Systematic Evaluation of TabPFN-TS and Chronos-2 for Zero-Shot Heat Load Forecasting in District Heating Networks

Ben Spoek; Karim K. Ben Hicham; Kai Derzsi; Philipp Althaus; Alexander Mitsos; Dirk Müller

cs.LGAug 20, 2026

Systematic Evaluation of TabPFN-TS and Chronos-2 for Zero-Shot Heat Load Forecasting in District Heating Networks

Authors: Ben Spoek, Karim K. Ben Hicham, Kai Derzsi, Philipp Althaus, Alexander Mitsos, Dirk Müller

Organizations: Chair of Energy Efficient Buildings and Indoor Climate, RWTH Aachen University, Mathieustr. 10, 52074 Aachen, Germany · Process Systems Engineering, RWTH Aachen University, Forckenbeckstr. 51, 52074 Aachen, Germany

Abstract

District heating energy hubs require reliable heat load forecasts for efficient operational scheduling. Forecasting models trained on historical data may require retraining as networks evolve. Zero-shot time-series foundation models and in-context forecasting therefore offer a promising alternative: they can adapt at inference time from recent observations rather than by repeated retraining. This study systematically evaluates TabPFN-TS and Chronos-2 for probabilistic heat load forecasting in two German district heating networks and compares them with trained baselines. We assess whether TabPFN-TS, whose underlying model is pretrained entirely on synthetic tabular rather than time-series data, can capture complex district heating dynamics. We analyze covariate choice, context length, temporal resolution, and forecast horizon on selected operating weeks, evaluate the selected configuration over the full year, and assess cross-network transfer. The principal benchmark assumes perfect weather forecasts; a separate sensitivity analysis uses retrospective weather predictions. Hourly 24-hour forecasting with a 12-week rolling context and ambient temperature provides a parsimonious configuration; longer context windows do not improve accuracy. Both TSFMs outperform all trained baselines in deterministic accuracy in the full-year benchmarks. Chronos-2 achieves the best deterministic scores, with TabPFN-TS remaining close: their CVRMSE values on the main data set are 12.48% and 13.07%, respectively. Chronos-2 also achieves lower continuous ranked probability scores in both networks, with TabPFN-TS remaining close. a TSFM-based Multi-Resolution Residual-Correction Forecaster combines an hourly base forecast with short-term high-resolution corrections. Relative to direct high-resolution forecasting, it generally reduces errors in total heat demand over 12-hour periods and recorded prediction times.

Figures & tables

Figure 1: Schematic structure of the Multi-Resolution Residual-Correction Forecaster.

Year	Hellinger distance $H$	KSWIN drift detections
2021	0.3921	65
2022	0.1601	26
2023	0.1827	27
2024	0.1583	31

Table 1: Distributional-change indicators for the Munich network based on 15-minute heat-load observations. Hellinger distances compare each year’s heat-load distribution with the preceding year; KSWIN drift-detection counts refer to changes detected within the indicated year.

Figure 2: Fourier magnitude spectra of the full available 15-minute heat load time series: (a) full period range and (b) periods up to one day. The x-axis is shown as period rather than frequency; marked periods indicate seasonal, weekly, daily, and sub-daily components.

Figure 3: Overall CVRMSE, CRPS, and mean steady-state prediction-call time for 24-hour heat load forecasts as a function of context length for the selected summer, winter, and transitional operating weeks.

Model	Model loading (s)	Estimated first-call overhead (s)	Steady-state inference (s/forecast)
TabPFN-TS	$16.49\pm 3.45$	$7.47\pm 1.23$	$0.947\pm 0.021$
Chronos-2	$29.78\pm 6.14$	$0.260\pm 0.019$	$0.01809\pm 0.00018$

Table 2: Controlled TSFM timing for hourly 24-hour forecasts with a 12-week context. Values are mean

\pm

standard deviation across five fresh processes.

Figure 4: Overall CVRMSE for 4-hour heat load forecasts at 15-minute resolution as a function of context length.

Figure 5: CVRMSE and

R^{2}

for daily 24-hour and weekly 168-hour forecasts at hourly resolution with a 12-week context window for TabPFN-TS and Chronos-2.

Figure 6: Munich predictions for the selected 24-hour forecast setup at hourly resolution with a 12-week context window.

	TabPFN-TS			Chronos-2
Weather covariates	CVRMSE (%)	$R^{2}$	MAE (kW)	CVRMSE (%)	$R^{2}$	MAE (kW)
Amb. temp.	11.42	0.970	102.6	10.60	0.974	96.0
Amb. temp., relative humidity	11.43	0.970	102.2	10.62	0.974	96.7
Amb. temp., wind speed	11.09	0.972	98.8	10.56	0.975	96.0
Amb. temp., precipitation	11.16	0.972	100.1	10.59	0.975	96.0
Amb. temp., precip., wind sp.	11.25	0.971	99.9	10.38	0.976	94.2

Table 3: Weather feature selection for 24-hour hourly forecasts with a 12-week context window for TabPFN-TS and Chronos-2.

Setup	CVRMSE (%)	$R^{2}$	MAE (kW)
Recent 12 (auto feat.)	11.42	0.970	102.6
Recent 12	11.69	0.969	106.9
Recent 6 + Relevant 6	12.69	0.963	113.0

Table 4: Context-data selection for TabPFN-TS hourly 24-hour forecasts. Context lengths are in weeks; “auto feat.” denotes automatic temporal features.

Period	Model	CRPS (kW)	Width (kW)	Rel. w. (%)
Winter	TabPFN-TS	92.95	498.9	22.1
	Chronos-2	85.56	488.4	21.6
Transitional	TabPFN-TS	93.81	370.3	28.5
	Chronos-2	95.20	317.7	24.5
Summer	TabPFN-TS	25.42	114.8	36.7
	Chronos-2	23.78	93.9	30.0

Table 5: CRPS and 80% prediction-interval widths for daily issued forecasts at hourly resolution with a 12-week context on the selected representative weeks.

		Aggregate metrics			Mean daily rank
Model	Rank shift	CVRMSE (%)	$R^{2}$	MAE (kW)	CVRMSE	$R^{2}$	MAE
Munich
Chronos-2		12.48 [10.88, 14.37]	0.962 [0.946, 0.972]	85.4 [75.9, 95.6]	3.04	3.01	3.11
TabPFN-TS		13.07 [11.49, 14.94]	0.959 [0.941, 0.969]	90.3 [79.9, 101.1]	3.89	3.86	3.83
TFT		14.61 [12.92, 16.61]	0.948 [0.928, 0.961]	102.1 [90.7, 114.3]	5.88	5.85	5.93
Direct LGBM		15.87 [14.25, 17.72]	0.939 [0.917, 0.953]	113.7 [99.1, 129.6]	6.49	6.42	6.49

Table 6: Full-year benchmark and transfer-validation results for hourly 24-hour forecasts in 2024. Brackets denote 95% paired seven-day block-bootstrap confidence intervals.

Panel of Figure 7 — Figure 7: Full-year model comparison based on daily CVRMSE. The upper panels show CD diagrams and the lower panels show pairwise win rates. Each heatmap cell gives the percentage of forecast days on which the row model outperforms the column model; exact ties count as half a win.

Figure 8: Approximate PIT histograms for the principal 2024 hourly, 24-hour forecasting benchmark in Munich and Flensburg.

Year	Static CVRMSE (%)	KSWIN CVRMSE (%)	$\Delta$ CVRMSE (percentage points)	Relative reduction (%)
2021	19.96 [18.24, 22.10]	19.09 [17.27, 21.34]	$-0.88$ [ $-1.42$ , $-0.28$ ]	4.4 [1.4, 7.2]
2022	19.55 [17.18, 22.68]	17.62 [14.96, 21.31]	$-1.93$ [ $-2.77$ , $-1.02$ ]	9.9 [4.8, 14.8]
2023	22.85 [20.40, 25.60]	19.67 [17.18, 22.73]	$-3.19$ [ $-4.08$ , $-2.20$ ]	13.9 [9.3, 18.1]
2024	20.69 [19.00, 22.49]	16.89 [15.09, 18.93]	$-3.80$ [ $-4.87$ , $-2.65$ ]	18.4 [12.7, 23.4]

Table 7: Annual mean CVRMSE across eight learned AutoGluon setups in Munich. Differences are KSWIN minus static; brackets denote 95% percentile confidence intervals.

