI as a prediction that is visually coherent yet violates governing physical laws, analogous to hallucinations in large language models, and we identify solutions of this kind that appear visually realistic yet are physically implausible. These hallucinations manifest as spurious interface structures and nonphysical concentration patterns inconsistent with expected transport behavior. We observe that the presence and type of hallucination correlate with the spectral bias of AI models. Guided by this insight, we propose DeepFingers, a hybrid framework that combines the Fourier Neural Operator and Deep Operator Network to promote balanced learning across spatial modes and accurately predict the spatiotemporal evolution of viscous fingering. By conditioning on both time and viscosity contrast, DeepFingers learns mappings between successive concentration fields across regimes. The framework accurately captures tip splitting, finger merging, and channel formation while preserving global metrics of mixing. The results highlight the need for further investigation into the limitations of AI models for physical systems.