Regularized ensemble: integrating frequentist-and-bayesian approach to polymer processing-to-property uncertainty

• A regularized ensemble (RE) strategy is introduced to quantify model uncertainty. • This strategy leverages both advantages of frequentist and Bayesian approach. • It provides a state-of-the-art accurate yet efficient uncertainty estimation. • A processing stability metric is derived to identify high quality process windows. • The RE strategy is generic to any material fabrication–property uncertainty. Data-driven modeling of polymer processing–property relationship is key to predict and design polymeric product properties. However, this modeling is generally challenged by the lack of prediction uncertainty and reliability evaluation. Here, relying on Bayesian ensembling (BE) approach, we introduce a “regularized ensemble” (RE) strategy—featured by implementation convenience and uncertainty tunability—to evaluate polymer processing–property uncertainty, exemplified by neural network modeling of injection-molded polypropylene toughness. Inherited from BE approach to leverage and integrate Bayesian theory into frequentist statistics, we find that the RE model offers an accurate yet efficient uncertainty estimation when compared to baseline models using classical frequentist or Bayesian approach, including deep ensemble, Bayesian neural network, and Gaussian process regression. Impressively, trained by the real-world small, noisy dataset of 27 samplings in a 4-dimension design space of molding conditions, the RE model exhibits up to two times toughness predictability compared to baseline models, with the estimated uncertainty properly covering the experimental variations, enabling us to derive a stability metric to identify the promising process windows that yield stable specimens of high toughness. Overall, this work establishes an optimal uncertainty evaluation paradigm empowered by RE strategy, versatile to quantify prediction reliability of polymer processing–property modeling and generically material property designs.