		Point forecast			Probabilistic forecast
Model	Weather cov.	CVRMSE (%)	$R^{2}$	MAE (kW)	CRPS (kW)
TabPFN-TS	Realized	11.89	0.974	72.2	50.9
	Predicted	12.77 (+7.4%)	0.971 (-0.4%)	77.8 (+7.7%)	55.0 (+8.1%)
Chronos-2	Realized	11.41	0.976	68.5	48.3
	Predicted	12.56 (+10.1%)	0.971 (-0.5%)	76.1 (+11.0%)	53.3 (+10.2%)

Table 8: Forecast quality with realized temperatures and coherent retrospective ECMWF temperature predictions for 208 matched Munich forecast starts from 7 June to 31 December 2024.

	Short-term forecast			12-hour integrated heat demand		Computation
Setup	CVRMSE (%)	$R^{2}$	MAE (kW)	E-CVRMSE (%)	E-bias (%)	RTF
TabPFN-TS
Base	21.63 [19.95, 23.47]	0.897 [0.880, 0.911]	125.3 [119.0, 132.1]	8.43 [7.79, 9.12]	-0.99 [-1.38, -0.60]	$2.24{\times}10^{-5}$
HFHR	21.13 [19.37, 23.08]	0.902 [0.884, 0.916]	115.4 [109.6, 121.7]	8.78 [7.92, 9.74]	-1.77 [-2.25, -1.32]	$3.86{\times}10^{-4}$
MRRC	21.15 [19.38, 23.10]	0.902 [0.884, 0.916]	114.8 [109.1, 120.9]	8.14 [7.52, 8.82]	-1.09 [-1.44, -0.74]	$2.70{\times}10^{-4}$
Chronos-2

Table 9: Munich Base, HFHR and MRRC forecast performance pooled over 2021–2024. Brackets denote 95% percentile confidence intervals.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1: Annual heat provided by the Munich district heating network for complete calendar years.

	Ambient temperature ( ∘ C)			Supply ( ∘ C)
Regime	Min.	Mean	Max.	Mean $\pm$ SD	Dates
Winter	-8.60	-0.51	11.20	$86.42\pm 4.42$	Jan. 15–21
Transitional	0.40	7.97	24.60	$83.63\pm 4.12$	Apr. 22–28
Summer	16.80	23.16	32.20	$84.14\pm 3.81$	Aug. 12–18

Appendix

Table S1 : Selected representative weeks from 2024 and their ambient- and supply-temperature statistics. Supply temperatures are reported as mean

\pm

standard deviation (SD) of the 672 unfiltered 15-minute observations in each week.

Model	Configuration	CVRMSE (%)	$R^{2}$	MAE (kW)	CRPS (kW)
TabPFN-TS	M $\rightarrow$ M	11.89 [9.93, 14.46]	0.974 [0.961, 0.982]	72.2 [61.7, 83.0]	50.85 [43.22, 58.62]
	F $\rightarrow$ F	14.85 [12.87, 17.12]	0.960 [0.941, 0.971]	92.0 [75.3, 109.8]	64.16 [52.57, 76.38]
	M $\rightarrow$ F	13.00 [11.12, 15.36]	0.969 [0.955, 0.978]	78.9 [66.7, 91.7]	55.96 [47.09, 65.16]
	M+F $\rightarrow$ F+F	12.77 [10.91, 15.13]	0.971 [0.957, 0.979]	77.8 [66.1, 89.9]	54.95 [46.52, 63.67]
Chronos-2	M $\rightarrow$ M	11.41 [9.34, 14.10]	0.976 [0.963, 0.984]	68.5 [58.9, 78.4]	48.32 [41.31, 55.47]
	F $\rightarrow$ F	12.74 [10.83, 15.18]	0.971 [0.956, 0.979]	77.0 [65.0, 89.6]	53.85 [45.20, 62.79]

Appendix

Table S2 : Temperature-covariate configurations on matched Munich forecast starts. The left and right sides of each arrow specify historical and future covariates.

