Sparse-view computed tomography (CT) reduces the number of acquired projections, but conventional sampling strategies are designed primarily for image reconstruction rather than for downstream physical inference. Here, we investigate optimal task-aware projection selection for directly predicting hemodynamics from sparse CT angiography (CTA) measurements. Using computational fluid dynamics simulations of intracranial aneurysms, we generate synthetic fan-beam CTA projections and train a Fourier neural operator (FNO) to predict two targets: the spatially resolved time-averaged wall shear stress (TAWSS) field and the spatially averaged TAWSS. The FNO was coupled with optimal input selection for simultaneous optimal sampling and training. Our goal was to investigate if agentic AI could discover optimal sampling strategies that outperform current methods. We compared fixed uniform and golden-angle sampling with three task-aware optimal selection strategies: Gumbel-Softmax, a Soft top-K method, and an agentic AI selector. The methods were compared at different view selection budgets. A detailed analysis of the AI agent was performed to understand its reasoning and performance. For spatially resolved TAWSS, Agentic and Soft top-K achieve the lowest mean errors (Agentic performs slightly better) and substantially outperform fixed sampling under extreme sparsity. For spatially averaged TAWSS, optimized selection becomes important at extremely sparse acquisitions. Analysis of the selected masks reveals multiple distinct subsets concentrated around informative regions. Moreover, masks optimized for hemodynamic prediction yield poor image reconstructions, showing that task-optimal acquisition differs fundamentally from reconstruction-optimal acquisition. This work suggests the possibility of designing sparse acquisitions directly around downstream physical quantities.

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