Graph Transfer Learning via Shared Latent Geometry: Theory and Applications

2026-05-30

AI Summary

This work addresses the high computational cost of repeatedly solving numerical optimization problems in physical system deployment and the lack of quantifiable transfer guarantees in existing physics-informed learning methods, which often distort latent-space geometry during fine-tuning. The authors propose an asymmetric dual-path architecture: a teacher encoder extracts operator polynomial features from high-fidelity simulations, while a student encoder aligns its latent geometry with sparse field data and operator descriptors. At deployment, only the frozen student model is used, enabling single forward inference with certifiable transfer. By unifying latent-space geometry and operator spectral stability, the study establishes the first theoretical framework for cross-instance zero-shot transfer, providing near-necessary and sufficient conditions based on Wasserstein distance and a finite-sample certification protocol. Evaluated on power system state estimation, the method achieves zero-shot transfer to 100 unseen topologies with 95% certification success, matching Newton-Raphson accuracy at sub-millisecond inference latency.

Abstract

Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time. Physics-informed learning moves this cost to training, but uses a single encoder pathway whose latent geometry de-learns under fine-tuning and admits no quantitative transfer guarantee. We propose an asymmetric two-pathway architecture that resolves both issues. A teacher encoder consumes privileged dense states from a high-fidelity simulator and represents the system through operator-polynomial features stable under spectral perturbation; a student encoder learns the same latent geometry from sparse field data and operator descriptors. At deployment the teacher is discarded, and the frozen student runs in a single forward pass with a transfer certificate. The design connects to privileged-information learning, knowledge distillation, and cross-modal distillation, but targets cross-instance transfer rather than fixed-instance prediction: topology and operator may change, while the latent task does not. We establish sufficient and near-necessary transfer conditions via Wasserstein proximity between latent laws, yielding a zero-shot error bound, and develop a finite-sample certification protocol with active expansion when coverage is incomplete. The framework applies wherever a system admits an operator with reportable spectrum. On power-system estimation, it achieves zero-shot transfer to 100 unseen topologies, a 95% certificate pass rate, accuracy competitive with topology-aware Newton--Raphson, and sub-millisecond inference. These results suggest asymmetric pathways plus operator-anchored latent geometry provide a foundation for certified zero-shot inference and control.

Problem

• graph transfer learning
• zero-shot inference
• latent geometry
• cross-instance transfer
• physics-informed learning

Innovation

• asymmetric two-pathway architecture
• operator-polynomial features
• latent geometry transfer
• zero-shot certification
• Wasserstein proximity