Model	CVRMSE (%)	$R^{2}$	MAE (kW)
Chronos-2	15.64 [13.44, 18.05]	0.941 [0.914, 0.958]	109.7 [93.8, 126.9]
TabPFN-TS	17.06 [14.58, 19.94]	0.929 [0.895, 0.950]	120.2 [102.2, 140.1]

Appendix

Table S3 : Full-year Munich results for non-overlapping weekly 168-hour forecasts at hourly resolution.

A. Scores after anomaly exclusion
Model	CVRMSE (%)	$R^{2}$	MAE (kW)
Chronos-2	11.83 [10.27, 13.76]	0.966 [0.950, 0.975]	82.1 [72.7, 92.2]
TabPFN-TS	12.58 [11.02, 14.49]	0.961 [0.944, 0.971]	87.8 [77.2, 98.8]
TFT	14.24 [12.62, 16.20]	0.950 [0.930, 0.962]	99.7 [88.1, 112.1]
Direct LGBM	15.47 [13.81, 17.40]	0.941 [0.919, 0.955]	110.5 [95.8, 126.4]
DeepAR	16.09 [14.46, 17.96]	0.936 [0.914, 0.952]	113.8 [98.0, 130.6]

Appendix

Table S4 : Munich anomaly-exclusion sensitivity, retaining 342 of 366 forecast days. pp denotes percentage points.

Network	Anomaly exclusion	Model	CRPS (kW)
Munich	No	TabPFN-TS	63.66 [56.26, 71.39]
Munich	No	Chronos-2	60.49 [53.67, 67.83]
Munich	Yes	TabPFN-TS	61.54 [54.08, 69.43]
Munich	Yes	Chronos-2	57.90 [51.11, 65.21]
Flensburg	No	TabPFN-TS	5942 [5115, 6825]
Flensburg	No	Chronos-2	5618 [4821, 6484]

Appendix

Table S5 : Probabilistic forecast quality for the 2024 full-year benchmark and anomaly-exclusion sensitivity.

Figure S2: PIT histograms for TabPFN-TS and Chronos-2 during the selected Munich operating weeks in 2024.

A. MAE
Year	Static MAE (kW)	KSWIN MAE (kW)	$\Delta$ MAE (kW)	Relative reduction (%)
2021	105.3 [95.8, 115.0]	100.0 [92.6, 107.4]	-5.3 [-9.3, -1.8]	5.0
2022	112.7 [101.7, 124.4]	101.0 [92.8, 109.8]	-11.7 [-17.6, -6.5]	10.4
2023	158.7 [137.4, 181.3]	134.1 [119.1, 150.4]	-24.6 [-33.9, -15.7]	15.5
2024	150.2 [131.5, 170.5]	120.1 [106.3, 134.7]	-30.1 [-40.1, -21.3]	20.0

Appendix

Table S6 : Annual mean MAE and

R^{2}

across eight learned AutoGluon setups in Munich.

Model	KSWIN triggered retraining	CVRMSE (%)	MAE (kW)	$R^{2}$
TabPFN-TS	–	14.83	86.1	0.949
Chronos-2	–	14.33	81.9	0.952
TFT	No Yes	16.94 16.57	104.8 98.9	0.933 0.936
AutoGluon Ensemble	No Yes	16.64 16.26	102.3 97.3	0.935 0.938
DeepAR	No Yes	20.34 16.38	131.2 98.4	0.904 0.937
Direct LGBM	No Yes	26.21 18.81	164.1 119.0	0.840 0.918

Appendix

Table S7 : Forecast performance over 2021–2024 in Munich.

Model	Initial marginal fitting time (s)
TFT	47.613
DeepAR	31.920
Direct LGBM	0.729
Direct XGBoost	1.044
Recursive LGBM	0.572
DLinear	14.335

Appendix

Table S8 : Initial marginal AutoGluon fitting times on the 2023 training data.

