Chronos-2 produced the lower point-forecast error in the preprint's main test of district-heating demand, with a CVRMSE, a percentage measure of prediction error, of 12.48% against 13.07% for TabPFN-TS. The study compared those two models with trained baselines across two German district-heating networks.
The result came from a zero-shot setup, meaning the models used rolling historical contexts and known future inputs without task-specific weight training. They produced quantile forecasts that represented uncertainty around the heat load, while the median of each forecast served as the single-number prediction.
For the broader analysis, the researchers selected hourly forecasts for the next 24 hours, using a 12-week rolling context and ambient temperature as the only weather input. The primary Munich record ran from 1 January 2020 to 31 January 2025 at a native 15-minute resolution.
A lead, but not a clean sweep
Chronos-2 kept its aggregate lead in the Flensburg transfer test. Relative errors were generally lower there than in Munich, and TabPFN-TS remained ahead of the trained AutoGluon models.
Point accuracy was not the only test. For full-year probabilistic forecasts, Chronos-2 had the lower CRPS score in both networks: 60.49 versus 63.66 kW in Munich and 5.62 versus 5.94 MW in Flensburg. The study also used a PIT calibration check, a way to see whether forecast probabilities line up with outcomes. The PIT distributions deviated from uniformity for both models, indicating residual calibration problems.
Forecast weather also mattered. In a weather-forecast sensitivity experiment, CVRMSE was 10.1% higher for Chronos-2 and 7.4% higher for TabPFN-TS. Paired 95% confidence intervals for changes in CVRMSE, MAE and R2 excluded zero.
The study also compared the zero-shot models with baselines using KSWIN-triggered retraining. Those retrained baselines had lower average error in every year, with relative CVRMSE reductions rising from 4.4% in 2021 to 18.4% in 2024.
Researchers then tested a two-stage setup called MRRC for high-frequency forecasts. It issued a 24-hour hourly base forecast every 12 hours, interpolated that forecast to 15-minute resolution, and added a 15-minute residual forecast for the next two hours every hour. Compared with direct high-frequency, high-resolution forecasting, MRRC's error on 12-hour integrated demand was 7.3% lower for TabPFN-TS and 7.5% lower for Chronos-2. Its recorded RTF values were also 30% and 18% lower, respectively.
What the test leaves open
To quantify variation around the full-year comparisons, the authors used 95% percentile confidence intervals from 10,000 paired circular block-bootstrap samples, with each block covering seven days.
The result has a narrow base. Both case studies were in Germany, and configuration selection and MRRC evaluation were restricted to Munich, limiting how confidently the findings can be carried to other networks. Munich data are not publicly available because of third-party restrictions, while Flensburg data are public; experimental code is reported as available on GitHub and Zenodo.
The document is an arXiv preprint, version 2. It acknowledges support from BMWE and the Werner Siemens Foundation and states that the funders had no role in the study. The authors declare no known competing financial interests or personal relationships that could have appeared to influence the reported work.
Paper data and sources
Original title: Systematic Evaluation of TabPFN-TS for Zero-Shot Probabilistic Heat Load Forecasting in District Heating Networks
Authors: Ben Spoek, Karim K. Ben Hicham, Kai Derzsi et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text