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

2026-08-11

AI Summary

Causal discovery in large-scale spatiotemporal systems is challenged by physical embedding of variables, quadratic growth of candidate interactions with system size, and time-varying causal structures. To address these issues, this work proposes GeoDCD, a novel framework that introduces geometric priors into neural causal discovery for the first time. GeoDCD leverages spatial coordinates to construct a learnable hierarchical structure and generates time-varying directed causal graphs through Jacobian sensitivity analysis of input–output mappings in a nonlinear predictor. The method enables linearly scalable inference and formulates mechanistic hypotheses without requiring interventional data. Evaluated on the Lorenz-96 system, GeoDCD achieves an F1 score of 0.99 and reduces structural Hamming distance by 36.8% compared to the best neural baseline. It further demonstrates scalability and physical plausibility by successfully identifying coherent causal pathways in real-world systems, including a ten-thousand-node sea-level pressure grid and a tram–road coupled network.

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.

Problem

• causal discovery
• spatiotemporal systems
• large-scale
• geometry-aware
• time-varying causal structure

Innovation

• geometry-aware causal discovery
• neural Jacobian sensitivity
• spatiotemporal dynamics
• learnable hierarchy
• neural Granger causality