# Distribution free uncertainty quantification in neuroscience-inspired deep operators

arXiv: https://arxiv.org/abs/2412.09369 · HTML: https://mlsanity.com/paper/2412.09369/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 8 of 8)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [Calibrated Uncertainty Quantification for Operator Learning via Conformal Prediction](https://mlsanity.com/paper/2402.01960/) (2024)
- [Artificial intelligence for partial differential equations in computational mechanics: A review](https://mlsanity.com/paper/2410.19843/) (2024)
- [Spiking Neural Operators for Scientific Machine Learning](https://mlsanity.com/paper/2205.10130/) (2022)
- [Neuroscience inspired scientific machine learning (Part-1): Variable spiking neuron for regression](https://mlsanity.com/paper/2311.09267/) (2023)
- [Randomized prior wavelet neural operator for uncertainty quantification](https://mlsanity.com/paper/2302.01051/) (2023)
- [Energy-based physics-informed neural network for frictionless contact problems under large deformation](https://mlsanity.com/paper/2411.03671/) (2024)

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

- [Event-driven physics-informed operator learning for reliability analysis](https://mlsanity.com/paper/2511.06083/) (2025)

## Abstract (arXiv)

Energy-efficient deep learning algorithms are essential for a sustainable future and feasible edge computing setups. Spiking neural networks (SNNs), inspired from neuroscience, are a positive step in the direction of achieving the required energy efficiency. However, in a bid to lower the energy requirements, accuracy is marginally sacrificed. Hence, predictions of such deep learning algorithms require an uncertainty measure that can inform users regarding the bounds of a certain output. In this paper, we introduce the Conformalized Randomized Prior Operator (CRP-O) framework that leverages Randomized Prior (RP) networks and Split Conformal Prediction (SCP) to quantify uncertainty in both conventional and spiking neural operators. To further enable zero-shot super-resolution in UQ, we propose an extension incorporating Gaussian Process Regression. This enhanced super-resolution-enabled CRP-O framework is integrated with the recently developed Variable Spiking Wavelet Neural Operator (VSWNO). To test the performance of the obtained calibrated uncertainty bounds, we discuss four different examples covering both one-dimensional and two-dimensional partial differential equations. Results demonstrate that the uncertainty bounds produced by the conformalized RP-VSWNO significantly enhance UQ estimates compared to vanilla RP-VSWNO, Quantile WNO (Q-WNO), and Conformalized Quantile WNO (CQ-WNO). These findings underscore the potential of the proposed approach for practical applications.