GradNet: A Gradient-Based Framework for Optimal Network Science

TL;DR

GradNet is a gradient-based optimization framework that designs and analyzes network architectures by treating topology as a differentiable object, revealing how optimal structures emerge from resource constraints across diverse systems.

Contribution

This paper introduces GradNet, a novel AI-enabled framework that optimizes network topology for various dynamical objectives under constraints, unifying network design and analysis.

Findings

Emergence of canonical network features from constrained optimization

Sparse bipartite structures optimize synchronization in oscillator networks

Factional splits in social networks and minimal spanning trees in quantum networks are reproduced

Abstract

Network science has traditionally examined how structure determines dynamics. Here we invert this paradigm: we ask how functional dynamics and resource constraints shape network architecture. We introduce GradNet, an AI-enabled optimization framework that treats network topology as a continuously differentiable object. This allows designing networks that optimize arbitrary dynamical objectives, from synchronization to communication capacity, under realistic constraints. Applying this framework across diverse systems reveals that canonical network features emerge spontaneously from constrained optimization rather than requiring explicit imposition. Optimizing Kuramoto oscillator synchronization under fixed coupling budgets produces sparse, bipartite, frequency-disassortative architectures that eliminate classical synchronization thresholds. Minimizing social tension in opinion dynamics reproduces the empirically observed factional split in Zachary's karate club network. Maximizing entanglement distribution in spatial quantum networks under distance-dependent costs recovers minimum spanning tree architectures. These results demonstrate that optimization acts as both an engineering tool for network design, scalable to networks exceeding $10^5$ nodes, and a scientific probe revealing fundamental structure-function relationships. By recasting network architecture as the solution to constrained optimization problems, this variational perspective offers a unified framework connecting network analysis, design, and inference across physical, biological, and technological systems.