Physics-Transfer Learning Derives Risk Bounds for Zero-Shot Generalization Across Complexity Ladders

The framework constructs computable feasibility and reliability indicators along progressive complexity gaps, deriving an operational upper bound on target risk from source empirical risk plus finite-sample terms under physical-consistency and stable-representation assumptions. Neural networks trained only on low-cost domains achieved accurate high-fidelity predictions across large distribution shifts, while the indicators flagged invalid mappings before failure occurred. This directly addresses failure modes in statistical domain adaptation when shifts involve mechanism changes rather than covariate drift.

Related work on physics-informed neural networks (Raissi et al., JCP 2019) and multi-fidelity Gaussian processes (Kennedy & O'Hagan, Biometrika 2000) provides the mechanistic scaffolding, yet PT adds explicit convergence guarantees as adjacent gaps shrink and data coverage increases. The approach could transfer to climate subgrid parameterization and alloy design where high-fidelity data remain prohibitively expensive. Current tests remain confined to two controlled system classes; broader validation across chaotic or many-body regimes is still absent.

The main limitation is reliance on the physical-consistency assumption holding exactly between adjacent domains; violation would invalidate the risk bound. Strengthening evidence requires a multi-institution benchmark suite with withheld target labels and prospective experimental follow-up within 18 months.