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This paper introduces a synergistic defense against adversarial attacks on neural operators, combining active learning with input denoising. Active learning uses differential evolution to identify model vulnerabilities and generate targeted training data, while input denoising employs a learnable bottleneck to filter adversarial noise. Results on the viscous Burgers' equation demonstrate an 87% reduction in combined error compared to standard training, highlighting the effectiveness of the combined approach.
Uniform sampling fails to adequately cover the vulnerability landscape of neural operators, as optimal training data is architecture-dependent, necessitating targeted data generation strategies.
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.
