Equivariant GNN-Decomposed Barrier Functions for Climate-Resilient Dynamic Resource Allocation

Abstract

Propose a novel framework for dynamic resource allocation under climate-induced uncertainties, reformulating the conventional centralized optimization as a distributed system of composable safety certificates. The core methodology replaces monolithic feasibility constraints with vector control barrier functions that are decomposed across infrastructure nodes using an equivariant graph neural network. This decomposition is achieved through a steerable message-passing architecture that propagates directional sensitivity gradients between neighboring nodes, thereby preserving global coherence through locally enforced safety conditions. Each node then executes a local constrained optimization, where the barrier function constraints are solved via a differentiable sequential least-squares programming layer that guarantees real-time tractability during rapid meteorological transitions. The equivariant property of the network ensures that spatial symmetries in climate data-such as rotations of wind fields or scaling of temperature profiles-are naturally respected, making the safety certificates robust to natural variations without additional data augmentation. Furthermore, the differentiable optimization layer permits end-to-end gradient flow, enabling reinforcement learning to jointly tune the barrier function parameters and the message-passing weights based on cumulative constraint violations and allocation equity. We demonstrate that this decomposed architecture transforms a historically monolithic and computationally intensive resource allocation problem into a set of lightweight, parallelizable local procedures. The significance of this work lies in its ability to provide strict safety guarantees for critical infrastructure-such as reservoirs, power substations, and supply depots-while operating under extreme climate stress