Bayesian expected uncertainty reduction (B-EUR) model: what makes environments worth exploring, with hypotheses for engineering design

Engineering designers explore under uncertainty, and the process of designing has a side that they enjoy in itself. What actions are worth trying, and what environments are worth exploring? We propose the Bayesian Expected Uncertainty Reduction (B-EUR) model, which formalises the value of trying an action as epistemic value in active inference: the expected reduction of uncertainty about action–outcome relations, summed over candidates. It identifies two properties of an exploration environment: transferability, or how far knowledge from one trial extends to neighbouring candidates, and output gain, or how strongly outcomes vary across candidates. Simulations predicted an inverted-U-shaped relationship of epistemic value with transferability, a positive effect of output gain, and an optimal transferability that decreases as trials accumulate. In a graph-shape guessing task with 44 participants, the value of trying, enjoyment and choices followed the predicted inverted U, and the optimal transferability for the value of trying decreased with observations; as predicted, larger output gain increased perceived uncertainty and choice frequency. B-EUR predicted choices better than competing measures. The study establishes a computational mechanism of reward-free exploration, tested in an abstract task, and derives hypotheses for prototyping, problem framing and design management that require validation in design contexts.