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Abstract

In computational design and fabrication, neural networks are becoming
important surrogates for bulky forward simulations. A long-standing,
intertwined question is that of inverse design: how to compute a design that
satisfies a desired target performance? Here, we show that the piecewise linear
property, very common in everyday neural networks, allows for an inverse design
formulation based on mixed-integer linear programming. Our mixed-integer
inverse design uncovers globally optimal or near optimal solutions in a
principled manner. Furthermore, our method significantly facilitates emerging,
but challenging, combinatorial inverse design tasks, such as material
selection. For problems where finding the optimal solution is not desirable or
tractable, we develop an efficient yet near-optimal hybrid optimization.
Eventually, our method is able to find solutions provably robust to possible
fabrication perturbations among multiple designs with similar performances.