Can Time-Series Foundation Models Serve as Simulators for Process Control?

Forecasting accuracy alone does not establish whether time-series foundation models (TSFMs) can simulate responses to specified control inputs or support effective control. We evaluate frozen TSFMs on noiseless linear processes with adjustable gain, time scale, and delay, varying historical control, input patterns, and inputs beyond the context range. We assess physical response fidelity, overall prediction accuracy, and closed-loop performance within model-predictive control. In matched comparisons, the tested TSFMs do not consistently outperform a history-validated linear baseline in prediction or control. Response diagnostics reveal direction, timing, and magnitude errors, while prediction and control rankings differ in some settings. These findings motivate jointly evaluating response fidelity, candidate judgments, and executed control rather than relying on forecasting accuracy alone.