Independent Latents, Robust Neural Operators

Neural operators have emerged as powerful surrogates for scientific computing, enabling rapid reconstruction of complex physical fields from sparse sensor observations. Despite their strong predictive capability, their reliability often degrades under noisy or corrupted measurements, limiting practical deployment in real-world sensing environments. We show that enforcing statistical independence in latent representations provides a simple yet effective mechanism for improving neural operator robustness. To this end, we introduce Neural Operator Independence Regularization (NOIR), an end-to-end training framework that promotes statistically independent latent features during operator learning. Unlike structured basis approaches such as POD-DeepONet and PCA-Net, which impose orthogonality primarily as an offline compression constraint, NOIR directly shapes latent representations during training to enhance resilience against input perturbations. Across three canonical PDE benchmarks and five additive sensor corruption settings, NOIR consistently improves reconstruction accuracy while preserving clean-data performance. Beyond predictive gains, the induced latent representations exhibit distinctive statistical signatures that reveal architecture-specific robustness characteristics under corruption. These findings identify latent statistical independence as a principled inductive bias for robust neural operator design and provide new insight into the internal structure of operator learning systems. All models, datasets, checkpoints, and training code are publicly available at \url{https://github.com/t55176853-cmyk/NOIR/}