Event-driven physics-informed operator learning for reliability analysis

TL;DR

NeuroPOL addresses the computational bottleneck in reliability analysis under uncertainty for high-dimensional, nonlinear multiphysics PDEs by replacing the costly full solution operator with a neuroscience-inspired, energy-efficient neural operator. It combines Wavelet Neural Operators with Variable Spiking Neurons and physics-informed losses, using a stochastic projection for gradient estimation to handle non-smoothed spiking dynamics. In five canonical PDEs (Burgers, Nagumo, Poisson, Darcy, Navier–Stokes with energy), NeuroPOL matches or closely mirrors Monte Carlo and vanilla PIWNO performance while significantly reducing energy consumption through lower spiking activity. This enables real-time reliability assessment and edge-enabled digital twins, with accurate estimates of $p_f$ and FPFT distributions.

Abstract

Reliability analysis of engineering systems under uncertainty poses significant computational challenges, particularly for problems involving high-dimensional stochastic inputs, nonlinear system responses, and multiphysics couplings. Traditional surrogate modeling approaches often incur high energy consumption, which severely limits their scalability and deployability in resource-constrained environments. We introduce NeuroPOL, \textit{the first neuroscience-inspired physics-informed operator learning framework} for reliability analysis. NeuroPOL incorporates Variable Spiking Neurons into a physics-informed operator architecture, replacing continuous activations with event-driven spiking dynamics. This innovation promotes sparse communication, significantly reduces computational load, and enables an energy-efficient surrogate model. The proposed framework lowers both computational and power demands, supporting real-time reliability assessment and deployment on edge devices and digital twins. By embedding governing physical laws into operator learning, NeuroPOL builds physics-consistent surrogates capable of accurate uncertainty propagation and efficient failure probability estimation, even for high-dimensional problems. We evaluate NeuroPOL on five canonical benchmarks, the Burgers equation, Nagumo equation, two-dimensional Poisson equation, two-dimensional Darcy equation, and incompressible Navier-Stokes equation with energy coupling. Results show that NeuroPOL achieves reliability measures comparable to standard physics-informed operators, while introducing significant communication sparsity, enabling scalable, distributed, and energy-efficient deployment.

Figures (8)

• Figure 1: Schematic for the information flow during NeuroPOL training. The model takes spatio-temporal inputs defined on a discretized grid and produces outputs using the VSN augmented WNO architecture. Training involves multiple loss components, including data loss and physics based loss. To enable gradient-based optimization, discontinuities in the VSN are approximated using a surrogate functions, and their gradients are used during backpropagation.
• Figure 2: Representative examples from the test dataset comparing NeuroPOL predictions with ground truth for Burgers PDE in example, E-I. The first row shows ground truth data, the second row the corresponding predictions, and the third row the absolute error.
• Figure 3: Comparison of FPFT PDFs obtained corresponding to different thresholds for the Burgers PDE in example, E–I. Each sub-figure contrasts the true PDF with those obtained using NeuroPOL predictions and PIWNO predictions.
• Figure 4: Representative examples from the test dataset comparing NeuroPOL predictions with ground truth for Nagumo PDE in example, E-II. The first row shows ground truth data, the second row the corresponding predictions, and the third row the absolute error.
• Figure 5: Comparison of FPFT PDFs obtained corresponding to different thresholds for the Nagumo PDE in example, E–II. Each sub-figure contrasts the true PDF with those obtained using NeuroPOL predictions and PIWNO predictions.