The safety-critical deployment of learning-based controllers requires reliable constraint satisfaction across heterogeneous dynamical regimes. One way to address this challenge within a physics-informed machine learning framework is to incorporate prior structural knowledge—such as forward-invariant feasibility constraints—directly into the control process. Here, we present a phenomenological study characterizing the macroscopic statistical signatures induced by a domain-agnostic constraint-enforcement layer across five safety-critical domains: thermal HVAC control, smart-grid frequency regulation, clinical CGM-based insulin safety, renewable microgrid management, and financial portfolio control. Across 842,511 historical samples spanning six orders of magnitude in timescale, we identify three reproducible signatures: (i) distributional truncation at feasibility boundaries, with no observed violations under enforcement; (ii) boundary redirection dynamics consistent with forward-invariant behavior; and (iii) systematic growth of intervention intensity as the safety boundary is approached. The zero-violation result corresponds to an exact 95% Clopper–Pearson upper bound of approximately 3.6 × 10⁻⁶ on the true violation probability. Prospective real-time validation in live market operations supports the persistence of these signatures under deployed conditions. Collectively, these observations support a physics-informed interpretation of enforced feasibility as boundary-limited probability flow compatible with reflected stochastic dynamics, while remaining agnostic to internal controller architectures, and suggest that physics-informed constraint enforcement provides an empirically grounded, domain-agnostic approach to safe learning-based control. This document is an updated and expanded version of the original preprint hosted on TechRxiv (DOI: 10.36227/techrxiv.177220350.08459501/v1). This version is being published on Zenodo to ensure continuous open access and citable stability during the TechRxiv platform migration.
Serra-Taylor et al. (Thu,) studied this question.