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Numerical simulations have revolutionized material design. However, although simulations excel at mapping an input material to its output property, their direct application to inverse design has traditionally been limited by their high computing cost and lack of differentiability. Here, taking the example of the inverse design of a porous matrix featuring targeted sorption isotherm, we introduce a computational inverse design framework that addresses these challenges, by programming differentiable simulation on TensorFlow platform that leverages automated end-to-end differentiation. Thanks to its differentiability, the simulation is used to directly train a deep generative model, which outputs an optimal porous matrix based on an arbitrary input sorption isotherm curve. Importantly, this inverse design pipeline leverages the power of tensor processing units (TPU)—an emerging family of dedicated chips, which, although they are specialized in deep learning, are flexible enough for intensive scientific simulations. This approach holds promise to accelerate inverse materials design.