Cyril Voyant

Understand before you compute.

I build physical and statistical models to help inform decisions in energy and medicine. I start with the question, existing knowledge and available data, then choose the tools. Learning and AI are useful when their contribution is demonstrated; evaluation and responsibility remain human.

MedicineEnergyLanguage

How I choose a model

I build models to inform decisions in energy and medicine, helping an engineer size a system, an operator anticipate production, a physicist interpret a dose, and tools that make them usable. I start from the problem: what is known about the system, the data available and the precision really needed. I use an explicit model when it fits, complete it with learning when a relation is missing, and keep extra complexity only when its benefit is demonstrated. AI is fully part of the toolbox; evaluation and responsibility stay human.

Portrait of Cyril Voyant, physicist and Research Director at Mines Paris–PSL.

Understand my research

Questions, findings, limitations and links to papers and code.

Learn with the courses

Choose a topic and level, then work through the chapters.

Use an interactive tool

Find a calculator or experiment, with its interface language and purpose.

I am a physicist and Research Director at Mines Paris–PSL, within the Centre Observation, Impacts, Énergie (O.I.E.), and Visiting Professor at the University of Kragujevac, Serbia. My work connects solar and photovoltaic forecasting, time series and frugal AI. My background also includes medical physics.

Can we know how predictable the sky is? When does a simple model beat a complex one? Which forecast errors matter in practice? Here I explain the results behind these questions, with the papers and code that support them.

One method, four complementary routes

The domain changes; the method does not. The route is chosen by the problem and the decision to inform, not by the tool; extra complexity is kept only when its benefit is demonstrated.

BED per fraction for the rectum, LQ and LQL

Compute directly

When the link is known, compute it with an explicit model, calibrated and validated on data; learning is added only for a demonstrated benefit.

Compute, don't learn: radiobiological dose equivalence · Simulate what you cannot yet measure: road tunnels · How forecastable is the sun?

Thyroglobulin over 80 months for 1, 2, 4 and 8 sessions, refractory and responding profiles

Hybridize

When the model falls short, complete it: keep the model, learn only what is missing.

Thyroid cancer and radioiodine: model first · Better persistence, without training a neural network

Pooled nRMSE over 1 to 24 hours against parameters stored (log scale): the per-cell ELM is the lowest point; models reading the whole field store far more parameters without lower error

Learn frugally

When the useful relations are not known well enough, evaluate what the data can teach, with only as much complexity as pays.

Seven signals, one ELM · Satellite forecasting: one cell or the whole field? · Frugal models for solar forecasting (in French)

The chain: request, language model, validator, validated code, result

AI in its place

Language models help people use validated tools; the calculation, the checking and the responsibility stay with validated codes and people.

Let the language model read, let the validated code compute

Map of the work: four columns for the steps of the approach (direct model; hybrid, model plus learning; frugal learning; heavy learning and language models) and three rows for the fields (medicine, energy, language), each published or open work written in its cell. — Each work sits in the step it needs: one column to the right only for a measured gain. U-Net and LSTM were tested, not kept.

Demonstrate trust

Judge against a reference, publish code, data and limits, make research findable and reusable.

Questioning how we do research: influence, integrity, excellence · AI in research: the AI Act, a lab charter and a toolbox · When RMSE hides a difference · Beyond pointwise errors: the γ-index · Academic visibility: why publishing isn't enough anymore · Research excellence in the age of AI: from SEO to GEO (in French)

Research stories

How forecastable is the sun?
Separating cloud-driven variability from the daily solar cycle: the sCV and forecastability indices, evaluated at 68 stations.

A better persistence forecast, without training a model
BLEND uses the recurring statistical structure of energy signals to improve a simple reference forecast.

When a displaced forecast is still useful
The γ-index evaluates spatial, temporal and intensity agreement within explicit tolerances.

Also explore multi-output energy forecasting with ELM and NICE: measuring improvement over persistence.

Watch and learn

Watch: Research Excellence in 2026
My talk on making research discoverable, verifiable and useful. Talk summary, references and preprint.

Solar forecasting: my course at Mines Paris–PSL
The UE14 course connects solar variability, time-series models, evaluation and frugal forecasting.

Full academic CV · Research projects · Google Scholar

Forecasting the sun with its uncertainty: ELM against persistence, live

At every moment, two models forecast the next four hours of a photovoltaic plant in Palaiseau. The bands target nominal coverages of 50% and 90%; their achieved coverage must be measured. The black curve shows observations.

