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

Can a time-series foundation model (TSFM) predict what happens when we change an input, and help choose actions that keep an output near its target? We introduce a benchmark covering five synthetic process families and twelve evaluation factors for prescribed-input prediction, with executed control tests on selected conditions from all five families. For each proposed action, known dynamics generate two trajectories from the same state: one with the action and one with the input held unchanged. Their difference reveals the action response. We assess that response, then use each predictor to select inputs in an executed control test. We compare three frozen TSFMs with four locally fitted models. On clean first-order systems with input delays, TSFM predictions include transient reversed responses, timing errors, and amplitude errors. On integrating processes, their response-skill point estimates exceed the tested finite-impulse-response and multilayer-perceptron models, and all three also achieve lower tracking error. A locally fitted autoregressive model nevertheless has the lowest family-equal core tracking error among learned models. Better prediction does not guarantee better control: among local models with identical fitted artifacts reused across stages, orderings reverse in 10.2% of weighted within-task comparisons on clean first-order tasks, retaining ties in the denominator. The benchmark evaluates physical response fidelity together with executed control, exposing capabilities and failures that forecasting scores alone do not capture.