Physics-Transfer Learning: A Physics-Constrained Theory for Zero-Shot Generalization Along the Ladder of Complexity
Abstract
Reliable out-of-distribution generalization remains a central challenge in machine learning, particularly when models are deployed in data-scarce high-fidelity domains. Existing approaches often rely on statistical distribution alignment, or invariance assumptions that can fail when domain shifts reflect changes in underlying mechanisms. Inspired by a longstanding paradigm in physics that understands complex systems by starting from tractable idealizations and progressively incorporating additional mechanisms and levels of fidelity, we propose physics-transfer (PT) learning, a physics-constrained learning theory for zero-shot generalization along a ladder of complexity. PT constructs chains of anchor domains (CADs) that connect low-cost source domains to complex targets and introduces computable feasibility and reliability indicators for assessing transfer before target-domain labels are observed. Under physical-consistency and stable-representation assumptions, we derive an operational upper bound on target risk in terms of source empirical risk, the PT indicators, and finite-sample errors, and establish convergence as adjacent complexity gaps shrink and data coverage improves. We evaluate PT on excited-state energy prediction in quantum systems and dynamical-transition prediction in classical systems using neural networks trained without target-domain labels. Across substantial distribution shifts, PT yields accurate high-fidelity predictions, while the indicators identify incorrect physical mappings before target-domain prediction fails. These results provide a model-agnostic framework for designing, diagnosing, and controlling generalization in data-scarce learning problems.
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BibTeX
@misc{zhao2026physicstransfer,
title = {{Physics-Transfer Learning: A Physics-Constrained Theory for Zero-Shot Generalization Along the Ladder of Complexity}},
author = {Yingjie Zhao and Zhiping Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22376},
eprint = {2610.22376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics-Transfer Learning: A Physics-Constrained Theory for Zero-Shot Generalization Along the Ladder of Complexity
AU - Yingjie Zhao
AU - Zhiping Xu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.22376
UR - https://arxiv.org/abs/2610.22376
AB - Reliable out-of-distribution generalization remains a central challenge in machine learning, particularly when models are deployed in data-scarce high-fidelity domains. Existing approaches often rely on statistical distribution alignment, or invariance assumptions that can fail when domain shifts reflect changes in underlying mechanisms. Inspired by a longstanding paradigm in physics that understands complex systems by starting from tractable idealizations and progressively incorporating additional mechanisms and levels of fidelity, we propose physics-transfer (PT) learning, a physics-constrained learning theory for zero-shot generalization along a ladder of complexity. PT constructs chains of anchor domains (CADs) that connect low-cost source domains to complex targets and introduces computable feasibility and reliability indicators for assessing transfer before target-domain labels are observed. Under physical-consistency and stable-representation assumptions, we derive an operational upper bound on target risk in terms of source empirical risk, the PT indicators, and finite-sample errors, and establish convergence as adjacent complexity gaps shrink and data coverage improves. We evaluate PT on excited-state energy prediction in quantum systems and dynamical-transition prediction in classical systems using neural networks trained without target-domain labels. Across substantial distribution shifts, PT yields accurate high-fidelity predictions, while the indicators identify incorrect physical mappings before target-domain prediction fails. These results provide a model-agnostic framework for designing, diagnosing, and controlling generalization in data-scarce learning problems.
ER -