Time-series Foundation Models for Predictive Control: The Role of Excitation

Mazen Amria; Jasper Hoffmann; Philipp Bordne; Anna Rothenhäusler; Lilli Frison; Harald Taxt Walnum; Sebastien Gros; Joschka Bödecker

cs.LGOct 5, 2026

Time-series Foundation Models for Predictive Control: The Role of Excitation

Authors: Mazen Amria, Jasper Hoffmann, Philipp Bordne, Anna Rothenhäusler, Lilli Frison, Harald Taxt Walnum, Sebastien Gros, Joschka Bödecker

Organizations: University of Freiburg, Germany · Norwegian University of Science and Technology, Norway

Abstract

Deploying model predictive control (MPC) requires constructing or identifying a predictive model for each target system. Time-series foundation models (TSFMs) offer an attractive option thanks to strong zero-shot forecasting capabilities across systems. However, low forecast error does not guarantee that a TSFM captures the system's response to the alternative actions considered by the controller. We study this gap using residential heat-pump control as a test bed, measuring the agreement between predicted and ground-truth effects of control interventions. Importantly, we find that TSFMs can recover the system's input-response relationship when the context contains sufficient independent control excitation. Common fine-tuning pipelines and feature smoothing reduce, but do not eliminate, the need for in-context excitation. Our results indicate that current TSFMs used for predictive control require sufficiently informative control variation in the inference context. Initial closed-loop results show promise for shorter context windows.

Figures & tables

Figure 1: Strong zero-shot forecasting on real-world building data. Average MAE of Chronos-2 [ 3 ] and a multi-step linear predictor for approximately linear room-temperature dynamics and nonlinear heat-pump power dynamics across context lengths. See Appendix A for details.

Figure 2: Excitation enables Chronos-2 to identify the control effect. Zero-shot Chronos-2 and a multi-step linear estimator predicting

T_{\text{room}}

from 21 days of unexcited MPC context (top) or excited APRBS context (bottom). Left: observational fit on the MPC control. Right: interventional fit, with constant offsets of

±6K

added to the reference MPC control. Under an unexcited context Chronos-2 fits the observational trajectory well but does not respond to offset-interventions on the controls; the linear estimator, on the same context, does separate them. With an excited context Chronos-2 recovers the response. The underlying optimization problem allows for a lower comfort temperature bound at night, resulting in periodically lower

T_{\text{room}}

Figure 3: In-context identification needs excitation. Response gain (top; ideal value

1

, dashed) and base-trajectory MAE (bottom) against context length, with columns ordered by increasing excitation of the observed context and the known future control held identical throughout. The foundation models recover a control response only under excitation, and only the per-window linear estimator’s data requirement, which cannot be fitted on short contexts, keeps them competitive.

Figure 4: Fine-tuning and EWMA features reduce, but do not eliminate, the need for in-context excitation. Response gain (top; ideal value

1

, dashed) and nominal-trajectory MAE (bottom) across context lengths, with columns ordered by increasing context excitation. Fine-tuning provides the largest benefit at short context lengths. Combining excited fine-tuning with EWMA features recovers substantial gain from one day of context even under no or low excitation, and performs best under medium and high excitation at short-to-intermediate contexts. Under unexcited operation, however, gain remains below one and does not improve with additional context.

		Initial Context is Unexcited			Initial Context is Excited
Predictor	Ctx	$\Delta E$ [kWh]	$\Delta D$ [K 2 h]	$\Delta$ Obj.	$\Delta E$ [kWh]	$\Delta D$ [K 2 h]	$\Delta$ Obj.
Chronos-2 (zero-shot)	2 d	$-4.8\pm 2.3$	$-13.6\pm 6.1$	$-141.0\pm 60.7$	$-6.9\pm 3.1$	$-28.4\pm 12.3$	$-291.2\pm 124.4$
	5 d	$-3.4\pm 2.2$	$+14.2\pm 5.7$	$+138.7\pm 58.1$	$-3.4\pm 1.6$	$+6.8\pm 3.2$	$+64.1\pm 32.8$
+ EWMA	2 d	$-6.2\pm 2.2$	$-21.0\pm 7.9$	$-216.3\pm 78.9$	$-6.9\pm 3.1$	$-34.9\pm 12.0$	$-356.0\pm 120.7$
	5 d	$-5.4\pm 1.8$	$-0.9\pm 1.2$	$-14.8\pm 12.1$	$-4.2\pm 1.6$	$-0.0\pm 0.7$	$-4.3\pm 7.3$
Chronos-2 (fine-tuned)	2 d	$-4.7\pm 2.3$	$-18.9\pm 7.0$	$-193.4\pm 70.6$	$-6.9\pm 3.0$	$-32.2\pm 12.0$	$-328.6\pm 120.9$

Table 1: Closed-loop performance relative to the multi-step linear baseline. Mean paired differences over

n=17

held-out buildings under matched evaluation conditions; negative is better. Values are mean

\pm

standard error. Here,

E

denotes total heat-pump energy use, and

D

the time-integrated squared comfort-bound violation. The objective is

\mathrm{Obj.}=E+10D

. Absolute baseline values are shown in the final block.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Control response on a real building. Indoor temperature forecast 24 h ahead under the measured supply setpoint (heavy dashed) and under that setpoint shifted by

\pm 6

K (light dashed), against the measurement (grey). Columns are the six most heating-active days at least 48 h apart, headed by their mean outdoor temperature and the share of the horizon the heat pump spent heating; rows cross context length with predictor, and each column shares a

y

axis. With a short context both predictors are almost insensitive to the control. The house ran under its own controller, so the offset plans have no measured response to score against and the figure shows only whether the forecast moves. The percentage under the date describes the time the heat-pump was active in the context.

Channel	TSFM type	Control role	Context	Horizon
$T_{\mathrm{room}}$	target	output	observed	predicted
$T_{\mathrm{hp,ret}}$	target	output	observed	predicted
$T_{\mathrm{hp,sup}}$	covariate	control	observed	given
$T_{\mathrm{amb}}$ , GHI, DNI, DHI	covariate	exogenous	measured	forecast

Appendix

Table 2: TSFM channels used throughout the experiments.

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Longer histories can improve time-series foundation models (TSFMs), but require substantially higher inference cost. We therefore ask whether contextual information can be provided more efficiently through a compact set of learned token embeddings. We introduce PaCTS, which generates a small set of instance-adaptive latent prompts in the form of continuous embedding tokens conditioned on the visible context. These prompts serve as compact context surrogates for frozen TSFMs. PaCTS constructs them from instance-specific global statistics and further refines them with segment-level temporal information, capturing both global characteristics and local temporal variations. The prompt module is jointly trained and deployed across heterogeneous time series with the frozen backbone. Extensive experiments demonstrate the effectiveness of prompts as context, consistently improving forecasting across context lengths and model architectures. With a shorter input context, PaCTS can outperform the same frozen backbone using double context while requiring substantially less inference computation. Compared with weight-space adaptation methods, PaCTS achieves stronger improvements and better out-of-distribution generalization.

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