Time-dependent reliability analysis of nonlinear dynamical systems under stochastic excitations is a critical yet computationally demanding task. Conventional approaches, such as Monte Carlo simulation, necessitate repeated evaluations of computationally expensive numerical solvers, leading to significant computational bottlenecks. To address this challenge, we propose \textit{CoNBONet}, a neuroscience-inspired surrogate model that enables fast, energy-efficient, and uncertainty-aware reliability analysis, providing a scalable alternative to techniques such as Monte Carlo simulations. CoNBONet, short for \textbf{Co}nformalized \textbf{N}euroscience-inspired \textbf{B}ayesian \textbf{O}perator \textbf{Net}work, leverages the expressive power of deep operator networks while integrating neuroscience-inspired neuron models to achieve fast, low-power inference. Unlike traditional surrogates such as Gaussian processes, polynomial chaos expansions, or support vector regression, that may face scalability challenges for high-dimensional, time-dependent reliability problems, CoNBONet offers \textit{fast and energy-efficient inference} enabled by a neuroscience-inspired network architecture, \textit{calibrated uncertainty quantification with theoretical guarantees} via split conformal prediction, and \textit{strong generalization capability} through an operator-learning paradigm that maps input functions to system response trajectories. Validation of the proposed CoNBONet for various nonlinear dynamical systems demonstrates that CoNBONet preserves predictive fidelity, and achieves reliable coverage of failure probabilities, making it a powerful tool for robust and scalable reliability analysis in engineering design.

翻译：摘要：随机激励下非线性动力系统的时变可靠性分析是一项关键但计算量庞大的任务。传统方法（如蒙特卡洛模拟）需要反复调用昂贵的数值求解器，导致显著的计算瓶颈。为应对这一挑战，我们提出了CoNBONet——一种神经科学启发的替代模型，能够实现快速、节能且具有不确定性感知的可靠性分析，为蒙特卡洛模拟等技术提供了可扩展的替代方案。CoNBONet（全称：一致性校正神经科学启发贝叶斯算子网络）既利用了深度算子网络的表达能力，又整合了神经科学启发的神经元模型，以实现快速、低功耗的推理。不同于高斯过程、多项式混沌展开或支持向量回归等传统替代模型在面向高维时变可靠性问题时可能面临的可扩展性挑战，CoNBONet通过神经科学启发的网络架构实现了快速节能的推理，借助分裂一致性预测提供了具有理论保障的校准不确定性量化，并通过将输入函数映射到系统响应轨迹的算子学习范式展现了强大的泛化能力。针对多种非线性动力系统的验证表明，CoNBONet在保持预测保真度的同时，实现了对失效概率的可靠覆盖，从而成为工程设计中鲁棒且可扩展的可靠性分析的有力工具。