Catastrophic Jump Phenomena in Infrastructure Deterioration: Overcoming Analytical Breakdown via RNNs and Billion-Scale Simulations

Background and Objective: The deterioration process of infrastructure is increasingly modeled to include sudden extreme risks (jump phenomena) that lead to sudden collapses. Mathematically formulating these non-continuous transitions as partial integro-differential equations (PIDEs) introduces significant computational challenges due to the non-locality of the integral term, complicating analytical derivations for optimal inspection intervals. This study aims to construct a theoretical computational framework to evaluate the boundaries of existing analytical methods and explore AI-based dynamic maintenance strategies under assumed jump–diffusion scenarios. Approach and Methodology: To address these computational challenges, this study first evaluates continuous degradation limits using perturbation methods and Physics-Informed Neural Networks (PINNs) on synthetic datasets as a baseline. Subsequently, we propose an AI-based dynamic maintenance strategy utilizing a recurrent neural network (RNN) architecture designed to reconstruct the deterioration context from sparse sequential observation histories. To analyze the extreme risks driven by the assumed non-local jumps, we executed ultra-large-scale Monte Carlo simulations reaching N=109 iterations, numerically comparing the RNN approach with simple state-threshold rules (Markovian approaches) under idealized conditions. Conclusions and Social Significance: The computational experiments demonstrated that within the synthetic framework, the RNN-based strategy yielded a theoretical jump-miss error rate of 2.74%. However, because this outcome relies heavily on increased unconstrained inspection frequencies and the network’s ability to identify synthetic correlations rather than genuine physical precursors, it serves as an illustrative proxy rather than a fully controlled comparison. Furthermore, the jump intensity distributions and cost models lack empirical justification from field data. Despite these fundamental limitations, this research provides a conceptual numerical baseline for integrating deep learning with stochastic jump–diffusion models, highlighting the critical need for rigorous empirical benchmarks in future dynamic asset management studies.