Sensoformer: Robust Sim-to-Real Inference on Variable-Geometry Sensor Sets via Physics-Structured Randomization

Inferring high-dimensional physical states from sparse, ad-hoc sensor arrays is a fundamental challenge across AI for Science and industrial IoT. Standard machine learning architectures struggle in these domains due to irregular, variable-cardinality sensor geometries and the profound sim-to-real distribution shift caused by unmodeled physical heterogeneities. To address these challenges, we propose Sensoformer, a set-attention framework integrated with Physics-Structured Domain Randomization (PSDR). By explicitly randomizing the underlying physical dynamics (e.g., propagation media, extreme noise, and network availability dropout) rather than just visual features, PSDR enforces the learning of domain-invariant physical operators. Using seismic source inversion as a rigorous real-world testbed, Sensoformer is pre-trained on 100,000 synthetics and evaluated on a highly complex real-world catalog. We demonstrate that Sensoformer achieves state-of-the-art precision and outperforms Message Passing Neural Networks (MPNNs) and Neural Operators (e.g., DeepONet) which struggle with extreme spatial sparsity and mixed-modality inputs. Furthermore, interpretability analysis reveals that the attention mechanism autonomously discovers optimal experimental design principles, dynamically prioritizing sparse orthogonal sensors to overcome information bottlenecks.