Autonomous Experiments in Infinite Dimensions: A Case Study in Bioformulation Phase Mapping

A fundamental challenge in scaling autonomous experimentation platforms beyond a few basic compositional and processing parameters is faithfully representing these complex variables for surrogate modeling and optimization. As autonomous workflows increasingly serve as quantified decision-making engines, the mathematical representation of experimental design variables for machine learning models becomes a critical bottleneck for operational efficiency. In this paper, we present a scalable, principled approach to navigate the complex design space of bioformulation phase mapping, which involves both compositional parameters (e.g., concentrations of proteins, excipients, and salts) and continuous processing parameters (e.g., temperature profiles). Specifically, we introduce a manifold-based data representation that enables efficient surrogate model construction and the active optimization of temperature profiles to measure protein phase separation. Because temperature profiles are continuous functions mapping measurement time to sample temperature, they inherently create an infinite-dimensional design space. By exploiting the underlying manifold structure of these functional profiles, our approach efficiently navigates this space. This methodology circumvents the curse of dimensionality, which typically degrades the performance of active learning in scaled autonomous workflows. Using an in silico case study emulating an autonomous phase-mapping campaign for protein phase separation, we demonstrate that the proposed manifold-based active learning approach is highly robust and yields superior performance compared to naive Bayesian active learning methods.