GMNO on MaxwellBench: Scaling Pretrained General Mesh Neural Operator Across Industrial-Standard Electromagnetism Simulations

Engineers routinely solve partial differential equations (PDEs) numerically to simulate physical phenomena and evaluate industrial designs. To alleviate the high computational cost of these simulations, neural operators have become a promising class of surrogate models for fast inference. While recent works have advanced neural operator architectures and begun to explore their scaling properties, most studies rely on heavily simplified PDE data that fail to reflect the structural complexity of industrial simulations. In practice, industrial simulation data have complex structure, require substantial domain expertise to interpret, and remain largely inaccessible to the broader machine learning community. We argue that a true foundation neural operator should generalize across industrial simulation scenarios that go far beyond simple parameter variations, while remaining governed by the same underlying PDEs. To bridge this gap, we introduce MaxwellBench, the first open-source industrial-standard benchmark comprising 14 datasets from distinct electromagnetism applications, and propose the General Mesh Neural Operator (GMNO), a neural operator with novel embedding architectures for handling complex multi-modal PDE data defined on meshes. We also develop a heterogeneous parallel training paradigm that enables large scale training on industrial-standard datasets. Extensive experiments show that GMNO consistently outperforms existing neural operator baselines on industrial-standard datasets. Furthermore, large scale pretraining yields strong out-of-distribution generalization, highlighting the promise of scaling neural operators on industrial applications.