  Scientific advancement is universally based on the dynamic interplay between
theoretical insights, modelling, and experimental discoveries. However, this
feedback loop is often slow, including delayed community interactions and the
gradual integration of experimental data into theoretical frameworks. This
challenge is particularly exacerbated in domains dealing with high-dimensional
object spaces, such as molecules and complex microstructures. Hence, the
integration of theory within automated and autonomous experimental setups, or
theory in the loop automated experiment, is emerging as a crucial objective for
accelerating scientific research. The critical aspect is not only to use theory
but also on-the-fly theory updates during the experiment. Here, we introduce a
method for integrating theory into the loop through Bayesian co-navigation of
theoretical model space and experimentation. Our approach leverages the
concurrent development of surrogate models for both simulation and experimental
domains at the rates determined by latencies and costs of experiments and
computation, alongside the adjustment of control parameters within theoretical
models to minimize epistemic uncertainty over the experimental object spaces.
This methodology facilitates the creation of digital twins of material
structures, encompassing both the surrogate model of behavior that includes the
correlative part and the theoretical model itself. While demonstrated here
within the context of functional responses in ferroelectric materials, our
approach holds promise for broader applications, the exploration of optical
properties in nanoclusters, microstructure-dependent properties in complex
materials, and properties of molecular systems. The analysis code that supports
the funding is publicly available at
https://github.com/Slautin/2024_Co-navigation/tree/main
