Topology-Aware Neural Graph Operator (TANGO) for Material Constitutive Laws

This work introduces TANGO (Topology-Aware Neural Graph Operator), a graph-based operator learning framework for predicting nonlinear mechanical response in disordered material networks. TANGO represents material networks as graphs, exemplified with polymer gels where nodes encode polymer chains or crosslinkers and edges distinguish chemical bonds from physical entanglements. Strain-conditioned, attention-based message passing propagates topological and local structural information, producing graph embeddings that a decoder maps to continuous stress-strain functions. Trained on coarse-grained molecular dynamics simulations of polymer networks, TANGO accurately predicts full stress-strain curves, recovers key mechanical properties (elastic modulus, ultimate strength, work to failure), and generalizes to unseen chain lengths. Inference is over five orders of magnitude faster than simulations, enabling high-throughput evaluation of network designs. These results demonstrate that topology-aware operator learning can efficiently capture nonlinear, connectivity-dependent mechanics in disordered materials, bridging graph representation learning and constitutive modeling.