Title: Graph Transfer Learning via Shared Latent Geometry: Theory and Applications

Abstract:

Deploying engineered physical systems often incurs substantial computational overhead during operation. Components such as schedulers, observers, model-predictive controllers, inverse-problem solvers, and state estimators typically lack closed-form solutions. Consequently, they are forced to numerically re-optimize for every single instance, requiring the operator to be re-provided each time. While physics-informed learning attempts to shift this burden to the training phase, it generally relies on a single encoder pathway. This approach suffers from latent geometry degradation during fine-tuning and offers no quantitative guarantees for transferability.

To address these limitations, we introduce an asymmetric two-pathway architecture. In this framework, a teacher encoder processes privileged, dense state data from a high-fidelity simulator, representing the system using operator-polynomial features that remain stable under spectral perturbation. Simultaneously, a student encoder learns to replicate this latent geometry using sparse field data and operator descriptors. At the deployment stage, the teacher is removed, and the frozen student executes inference in a single forward pass, supported by a transfer certificate.

Although this design draws upon concepts from privileged-information learning, knowledge distillation, and cross-modal distillation, its primary objective is cross-instance transfer rather than fixed-instance prediction. This allows for changes in topology and operators while keeping the latent task constant. We derive sufficient and nearly necessary transfer conditions based on the Wasserstein proximity between latent laws, which provides a zero-shot error bound. Additionally, we present a finite-sample certification protocol that incorporates active expansion to handle incomplete coverage.

This framework is applicable to any system where an operator with a reportable spectrum exists. In tests involving power-system estimation, the method successfully achieved zero-shot transfer across 100 previously unseen topologies. It demonstrated a 95% certificate pass rate, inference speeds under one millisecond, and accuracy levels comparable to topology-aware Newton--Raphson methods. These findings indicate that combining asymmetric pathways with operator-anchored latent geometry establishes a robust foundation for certified zero-shot inference and control.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC