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Microfluidics enable high-precision and cost-effective processing of biological and chemical substances. However, designing and fabricating microfluidic chips typically requires substantial expertise and numerous design iterations, posing considerable barriers to entry for nonexperts. We introduce μFluidicGenius (μFG), an open-access, machine learning (ML)-augmented design tool that enables nonexpert users to rapidly create functional microfluidic circuits. Users simply define the spatial placement of reservoirs, specify the channel connections between them, and assign desired flow rates through this layout. Leveraging a hybrid algorithmic framework that integrates ML models with mathematical modeling, μFG automatically generates spatially coded maze structures that implement the precise fluidic resistances needed to meet the target flow distribution. These resistive elements are optimized to fit within the available geometry and can reproduce complex flow profiles, such as physiologically relevant flow rates in multi-organ-on-chip platforms. The resulting microfluidic designs are directly exportable for three-dimensional printing. Experimental validation demonstrates that μFG-generated circuits reproduce target flow distributions with 90% accuracy. By streamlining and automating microfluidic circuit creation, μFG not only lowers the barrier to entry for nonexperts but also showcases a principled and efficient application of ML to fluidic system design, enabling rapid and customizable development of complex microfluidic architectures.