  Inertial fluid flow deformation around pillars in a microchannel is a new
method for controlling fluid flow. Sequences of pillars have been shown to
produce a rich phase space with a wide variety of flow transformations.
Previous work has successfully demonstrated manual design of pillar sequences
to achieve desired transformations of the flow cross-section, with experimental
validation. However, such a method is not ideal for seeking out complex
sculpted shapes as the search space quickly becomes too large for efficient
manual discovery. We explore fast, automated optimization methods to solve this
problem. We formulate the inertial flow physics in microchannels with different
micropillar configurations as a set of state transition matrix operations.
These state transition matrices are constructed from experimentally validated
streamtraces. This facilitates modeling the effect of a sequence of
micropillars as nested matrix-matrix products, which have very efficient
numerical implementations. With this new forward model, arbitrary micropillar
sequences can be rapidly simulated with various inlet configurations, allowing
optimization routines quick access to a large search space. We integrate this
framework with the genetic algorithm and showcase its applicability by
designing micropillar sequences for various useful transformations. We
computationally discover micropillar sequences for complex transformations that
are substantially shorter than manually designed sequences. We also determine
sequences for novel transformations that were difficult to manually design.
Finally, we experimentally validate these computational designs by fabricating
devices and comparing predictions with the results from confocal microscopy.
