Optimizing Thermoplastic Starch Film with Heteroscedastic Gaussian Processes in Bayesian Experimental Design Framework

The development of thermoplastic starch (TPS) films is crucial for fabricating sustainable and compostable plastics with desirable mechanical properties. However, traditional design of experiments (DOE) methods used in TPS development are often inefficient. They require extensive time and resources while frequently failing to identify optimal material formulations. As an alternative, adaptive experimental design methods based on Bayesian optimization (BO) principles have been recently proposed to streamline material development by iteratively refining experiments based on prior results. However, most implementations are not suited to manage the heteroscedastic noise inherently present in physical experiments. This work introduces a heteroscedastic Gaussian process (HGP) model within the BO framework to account for varying levels of uncertainty in the data, improve the accuracy of the predictions, and increase the overall experimental efficiency. The aim is to find the optimal TPS film composition that maximizes its elongation at break and tensile strength. To demonstrate the effectiveness of this approach, TPS films were prepared by mixing potato starch, distilled water, glycerol as a plasticizer, and acetic acid as a catalyst. After gelation, the mixture was degassed via centrifugation and molded into films, which were dried at room temperature. Tensile tests were conducted according to ASTM D638 standards. After five iterations and 30 experiments, the films containing 4.5 wt% plasticizer and 2.0 wt% starch exhibited the highest elongation at break (M = 96.7%, SD = 5.6%), while the films with 0.5 wt% plasticizer and 7.0 wt% starch demonstrated the highest tensile strength (M = 2.77 MPa, SD = 1.54 MPa). These results demonstrate the potential of the HGP model within a BO framework to improve material development efficiency and performance in TPS film and other potential material formulations.