Distribution free uncertainty quantification in neuroscience-inspired deep operators

TL;DR

This paper introduces a novel uncertainty quantification framework for neuroscience-inspired deep operators, combining conformal prediction, randomized priors, and super-resolution techniques to improve reliability in PDE predictions.

Contribution

It proposes the CRP-O framework integrating RP networks and SCP for uncertainty quantification in neural operators, with an extension for super-resolution using Gaussian Processes.

Findings

Uncertainty bounds significantly outperform existing methods.

Enhanced super-resolution improves UQ accuracy.

Framework applicable to PDE problems in 1D and 2D.

Abstract

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.