(134a) Hybrid Mechanistic Multi-Stage Game Theory for Proactive and Adaptive Gas Utilization Under Uncertainty

The shift to a low-carbon economy necessitates a resilient and adaptive hydrogen supply chain capable of enduring renewable energy intermittency, demand surges, and infrastructure challenges [1-4]. This work introduces a multi-stage optimization framework that combines Inverse Physics-Informed Neural Networks (IPINNs) with advanced game-theoretic approaches to proactively enhance resilience across hydrogen production, storage, and distribution. IPINNs integrate mechanistic parameters—such as hydrogen flow rates, pressure dynamics, thermal behavior, and storage resilience—within a data-driven optimization process, using inverse design to translate resilience objectives, such as supply continuity and fault tolerance, back to actionable operational parameters.

The multi-stage structure comprises an outer loop for proactive, strategic planning and an inner loop for adaptive real-time responses. In the outer loop, cooperative game theory models [5] align stakeholders—hydrogen producers, storage operators, and distributors—around joint resilience goals, incentivizing coalition formation to optimize resource allocation, manage shared reserves, and equitably distribute resilience costs. This collaborative setup fosters mutual gains by encouraging shared infrastructure investments and pooled emergency reserves to anticipate and buffer against potential disruptions. In contrast, the inner loop leverages dynamic, non-cooperative game theory to manage time-dependent adaptation, where each stakeholder employs mixed strategies to maximize resilience individually in real-time. For example, hydrogen producers adjust output based on fluctuating renewable inputs, storage facilities fine-tune inventory to meet downstream demand, and distributors dynamically optimize routing to handle load variability. Feedback loops ensure that actions by one stakeholder initiate corresponding adjustments by others, creating a self-stabilizing network capable of mitigating operational shocks.

The complex interactions in each stage yield a Mixed-Integer Nonlinear Programming (MINLP) challenge [6], further complicated by the high dimensionality and non-linearity inherent to game-theoretic formulations. We address this with advanced decomposition techniques, such as Benders decomposition [7] and column-and-constraint generation [8], breaking the problem into tractable sub-problems and enhancing scalability. Furthermore, a hybrid approach combining robust optimization with multi-agent reinforcement learning (MARL) [9] enables stakeholders to learn optimal adaptive strategies through simulated interactions, autonomously generating resilient strategies that accommodate infrastructure failures, renewable fluctuations, and demand spikes. Simulation results demonstrate that our IPINN and game-theory-based model outperforms traditional deterministic and scenario-based models, delivering up to a 30% improvement in supply chain stability and adaptability. By integrating physics-based modeling with a structured game-theoretic strategy, this framework represents a critical advancement in establishing a proactive, adaptive, and resilient hydrogen supply chain essential for a sustainable energy transition.

References

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[7] F. You, I.E. Grossmann, Multicut Benders decomposition algorithm for process supply chain planning under uncertainty, Annals of Operations Research 210 (2013) 191-211.

[8] B. Zeng, L. Zhao, Solving two-stage robust optimization problems using a column-and-constraint generation method, Operations Research Letters 41 (2013) 457-461.

[9] K. Zhang, Z. Yang, T. Başar, Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms, in: K.G. Vamvoudakis, Y. Wan, F.L. Lewis, D. Cansever (Eds.) Handbook of Reinforcement Learning and Control, Springer International Publishing, Cham, 2021, pp. 321-384.