Geometry-aware neural causal discovery for large-scale spatiotemporal systems

Abstract

Causal discovery at large spatiotemporal scale is difficult: variables are physically embedded, candidate interactions grow quadratically with system size, and causal structure changes with system state. We introduce GeoDCD, a geometry-aware neural framework that uses spatial coordinates to initialize a learnable hierarchy and converts a trained nonlinear predictor into time-varying directed graphs through input-output Jacobian sensitivity analysis. On chaotic Lorenz-96 dynamics, GeoDCD attains an F1 score of 0.99, reducing structural Hamming distance by 36.8% relative to the strongest neural baseline, and still leads flat baselines when coordinates are uninformative. Runtime scales approximately linearly over the evaluated range, enabling discovery on a 10,512-node sea-level-pressure grid. Applied to observations, GeoDCD identifies circulation-consistent gateways, resolves El Nino/La Nina-dependent reorganization, and separates energy-to-traffic from traffic-to-energy influence in coupled electric-vehicle and road systems. Edges are neural-Granger sensitivities rather than interventional effects, positioning GeoDCD for mechanistic hypothesis generation where interventions are unavailable.