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Optimized sensing is important for computational imaging in low-resource environments, when images must be recovered from severely limited measurements. In this paper, we propose a physics-constrained, fully differentiable, autoencoder that learns a probabilistic sensor-sampling strategy for optimized sensor design. The proposed method learns a system's preferred sampling distribution that characterizes the correlations between different sensor selections as a binary, fully-connected Ising model. The learned probabilistic model is achieved by using a Gibbs sampling inspired network architecture, and is trained end-to-end with a reconstruction network for efficient co-design. The proposed framework is applicable to sensor selection problems in a variety of computational imaging applications. In this paper, we demonstrate the approach in the context of a very-long-baseline-interferometry (VLBI) array design task, where sensor correlations and atmospheric noise present unique challenges. We demonstrate results broadly consistent with expectation, and draw attention to particular structures preferred in the telescope array geometry that can be leveraged to plan future observations and design array expansions.