Physics-Guided Knowledge Graphs for Verifiable Wildfire Prediction

Machine learning models trained on historical fire data can violate basic physical laws, for example, by predicting fires in unreachable locations or assigning probabilities inconsistent with environmental conditions. These violations erode trust and hinder deployment in safety-critical settings where physical consistency is essential. This work introduces a verifiable wildfire prediction framework that couples a spatio-temporal knowledge graph with hard physics and reachability constraints enforced inside a convex optimization layer, yielding solver certificates with feasibility guarantees (Karush-Kuhn-Tucker (KKT) residuals \(\le 10^{-6}\) ) for every evaluation day. Multi-source geospatial data are fused via a knowledge graph capturing spatial connectivity and temporal dynamics. Physics constraints are imposed through a convex quadratic program (QP): reachability is computed via multi-source Dijkstra on a weighted spatial graph and encoded as linear equalities in the QP, rather than imposed post-hoc. To prevent unit mismatches, probability is tied to a normalized, unitless rate of spread, thereby preserving convexity. Applied to standard ML baselines, the framework improves prediction accuracy while enforcing 100% physics compliance, with solver certificates and daily audit artifacts providing operational accountability alongside performance metrics.