Operator Boosting Creates Compact, Accurate PDE Surrogates

Neural operators are widely employed as surrogate solution maps for partial differential equations (PDEs), but their full-size versions can be computationally expensive for storage, deployment, and evaluation in scientific workflows requiring many queries. This research addresses this challenge by introducing Operator Boosting, a novel stagewise residual-learning framework. Instead of training a large model and then compressing it, Operator Boosting directly constructs compact neural-operator surrogates. The method begins with an empirical mean predictor and then iteratively trains a sequence of small, same-family neural operators on the residual fields. Each correction is incorporated with a validation-selected shrinkage factor. The framework was instantiated with various neural operator types, including Fourier neural operators (FNOs), DeepONets, and convolutional neural operators (CNOs). Across 30 dataset-architecture pairs, the boosted tiny stacks demonstrated positive mean accuracy gains in many cases, while consistently reducing the trainable parameter count by approximately 72-95%. Empirical Pareto improvements were observed on several PDE benchmarks, indicating that Operator Boosting often enhances the accuracy-parameter trade-off for neural PDE surrogates.