Do time-series foundation models need control excitation for predictive control?

Low forecast error does not imply correct control response

Model predictive control (MPC) needs a predictive model that answers an interventional question: what happens to the output if the controller chooses a different future input? Standard forecasting answers an observational question instead, because it scores predictions on trajectories produced by the fixed controller that generated the data. A model can therefore achieve low error by capturing passive dynamics, exogenous disturbances, or regularities of the data-generating policy without correctly modeling out-of-distribution control inputs.

The paper makes this gap concrete in residential heat-pump control. Zero-shot Chronos-2 outperformed a multi-step linear predictor on real-world building data for both room-temperature and heat-pump power forecasting across context lengths, yet that advantage did not establish that the model captured the input-output relationships required for control. The authors therefore separate nominal forecast accuracy from input-response fidelity rather than treating the first as evidence for the second.

Matched intervention probes isolate the response gain

To measure control fidelity, the authors build sets of matched probes that share the building, context, initial state, and weather but differ in their future control. Each probe is simulated to obtain its ground-truth intervention outcome. After centering realized and predicted trajectories around their per-step probe means, they compute the response gain: the pooled least-squares coefficient of predicted on realized deviations. A gain near 1 indicates a correctly scaled response, while a gain near 0 indicates little sensitivity to the control.

Response gain complements rather than replaces nominal forecast error. It removes errors shared across probes and evaluates only the response component, so it tests a necessary condition for model-based control without establishing complete trajectory agreement or closed-loop performance. In the open-loop experiments, the prediction horizon is fixed at 24 hours and context lengths of 1, 2, 5, and 21 days are evaluated. Context controls are replaced with an APRBS excitation signal, while forecast-window interventions use constant offsets to the reference MPC controls.

Unexcited context fits the trajectory but misses the intervention

With 21 days of unexcited MPC context, Chronos-2 fit the observational trajectory well but did not respond to constant offset interventions on the controls. The multi-step linear estimator, fitted on the same context window, did separate the offset trajectories. The authors note that the class of mappings representable by Chronos-2 is much richer, while the linear model's inductive bias is expected to be very close to the true simulator dynamics, making it a competitive baseline.

With an excited APRBS context, Chronos-2's ability to estimate the effect of the control intervention greatly improved. Increasing context length alone, without excited data, reduced the predictive error of all TSFMs on the nominal control trajectory but did not improve their gain. Under excitation, gain increased with both context length and excitation amplitude, approaching 1 under high excitation and maximum context length. In these experiments, sufficient excitation amplitude rather than context length alone was required for reliable in-context system identification.

EWMA features shorten the context needed for the same gain

Adding three exponentially weighted moving average (EWMA) control channels at different time scales significantly reduced the context length Chronos-2 required to reach the same gain level, but it did not increase the maximum gain obtainable at a given excitation level. The improvement came at a cost in nominal accuracy: MAE increased across excitation regimes, although longer context reduced MAE within each regime.

The per-window linear estimator achieved the strongest gain over most of the sweep and the lowest long-context MAE in every regime, but it could not be fitted reliably with little context. Chronos-2 matched or exceeded its gain only under the strongest excitation with the longest context; elsewhere the TSFMs underestimated the response magnitude. The authors conclude that in-context identification requires informative and potentially disruptive excitation and rarely outperforms explicit identification when sufficient data are available.

Fine-tuning reduces the excitation requirement without removing it

Cross-building fine-tuning improved response gain primarily when context was limited, and fine-tuning on excited trajectories outperformed fine-tuning on closed-loop MPC data. Combining excited fine-tuning with EWMA features gave the strongest gains: with one day of context, this variant already recovered a substantial response under no or low excitation, and under medium or high excitation it dominated at short-to-intermediate context lengths. These improvements incurred no systematic accuracy penalty, as its nominal MAE was generally lowest or close to lowest.

Fine-tuning nevertheless did not fully replace excitation. Under unexcited operation, gain remained well below 1 and did not improve with additional context, and given sufficient history the per-window linear estimator eventually performed better. Medium or high excitation allowed the fine-tuned EWMA model to approach unit gain, with differences between models diminishing as context grew. Fine-tuning and multiscale features therefore transfer useful prior information and substantially reduce the required context and excitation, but informative variation in the target system remains necessary for full identification.

Closed-loop gains appear even from an unexcited initial context

In a preliminary and separate closed-loop evaluation, the predictors were compared within MPC on 17 held-out buildings under matched evaluation conditions, using the improved cross-entropy method for trajectory optimization. Performance is reported as mean paired differences relative to the multi-step linear baseline, where negative is better; E denotes total heat-pump energy use, D the time-integrated squared comfort-bound violation, and the objective is Obj. = E + 10D.

Chronos-2 improved the closed-loop objective, particularly with an excited context and EWMA correction. The authors state that these experiments do not establish a direct relationship between open-loop response gain and closed-loop performance. Surprisingly, performance was good even when the initial context at the start of an episode was unexcited. The authors hypothesize that future control actions selected by the optimizer are subsequently executed and enter the rolling context, thereby providing implicit excitation; the open-loop experiments instead used context generated by a deterministic MPC with no learning or inference dynamics. Verifying this mechanism directly is left for future work.

Prioritize excitation and context design over forecast error

The paper's practical priority is that context is a central design variable for TSFM-based control. Nominal forecast accuracy alone does not reveal whether a model will respond correctly to the alternative actions a controller considers, so a low MAE on the factual trajectory is not sufficient evidence for deployment. The decision-relevant comparison is between excitation regimes and context lengths: unexcited context leaves gain below 1 regardless of additional context, while medium or high excitation lets fine-tuned EWMA models approach unit gain, and a compact linear identifier remains competitive given sufficient excited history.

The authors' evaluation is primarily synthetic, leaving open how well these findings transfer to real-world systems, and they suggest future work on TSFMs designed specifically for control, including whether naturally occurring control variation such as price-responsive operation can further reduce the need for dedicated excitation. The open question they leave is how to retain control-informative observations and how much excitation is required for reliable input-output identification. For readers weighing a TSFM against an explicit identifier, the paper's threshold is therefore not forecast error but whether the inference context contains enough independent control variation to identify the response.

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