Which baseline must a solar model beat? When is deep learning worth it?

Start with persistence, then a phase-aware reference, an autoregression and a frugal learner. Keep a deep network only if it brings a measured gain on the same protocol. Deep learning can be worth it. It has to show this against references that cost almost nothing to run.

Cyril Voyant · Mines Paris – PSL, Centre O.I.E. · 2 November 2026

Reading the quantities. MAE is mean absolute error; RMSE is root mean squared error and gives large errors more weight. nRMSE normalizes RMSE by the mean observation on the evaluated data. AR is autoregression; ELM (extreme learning machine) fits output weights while keeping a fixed random hidden layer. In the NICE formulas, the subscript p denotes persistence; the statistical p-value reported by a test is a different quantity. sCV describes signal variability and F combines variability with temporal dependence.

What to test, in order

  1. Simple persistence. The last observed value: the minimal reference of any forecast.
  2. A reference that knows the cycle. Clear-sky-index persistence, or BLEND, which combines immediate memory with the value at the same phase of the cycle. BLEND works from raw irradiance and its weights are in closed form (Voyant et al., 2026).
  3. An autoregression. Fitted by least squares on recent lags.
  4. A frugal learner. An Extreme Learning Machine (Huang, Zhu and Siew, 2006) keeps a random hidden layer and fits its output weights analytically.
  5. A deep network. LSTM, U-Net or larger, under the same split, horizons and tuning budget.

Two published or teaching results

Ajaccio, 2007 test year, one hour ahead (course UE14). The daytime nRMSE is 22.0 % for smart persistence, 21.3 % for AR(2) and 20.5 % for an ELM. The steps are small, and each is measured.

Corsican electricity system, six years of hourly data (Applied Energy, 2026). A multiple-output ELM is compared with persistence, single-output formulations and an LSTM under a realistic tuning budget. At one hour, nRMSE is 0.179 for solar generation.

What counts as a gain

  • The same targets, scope and horizon for all models.
  • Training rows kept apart from evaluation rows, including any scaling.
  • A difference tested across stations or periods, not only an average.
  • Costs reported with the error: parameters, training time, what the device can store.

Limits

These results concern the datasets and protocols studied. BLEND does not outperform every optimized method; autoregressive or learned predictors can do better under some conditions. Nothing here is a universal ranking.

To read and to use

References

  1. Cyril Voyant, Candice Banes, Luis Garcia-Gutierrez, Gilles Notton, Milan Despotovic, Zaher Mundher Yaseen. Symmetry-constrained forecasting of periodically correlated energy processes. Applied Mathematical Modeling 157, 116988 (2026).
  2. Cyril Voyant, Milan Despotovic, Luis Garcia-Gutierrez, Mohammed Asloune, Yves-Marie Saint-Drenan, Jean-Laurent Duchaud, Ghjuvan Antone Faggianelli, Elena Magliaro. Short-term forecasting of energy production and consumption using extreme learning machine: A comprehensive MIMO based ELM approach. Applied Energy 410, 127599 (2026).