# Event-driven physics-informed operator learning for reliability analysis

arXiv: https://arxiv.org/abs/2511.06083 · HTML: https://mlsanity.com/paper/2511.06083/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 8 Nov 2025.

## Builds on (most cited first, 17 of 17)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [NOMAD: Nonlinear Manifold Decoders for Operator Learning](https://mlsanity.com/paper/2206.03551/) (2022)
- [Physics informed WNO](https://mlsanity.com/paper/2302.05925/) (2023)
- [Rate Coding or Direct Coding: Which One is Better for Accurate, Robust, and Energy-efficient Spiking Neural Networks?](https://mlsanity.com/paper/2202.03133/) (2022)
- [Stochastic projection based approach for gradient free physics informed learning](https://mlsanity.com/paper/2209.13724/) (2022)
- [Neuroscience inspired scientific machine learning (Part-1): Variable spiking neuron for regression](https://mlsanity.com/paper/2311.09267/) (2023)
- [Generative adversarial wavelet neural operator: Application to fault detection and isolation of multivariate time series data](https://mlsanity.com/paper/2401.04004/) (2024)
- [Hybrid variable spiking graph neural networks for energy-efficient scientific machine learning](https://mlsanity.com/paper/2412.09379/) (2024)
- [Distribution free uncertainty quantification in neuroscience-inspired deep operators](https://mlsanity.com/paper/2412.09369/) (2024)

## Built on by (most cited first, 1 of 1)

- [SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications](https://mlsanity.com/paper/2603.21674/) (2026)

## Abstract (arXiv)

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, textitthe 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.