Physics as Representation, Not Regularization: Mechanism and Measurement in Probabilistic Solar Forecasting under Distribution Shift

Physics-informed machine learning is motivated by two promises: better predictions in-distribution, and better behaviour outside it. We test both in probabilistic solar forecasting by separating two mechanisms for injecting the same physical information into one shared backbone. Representation exposes physically derived quantities (clear-sky irradiance, solar geometry, air mass) to the predictor as inputs; regularization places physics-based penalties in the training objective, where they shape weights and then vanish at inference. Using 42 inverter systems on five campuses, 19 quantile levels and a parameter-matched physics-free control, we find the two mechanisms are not interchangeable. Representation improves CRPS by 2.21% (95% CI [-4.13, -0.45], five seeds, campus-clustered bootstrap), improves all 42 inverters, cuts implausible night-time generation by a factor of 50, and replicates in a gradient-boosting model of a different family (-1.03%, [-1.49, -0.46]). Regularization alone yields -0.61% ([-2.76, +0.35]) — indistinguishable from zero. Under leave-one-campus-out evaluation, however, transfer is heterogeneous rather than uniform: the representation advantage persists on two campuses, is absent on a third, and reverses on a single-inverter fourth. A single fold — the usual practice — could have supported any of these conclusions. We further show that the large cross-population degradation such a protocol reports (+66% on one fold) is a capacity artefact; measured on identical rows it is at most about 9%. With five campuses the smallest attainable pooled p-value is 0.0625, so we report intervals rather than verdicts. The practical conclusion is that how physics enters a forecaster, and how transfer is measured, change the reported answer more than the physics itself.