Model	Fitting-to-prediction time ratio
TFT	5.706
DeepAR	26.603
Direct LGBM	1.595
Direct XGBoost	0.491
Recursive LGBM	0.254
DLinear	45.761

Appendix

Table S9 : Additional fitting cost of KSWIN-triggered retraining over 2021–2024.

Backbone	Comparison	$\Delta$ CVRMSE (pp)	$\Delta$ MAE (kW)	$\Delta$ E-CVRMSE (pp)
TabPFN-TS	MRRC $-$ Base	$-0.48$ [ $-0.75$ , $-0.20$ ]	$-10.51$ [ $-12.04$ , $-9.07$ ]	$-0.29$ [ $-0.36$ , $-0.21$ ]
	MRRC $-$ HFHR	0.02 [ $-0.10$ , 0.13]	$-0.62$ [ $-1.08$ , $-0.19$ ]	$-0.64$ [ $-1.14$ , $-0.20$ ]
Chronos-2	MRRC $-$ Base	$-1.03$ [ $-1.53$ , $-0.39$ ]	$-14.91$ [ $-16.59$ , $-13.35$ ]	$-0.27$ [ $-0.34$ , $-0.19$ ]
	MRRC $-$ HFHR	0.17 [ $-0.01$ , 0.39]	0.61 [0.16, 1.06]	$-0.61$ [ $-1.11$ , $-0.16$ ]

Appendix

Table S10 : Paired MRRC-minus-comparator differences for the pooled 2021–2024 evaluation.

Explore similar work

Benchmarking Time Series Foundation Models for Load Forecasting Under Covariate Uncertainty
Oct 5, 2026Tomas Kaljevic, Ivan Arzola, Yu ZhangAccurate Short-Term Electricity Load Forecasting
Department of Electrical and Computer Engineering University of California, Santa Cruz
A Benchmark for Electrical Load Forecasting Across Grid Levels: Time-Series Transformers Outperform Established Methods
Jul 17, 2026Matthias Hertel, Sebastian Pütz, Jonathan Kolar +3Accurate Short-Term Electricity Load Forecasting Forecasting Backbone
Karlsruhe Institute of Technology, Germany · Helmholtz AI, Germany
Benchmarking Transformer and xLSTM for Time-Series Forecasting of Heat Consumption
May 10, 2026Marja Wahl, Daniel R. Bayer, Sven Rausch +1Forecasting Backbone Time Series Forecasting
RAUSCH Technology GmbH, Würzburg, Germany · Modeling and Simulation, University of Würzburg, Würzburg, Germany

Oct 5, 2026, cs.LGJ/K move · Enter open · S save

Benchmarking Time Series Foundation Models for Load Forecasting Under Covariate Uncertainty

Tomas Kaljevic, Ivan Arzola, Yu Zhang

Department of Electrical and Computer Engineering University of California, Santa Cruz

Accurate Short-Term Electricity Load Forecasting

Open paper AskPDF arXiv

Accurate short-term load forecasting (STLF) is essential for the reliable and efficient operation of modern power systems. While time series foundation models (TSFMs) have recently demonstrated remarkable performance across a wide range of forecasting tasks, their effectiveness for STLF under realistic operational conditions remains largely unexplored. In this paper, we present a comprehensive benchmark of four trained-from-scratch (TFS) models and four TSFMs across three real-world load forecasting datasets under operational scenarios that differ in the availability and quality of future covariate information. Our results show that Chronos-2 consistently achieves state-of-the-art performance in both zero-shot and fine-tuned settings when future covariates are available or accurately forecast. However, its performance degrades as covariate forecasts become increasingly noisy, whereas TimesNet exhibits greater robustness under severe covariate uncertainty. These findings demonstrate the effectiveness of covariate-informed TSFMs for STLF while highlighting the critical role of robust covariate modeling in real-world forecasting applications.

Abstract

Explore similar work

Benchmarking Time Series Foundation Models for Load Forecasting Under Covariate Uncertainty

A Benchmark for Electrical Load Forecasting Across Grid Levels: Time-Series Transformers Outperform Established Methods

Benchmarking Transformer and xLSTM for Time-Series Forecasting of Heat Consumption