Designer Porous Media: Porous Media Topology Optimization with Automatic Differentiation*

Porous media are widely used in industrial processes for mixing, filtration, and separation. Tailoring the topology of porous media to achieve specific flow characteristics is a high dimensional optimization problem that can be intractable to solve with existing methods. By implementing a fully-differentiable Navier-Stokes solver that accounts for the presence of solid obstacles and enables efficient computation of gradients through fluid simulations, we develop a versatile technique for designing porous media for a wide range of applications. In contrast to the use of machine learning for inverse design, this method is fully physics-based and does not require learning from data. With this technique, we solve various inverse problems, ranging from finding porous media designs that optimize dispersion and mixing to flow sculpting — designing the placement of obstacles in a flow to shape tracer particles into target configurations. We also demonstrate progress toward designing an analog fluid classifier in a porous medium.