Uncertainty-Informed Meta Pseudo Labeling for Surrogate Modeling with Limited Labeled Data

Deep neural networks, particularly neural operators, provide an efficient alternative to costly simulations in surrogate modeling. However, their performance is often constrained by the need for large-scale labeled datasets, which are costly and challenging to acquire in many scientific domains. Semi-supervised learning reduces label reliance by leveraging unlabeled data yet remains vulnerable to noisy pseudo-labels that mislead training and undermine robustness. To address these challenges, we propose a novel framework, Uncertainty-Informed Meta Pseudo Labeling (UMPL). The core mechenism is to refine pseudo-label quality through uncertainty-informed feedback signals. Specifically, the teacher model generates pseudo labels via epistemic uncertainty, while the student model learns from these labels and provides feedback based on aleatoric uncertainty.