Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Model

2026-03-22

AI Summary

This work addresses the challenge of propagating interval uncertainty in engineering systems, which traditionally relies on computationally expensive optimization to determine output bounds. The authors reformulate this task as an interval-valued regression problem and propose using neural network surrogates to directly predict upper and lower output bounds, thereby avoiding repeated calls to costly simulations or optimization routines. For the first time, the study systematically investigates the application of both multilayer perceptrons (MLPs) and Deep Operator Networks (DeepONets) for interval prediction, comparing three strategies: standard propagation, IBP/CROWN bound propagation, and interval neural networks (INNs). Experimental results demonstrate that the proposed approach achieves comparable estimation accuracy while significantly improving computational efficiency, outperforming conventional optimization-driven methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

In engineering, uncertainty propagation aims to characterise system outputs under uncertain inputs. For interval uncertainty, the goal is to determine output bounds given interval-valued inputs, which is critical for robust design optimisation and reliability analysis. However, standard interval propagation relies on solving optimisation problems that become computationally expensive for complex systems. Surrogate models alleviate this cost but typically replace only the evaluator within the optimisation loop, still requiring many inference calls. To overcome this limitation, we reformulate interval propagation as an interval-valued regression problem that directly predicts output bounds. We present a comprehensive study of neural network-based surrogate models, including multilayer perceptrons (MLPs) and deep operator networks (DeepONet), for this task. Three approaches are investigated: (i) naive interval propagation through standard architectures, (ii) bound propagation methods such as Interval Bound Propagation (IBP) and CROWN, and (iii) interval neural networks (INNs) with interval weights. Results show that these methods significantly improve computational efficiency over traditional optimisation-based approaches while maintaining accurate interval estimates. We further discuss practical limitations and open challenges in applying interval-based propagation methods.

Problem

• uncertainty quantification
• interval propagation
• surrogate modeling
• output bounds
• robust design

Innovation

• interval propagation
• neural network surrogate
• uncertainty quantification
• interval regression
• DeepONet