Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators

TL;DR

This paper introduces a combined active learning and input denoising approach to enhance the robustness of neural operators against adversarial attacks, crucial for safety-critical applications.

Contribution

It proposes a novel synergistic defense method that adaptively targets vulnerabilities and filters adversarial noise, significantly improving neural operator robustness.

Findings

Achieves 87% reduction in combined error on viscous Burgers' equation benchmark.

Outperforms standalone active learning and input denoising methods.

Suggests architecture-dependent training data is essential for robustness.

Abstract

Neural operators have emerged as fast surrogate models for physics simulations, yet they remain acutely vulnerable to adversarial perturbations, a critical liability for safety-critical digital twin deployments. We present a synergistic defense that combines active learning-based data generation with an input denoising architecture. The active learning component adaptively probes model weaknesses using differential evolution attacks, then generates targeted training data at discovered vulnerability locations while an adaptive smooth-ratio safeguard preserves baseline accuracy. The input denoising component augments the operator architecture with a learnable bottleneck that filters adversarial noise while retaining physics-relevant features. On the viscous Burgers' equation benchmark, the combined approach achieves a 2.04% combined error (1.21% baseline + 0.83% robustness), representing an 87% reduction relative to standard training (15.42% combined) and outperforming both active learning alone (3.42%) and input denoising alone (5.22%). More broadly, our results, combined with cross-architecture vulnerability analysis from prior work, suggest that optimal training data for neural operators is architecture-dependent: because different architectures concentrate sensitivity in distinct input subspaces, uniform sampling cannot adequately cover the vulnerability landscape of all models. These findings have potential implications for the deployment of neural operators in safety-critical energy systems including nuclear reactor monitoring.