CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis

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 $\mathit{\text{CoNBONet}}$, 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 $\mathbf{\text{Co}}$nformalized $\mathbf{\text{N}}$euroscience-inspired $\mathbf{\text{B}}$ayesian $\mathbf{\text{O}}$perator $\mathbf{\text{Net}}$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 $\mathit{\text{fast}}\mathit{\text{and}}\mathit{\text{energy-efficient}}\mathit{\text{inference}}$ enabled by a neuroscience-inspired network architecture, $\mathit{\text{calibrated}}\mathit{\text{uncertainty}}\mathit{\text{quantification}}\mathit{\text{with}}\mathit{\text{theoretical}}\mathit{\text{guarantees}}$ via split conformal prediction, and $\mathit{\text{strong}}\mathit{\text{generalization}}\mathit{\text{capability}}$ 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.