ObservedELMPersistence50% and 90% bands

90% interval score: width and penalty for observations outside the interval (lower is better)

ELM–

Persistence–

Reading the animation: glossary

Deterministic forecast ŷ: A single forecast value, the solid line of each model.
Prediction interval: A range [lower bound, upper bound] that should contain the observation with a stated probability: the coloured bands.
Nominal coverage (1 − α): The target probability: 50% for the dark band, 90% for the light band (α = 0.1).
σ, residual standard deviation: The model’s typical error, measured on the training period, one value per model and horizon.
Factor k and lookup table (LUT): For each target coverage, the table gives the multiple of σ to use: interval = ŷ ± k·σ. It is built once, on training data, without assuming Gaussian errors (for Gaussian errors, k ≈ 1.64 at 90%).
Lower bound ≥ 0: A plant’s power is zero or positive: a bound below zero has no physical meaning, so it is raised to 0.
PICP (Prediction Interval Coverage Probability): Observed coverage: the share of observations falling inside the interval. A 90% interval is reliable if its PICP is close to 90%.
MIL (Mean Interval Length): Mean interval width, in kW. At equal coverage, narrower is more useful: this is sharpness.
Interval score: Interval width plus a penalty of 2/α = 20 times the miss when the observation falls outside: it rewards both reliability and sharpness; lower is better.
Persistence: The simplest reference: the near future looks like now, the forecast is the last observed value.
ELM (Extreme Learning Machine): A one-hidden-layer neural network whose input weights are drawn at random and only output weights are learned, by regularized least squares: fast and frugal.

Scores accumulate over revealed daytime targets, pooling horizons from 30 min to 4 h; one observation contributes at several horizons.

Public Palaiseau data (30-min steps) and the ridge ELM of the PV_ELM_pred repository; simple persistence: the last observed value. Both models use the Appendix C method: an empirical table maps target coverage to factor k, learned from training residuals, then the interval is forecast ± kσ. One table and residual standard deviation per model and horizon. Three days were selected for their variability: this is not a representative test or a manuscript result. Software: Martin Leiva, Xavier Silvani, Gilles Notton, Cyril Voyant and Alan Julien. Cite the software and its team.

Lookup table, method and reference

Method applied here: Cyril Voyant, Milan Despotovic, Gilles Notton, Yves-Marie Saint-Drenan, Mohammed Asloune, Luis Garcia-Gutierrez, On the Importance of Clearsky Model in Short-Term Solar Radiation Forecasting (2025), Appendix C. Symmetric intervals ŷ ± kα σ are calibrated from training residuals, then applied to later forecasts. The Palaiseau table is recalculated for this PV application; these are not Figure C.9 values or the paper’s SIAR results.

Reading the table. For coverage c = 1 − α, k(c) is the empirical quantile of |y − ŷ|/σ on training data. The residual standard deviation σ uses n − 1 in its denominator. Model and table use the first half of the series; the three displayed days are in the last quarter. Interpolate k between tabulated coverages (1% steps). Only addition to Appendix C: the lower bound is raised to 0, since a photovoltaic plant never produces negative power. As the observation is always positive, coverage (PICP) is unchanged; only the mean width (MIL) shrinks. Nominal coverage is not a guarantee out of sample.

The interval score is IS = (U − L) + (2/α) max(L − y, 0) + (2/α) max(y − U, 0), with α = 0.10. It complements PICP and MIL by penalising observations outside the band. It is not the CRPS in Appendix D.

Palaiseau tables, σ in kW, dimensionless k factors
Model	Horizon	σ (kW)	k(50 %)	k(80 %)	k(90 %)
ELM	30 min	1.588	0.430	1.067	1.605
ELM	60 min	1.851	0.481	1.151	1.667
ELM	90 min	2.032	0.515	1.183	1.683
ELM	120 min	2.172	0.534	1.187	1.700
ELM	150 min	2.283	0.538	1.207	1.719
ELM	180 min	2.367	0.529	1.211	1.710
ELM	210 min	2.434	0.540	1.223	1.712
ELM	240 min	2.479	0.546	1.207	1.714
Persistence	30 min	1.837	0.425	1.030	1.556
Persistence	60 min	2.514	0.526	1.255	1.615
Persistence	90 min	3.107	0.573	1.346	1.687
Persistence	120 min	3.674	0.586	1.389	1.740
Persistence	150 min	4.222	0.595	1.402	1.759
Persistence	180 min	4.717	0.596	1.414	1.769
Persistence	210 min	5.118	0.603	1.413	1.784
Persistence	240 min	5.455	0.599	1.429	1.780

About

Cyril Voyant is a physicist and Research Director at Mines Paris – PSL (Centre O.I.E.). Combining medical physics in radiotherapy (since 2003) and energy-forecasting research (PhD in 2011), he works on solar and energy forecasting, forecast evaluation, frugal AI and language-model interfaces to scientific codes. Background, research, projects, recognition and contact.