Operations Research Meets Machine Learning: Bayesian Optimization for Accelerating the Product Development in Additive Manufacturing and Thermoelectric Materials

The design of chemical-based products and functional materials is vital to modern technologies, yet remains challenging due to costly and time-consuming manufacturing processes. These processes often involve tens of variables, resulting in hundreds of thousands of possible experiments, with each experiment carrying significant resource costs. In such high-dimensional domains, traditional Edisonian, trial-and-error approaches become prohibitively expensive and inefficient at identifying optimal experimental conditions. Consequently, there is a critical need to shift from these conventional methods to more systematic, data-driven decision-making. Machine learning (ML) and operations research (OR) offer promising approaches to address these challenges through novel optimization frameworks. By building surrogate models that capture the relationships between decision variables and targeted objectives, ML enables predictive modeling of complex manufacturing processes. OR then integrates these pre-trained models into a unified optimization framework, facilitating data-driven, rational, and scientifically grounded decisions that accelerate product development while minimizing experimental costs. In this work, we present an ML- and OR-based framework that combines Bayesian optimization (BO) with first-principles knowledge. We demonstrate its effectiveness in solving industrial manufacturing optimization problems across additive manufacturing and thermoelectric material domains, including flash sintering, plasma sintering, and aerosol jet printing. Our framework accelerates the identification of optimal experimental conditions while reducing both economic and labor costs. Moreover, by incorporating physical knowledge in multiple ways, it is ideally suited for data-scarce, customized, and expensive experiments. It is a general framework that is not restricted to any single application domain.

化学基产品与功能材料的设计研发对现代技术发展至关重要，但受制于高昂的制造成本与冗长的工艺流程，该领域仍面临诸多挑战。此类制造流程通常涉及数十个调控变量，由此可衍生出数十万种潜在实验方案，且每一项实验均需耗费可观的资源成本。在这类高维研究场景中，传统的爱迪生式试错法（Edisonian trial-and-error）在筛选最优实验条件时，不仅成本高得令人望而却步，且效率极低。因此，业界亟需从这类传统方法转向更具系统性的数据驱动型决策模式。机器学习（ML）与运筹学（OR）可通过创新性优化框架，为应对此类挑战提供极具潜力的解决路径。通过构建能够捕捉决策变量与目标函数间关联关系的代理模型（surrogate model），机器学习可实现复杂制造流程的预测建模。随后运筹学可将这些预训练好的代理模型整合至统一的优化框架中，助力实现数据驱动、逻辑严谨且基于科学原理的决策，从而在降低实验成本的同时加速产品研发进程。本研究提出了一种融合机器学习与运筹学的框架，该框架将贝叶斯优化（Bayesian Optimization, BO）与第一性原理知识（first-principles knowledge）相结合。我们通过在增材制造（additive manufacturing）与热电材料（thermoelectric material）两大领域（涵盖闪烧烧结（flash sintering）、等离子烧结（plasma sintering）及气溶胶喷射打印（aerosol jet printing）等场景）的工业制造优化问题中开展验证，证实了该框架的有效性。本框架可在快速筛选最优实验条件的同时，降低经济与人力成本。此外，通过多维度融入物理知识，该框架尤其适用于数据稀缺、定制化且实验成本高昂的研发场景。该框架具备通用性，不受限于单一应用领域。