Analysis of protein activity data by Gaussian stochastic process models

Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables

Although Bayesian Optimization (BO) has been employed for accelerating materials design in computational materials engineering, existing works are restricted to problems with quantitative variables. However, real designs of materials systems involve both qualitative and quantitative design variables representing material compositions, microstructure morphology, and processing conditions. For mixed-variable problems, existing Bayesian Optimization (BO) approaches represent qualitative factors by dummy variables first and then fit a standard Gaussian process (GP) model with numerical variables as the surrogate model. This approach is restrictive theoretically and fails to capture complex correlations between qualitative levels. We present in this paper the integration of a novel latent-variable (LV) approach for mixed-variable GP modeling with the BO framework for materials design. LVGP is a fundamentally different approach that maps qualitative design variables to underlying numerical LV in GP, which has strong physical justification. It provides flexible parameterization and representation of qualitative factors and shows superior modeling accuracy compared to the existing methods. We demonstrate our approach through testing with numerical examples and materials design examples. The chosen materials design examples represent two different scenarios, one on concurrent materials selection and microstructure optimization for optimizing the light absorption of a quasi-random solar cell, and another on combinatorial search of material constitutes for optimal Hybrid Organic-Inorganic Perovskite (HOIP) design. It is found that in all test examples the mapped LVs provide intuitive visualization and substantial insight into the nature and effects of the qualitative factors. Though materials designs are used as examples, the method presented is generic and can be utilized for other mixed variable design optimization problems that involve expensive physics-based simulations.

Regression spline models and model calibration in the identification of protein storage conditions

The study of protein-construct activity provides valuable insight in the early stages of drug discovery. Identification of optimal storage conditions that maintain activity of the constructs is an important issue. In the study reported herein, a space-filling design was used to assess the effects of eight design variables--buffer, pH, NaCl, protein concentration, reducing agent, detergent, MgCl2, and temperature--on protein activity. A regression spline analysis is presented, and settings of the explanatory factors resulting in the best predicted protein activity over the explored space are identified. The models are selected initially based on the Akaike information criterion and later assessed via root mean square error and cross-validation root mean square error. Detergent, buffer, temperature, and smooth functions of pH and protein concentration were found to have large effects on protein activity. The models were calibrated via calculation of the empirical distribution of the cross-validation root mean square error. In this framework several models provide a similar fit, and further experimentation is required for more definitive conclusions regarding protein storage conditions to be made. The cross-validation root mean square error calibration of models is recommended for applications involving comparisons of models with respect to their predictive ability.