The arms industry as a commercial determinant of health in the Middle East: a call for research.

Hydrodynamic instabilities such as viscous fingering influence many natural and engineered systems, including chemical, pharmaceutical, food processing, mantle convection, and groundwater systems. Viscous fingering arises at the interface between two fluids of differing viscosities when a less viscous fluid displaces a more viscous fluid. This instability occurs both in porous media and in confined non-porous geometries such as Hele-Shaw cells. This classical fluid mechanics phenomenon, primarily driven by the Saffman–Taylor instability, has been extensively studied in both miscible and immiscible fluid systems. In miscible flow displacements, such as water displacing glycerin in Hele-Shaw cells or CO displacing crude oil or water in petroleum or geothermal reservoirs, the advancing interface evolves into intricate finger-like patterns that grow increasingly complex as the instability develops throughout the domain. Accurate prediction of such instabilities is crucial for numerous applications, including enhanced oil recovery, CO sequestration, groundwater remediation, hydraulic fracturing, and the design of microfluidic systems in biomedical engineering. Uncontrolled finger propagation can significantly degrade operational performance by prolonging contaminant removal, reducing reservoir sweep efficiency, and increasing the amount of CO required for effective sequestration. On the other hand, enhancement of fingering has been proposed as a mechanism for faster mixing under laminar flow conditions. Recently, the complexity and randomness of the fingers have been utilized to propose an anti-counterfeiting technology. Predicting viscous fingering is challenging because small perturbations can rapidly evolve into complex flow patterns across multiple scales. Numerical simulation of viscous fingering presents notable challenges due to the nonlinear and multiscale nature of the phenomenon. The system is governed by coupled partial differential equations (PDEs) derived from the conservation of mass and momentum. These equations link physical parameters such as fluid viscosity and density to the evolving state variables like the fluid concentration field. Through non-dimensionalization, key dimensionless groups such as the viscosity ratio and the Peclet number Pe emerge to characterize the dynamics of the instability. Solving these PDEs over large domains (equivalently, large Pe) and large viscosity ratios often relies on direct numerical simulation (DNS) techniques, commonly employing finite volume or finite element methods for spatial discretization, along with time-stepping schemes such as Euler integration. However, due to the sensitivity of the flow to perturbations in medium properties and initial conditions and the complex feedback between advection and diffusion, many simulations diverge from experimental or field-scale observations, particularly as fingering patterns evolve into highly intricate structures. Recent progress in AI modeling of fluid flow, especially deep learning models, offers promise in addressing these challenges. This study demonstrates that deep learning models can produce visually convincing predictions that nonetheless violate fundamental physical principles, a failure mode analogous to hallucinations in large language models. Hallucination of AI models has been extensively documented and studied in large language models, prompting major efforts to understand its societal impact and develop mitigation strategies. By contrast, this class of error has received little explicit attention in AI models of physical systems: hallucination has not previously been defined for scientific models, and the field has largely relied on aggregate error metrics that often perform adequately, leaving physically inconsistent yet visually coherent predictions uncharacterized. We define hallucination in AI models of fluid flow as a model prediction that is visually coherent and statistically plausible yet violates governing physical laws or known flow dynamics, and whose error cannot be attributed to known numerical or discretization artifacts of a reference solver. Guided by this definition, we identify and systematically characterize hallucination in AI models of fluid dynamics. Using modern architectures including Vision Transformers (ViT), we demonstrate that AI models trained to predict viscous fingering dynamics can exhibit physically inconsistent behavior despite maintaining visual coherence. We further link hallucination in fluid-dynamics AI models to spectral bias, wherein learning architectures disproportionately favor certain length scales at the expense of others: across models, the presence and type of hallucination track the direction of spectral imbalance.