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

Shailesh Garg, Souvik Chakraborty

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 \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.

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

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 \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.
Paper Structure (14 sections, 51 equations, 9 figures, 10 tables, 2 algorithms)

This paper contains 14 sections, 51 equations, 9 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Conformalized Neuroscience-Inspired Bayesian Operator Network
  4. Analytical Study of Energy Efficiency of VSN Layers
  5. Compute Energy: Dense versus Event-Driven Execution
  6. Accumulation and Control Overhead
  7. Memory Access Energy
  8. Energy Model
  9. Numerical Analysis and Implications
  10. Numerical Illustration
  11. Example I: single DOF base isolator system
  12. Example II: Multi DOF system with nonlinear oscillator
  13. Example III: 76 DOF engineering system
  14. Conclusion

Figures (9)

  • Figure 1: Schematic for information flow in CoNBONet.
  • Figure 2: Ratio of energy consumed by densely connected ANN layer vs densely connected VSN layer, when run for a single Spike Time Step (STS). It is assumed that all output nodes will produce spikes.
  • Figure 3: Ratio of energy consumed by densely connected ANN layer vs densely connected VSN layer, when run for two STSs.
  • Figure 4: Mean prediction from the CoNBONet compared against the ground truth with calibrated confidence intervals shown as the blue patch, for example E-I.
  • Figure 5: Probability of failure at different time steps in example E-I.
  • ...and 4 more figures