  Both computational and experimental material discovery bring forth the
challenge of exploring multidimensional and often non-differentiable parameter
spaces, such as phase diagrams of Hamiltonians with multiple interactions,
composition spaces of combinatorial libraries, processing spaces, and molecular
embedding spaces. Often these systems are expensive or time-consuming to
evaluate a single instance, and hence classical approaches based on exhaustive
grid or random search are too data intensive. This resulted in strong interest
towards active learning methods such as Bayesian optimization (BO) where the
adaptive exploration occurs based on human learning (discovery) objective.
However, classical BO is based on a predefined optimization target, and
policies balancing exploration and exploitation are purely data driven. In
practical settings, the domain expert can pose prior knowledge on the system in
form of partially known physics laws and often varies exploration policies
during the experiment. Here, we explore interactive workflows building on
multi-fidelity BO (MFBO), starting with classical (data-driven) MFBO, then
structured (physics-driven) sMFBO, and extending it to allow human in the loop
interactive iMFBO workflows for adaptive and domain expert aligned exploration.
These approaches are demonstrated over highly non-smooth multi-fidelity
simulation data generated from an Ising model, considering spin-spin
interaction as parameter space, lattice sizes as fidelity spaces, and the
objective as maximizing heat capacity. Detailed analysis and comparison show
the impact of physics knowledge injection and on-the-fly human decisions for
improved exploration, current challenges, and potential opportunities for
algorithm development with combining data, physics and real time human
decisions.
