Function Space Representations for Complex Material Workflows

Self-driving laboratories (SDL) are primed to improve the pace of material discovery and provide tangible solutions to emergent energy, health care, and sustainability applications using a combination of robotic agents and machine learning tools. They replace the traditional, time-consuming experimental-based ideate-synthesize-characterize loop with a more efficient set of agents that accelerate them in all aspects by being able to autonomously make decisions consistent with the physics and chemistry of the underlying system. Data-driven methods are the primary workhorse for developing autonomous agents and have been successfully applied in various applications ranging from closed-loop mapping of synthesis-property relationships to material retrosynthesis of semiconductors, nanoparticles, and 3D printed structures. However, unlike other autonomous agents developed elsewhere, SDL generates a data set of different modalities ranging from scalar outputs (e.g.: efficiency) to a function (e.g.: spectroscopy measurement). I will describe the challenges associated with building models for knowledge extraction and autonomous decision-making using functional data generated to study the nanoscale structure of colloidal and polymer materials and provide a tractable mathematical framework using the differential geometry of function spaces.