[Paper Review] CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis

Shailesh Garg, Souvik Chakraborty|arXiv (Cornell University)|Mar 23, 2026

Probabilistic and Robust Engineering Design0 citations

TL;DR

CoNBONet is a neuroscience-inspired, energy-efficient Bayesian operator network with split conformal prediction, designed for fast, uncertainty-aware time-dependent reliability analysis of nonlinear dynamical systems. It uses Variable Spiking Neurons within a DeepONet framework to learn input–output operators and calibrates predictive intervals for reliability estimates.

ABSTRACT

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 extit{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 extbf{Co}nformalized extbf{N}euroscience-inspired extbf{B}ayesian extbf{O}perator extbf{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 extit{fast and energy-efficient inference} enabled by a neuroscience-inspired network architecture, extit{calibrated uncertainty quantification with theoretical guarantees} via split conformal prediction, and extit{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.

Motivation & Objective

• Motivate reliability analysis for nonlinear, high-dimensional dynamical systems under stochastic loading and the computational bottlenecks of Monte Carlo methods.
• Develop a surrogate operator learning framework that is energy-efficient and uncertainty-aware for time-dependent responses.
• Incorporate neuroscience-inspired Variable Spiking Neurons into a DeepONet architecture to achieve sparse, event-driven inference.
• Introduce Bayesian treatment of network weights to enable predictive uncertainty estimation, enhanced by split conformal prediction for calibrated intervals.
• Demonstrate the approach on single-DOF and multi-DOF nonlinear systems to validate predictive fidelity and calibrated failure-probability estimates.

Proposed method

• Adopt DeepONet to learn the input function f(t;ξ) → system response u(t;ξ) with branch (input) and trunk (time) networks.
• Replace dense activations with Variable Spiking Neurons in the branch network to enable event-driven, energy-efficient computation.
• Introduce a Bayesian treatment of network weights with variational inference to obtain predictive mean and variance for u.
• Apply reparameterization and a loss based on ELBO to train the probabilistic network, enabling posterior-weight sampling for predictions.
• Calibrate uncertainty via split conformal prediction using a separate calibration dataset to produce time-step specific prediction intervals.
• Provide an algorithm for training CoNBONet (Algorithm 1) and for time-dependent reliability estimation (Algorithm 2).

Experimental results

Research questions

• RQ1 Can CoNBONet accurately learn time-dependent input–output operators for stochastic loading scenarios?
• RQ2 Do Variable Spiking Neurons within DeepONet provide substantial energy efficiency gains without sacrificing predictive fidelity?
• RQ3 Can Bayes and conformal prediction provide reliable, calibrated uncertainty quantification for reliability estimates like first time-to-failure?
• RQ4 How does CoNBONet perform on single-DOF and multi-DOF nonlinear dynamical systems compared with traditional surrogates?
• RQ5 What are the theoretical and practical implications of calibrating prediction intervals for time-dependent reliability?

Key findings

• CoNBONet combines neuroscience-inspired computation with Bayesian operator learning to enable fast, energy-efficient, uncertainty-aware reliability analysis.
• Split conformal prediction calibrates predictive intervals, ensuring calibrated failure-probability estimates at target confidence levels.
• Validation on nonlinear dynamical systems shows preserved predictive fidelity and calibrated reliability estimates under sparse event-driven communication.
• The framework provides theoretically guaranteed coverage for new data via conformal calibration, under exchangeability assumptions.
• Energy-efficiency analysis suggests substantial reductions in computation energy when input activity is sparse, with potential further gains on neuromorphic hardware.