How Topology Shapes the Phase Behavior of Polyelectrolytes

What the math gives to ML

The paper provides a differentiable, topology-dependent free-energy functional in which each component contributes through chain entropy, pairwise interactions, and a wavevector-resolved Coulomb correlation term. The transferable asset is the log-integral response, which couples all mixture fractions through a shared spectral quantity rather than imposing independent pairwise penalties. A practical neural-network adaptation is a topology-aware phase-separation regularizer for mixture embeddings or MoE experts, using differentiable quadrature to control whether representation groups specialize or remain mixed.