Flexible formulation of value for experiment interpretation and design

The challenge of optimal design of experiments pervades materials science, physics, chemistry, and biology. Bayesian optimization has been used to address this challenge but requires framing experimental campaigns through the lens of maximizing some observable. However, this framing is insufficient for epistemic research goals that seek to comprehensively analyze a sample space, without an explicit scalar objective. In this work, we propose a flexible formulation of scientific value that recasts a dataset of input conditions and higher -dimensional observable data into a continuous, scalar metric. Intuitively, the function measures where observables change significantly, emulating the perspective of experts driving an experiment. We demonstrate this as a collaborative analysis tool and objective for optimization technique using two simulated and two experimental examples. The method is flexible, easily deployed, seamlessly compatible with existing optimization tools, can be extended to multi -modal and multi -fidelity experiments, and can integrate existing models of an experimental system.