General-Purpose Inverse Design of Heterogeneous Finite-Sized Assemblies

Designing heterogeneous, self-assembling systems is a central challenge in soft matter and biology. We present a framework that uses gradient-based optimization to invert an analytical yield calculation, tuning systems toward target equilibrium yields. We design systems ranging from simple dimers to temperature-controlled shells to polymerizing systems, achieving precise control of self- and non-self-limiting assemblies. By operating directly on closed-form calculations, our framework bypasses trajectory-based instabilities and enables efficient optimization in challenging regimes.