Bayesian Co-Navigation—Active Learning for Design of Material Digital Twins

Throughout history, science has aimed to uncover fundamental mechanisms and describe them through theoretical models to explain physical phenomena. Progress in this field depends on the dynamic interaction between theoretical insights, modeling, and experimental discoveries. However, integrating theoretical descriptions with experimental data is often a slow process, traditionally driven by community collaboration or additional efforts to incorporate data into models. The ability to dynamically design and refine theoretical models based on real-time experimental insights not only accelerates the integration of theory and experimentation but also lays the foundation for developing "digital twins" for material systems – a cutting-edge focus in the materials science community. A digital twin is a high-fidelity digital representation closely mirroring the current form and the functional responses of a specified physical object based on real-time experimental feedback. Digital twins should not only model material’s macroscopic behavior but also uncover the microscopic physical phenomena impacting them. This capability enables addressing the inverse problem and optimizing theoretical model parameters to yield desired macroscopic responses.<br/>We present a Bayesian co-navigation framework that guides the exploration and optimization of a material system's target functionality, using a theoretical model as a digital twin of the material system. The proposed workflow operates through two parallel iterative active learning loops: one theoretical and one experimental. Supposing significant computational cost of direct calculations by the theoretical model, Deep Kernel Learning (DKL) is employed as a surrogate model to explore the theoretical model's object space. At each exploration step, the theoretical DKL model is trained using the data available at that specific iteration. The next object to be investigated is selected using the classical Bayesian Optimization paradigm. The experimental loop is built on the same principles, predicting the experimental functionality and its uncertainty for the respective object space. The core idea of the Bayesian co-navigation lies in the utilization of the third <i>outer theory update loop</i> to align the theory and experiment. In this loop, we apply the theoretical DKL model to predict the target property of the experimentally investigated objects. Important, theoretical exploration and experimental measurements must be performed in identical or reflecting to each other object spaces, and their outputs must be comparable. The error function between the theoretical prediction and experimental observation is employed to tune the theoretical model to minimize the epistemic uncertainty. In other words, the outer theory update loop leverages real-time experimental feedback to transform the theoretical model into a digital twin of the material being explored.<br/>The effectiveness of the framework was validated through the investigation of the local ferroelectric properties of a PbTiO₃ thin film. The FerroSim lattice spin model, which predicts polarization hysteresis based on local domain arrangements, was utilized as the theoretical model. For the experimental study, local ferroelectric hysteresis loops were measured using a scanning probe microscope. Our experimentations showed a consistent reduction in the mismatch between experimental data and theoretical predictions, confirming the reliability of the approach.<br/>The co-navigational approach can be used for a diverse array of systems and theoretical models without any limitation on the nature of describing phenomena or model complexity. The implementation of the co-navigational approach is expected to significantly simplify the creation of digital twins for the materials.