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1. Learning and Optimization with Bayesian Hybrid Models

   https://doi.org/10.23919/ACC45564.2020.9148007  

   Eugene, E. A; Gao, X.; Dowling, A. W. (July 2021, 2020 American Control Conference (ACC))

   null (Ed.)

   Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with fewer data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty. 

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2. Chemically-informed data-driven optimization (ChIDDO): leveraging physical models and Bayesian learning to accelerate chemical research

   https://doi.org/10.1039/D2RE00005A  

   Frey, Daniel; Shin, Ju Hee; Musco, Christopher; Modestino, Miguel A. (April 2022, Reaction Chemistry & Engineering)

   Current methods of finding optimal experimental conditions, Edisonian systematic searches, often inefficiently evaluate suboptimal design points and require fine resolution to identify near optimal conditions. For expensive experimental campaigns or those with large design spaces, the shortcomings of the status quo approaches are more significant. Here, we extend Bayesian optimization (BO) and introduce a chemically-informed data-driven optimization (ChIDDO) approach. This approach uses inexpensive and low-fidelity information obtained from physical models of chemical processes and subsequently combines it with expensive and high-fidelity experimental data to optimize a common objective function. Using common optimization benchmark objective functions, we describe scenarios in which the ChIDDO algorithm outperforms the traditional BO approach, and then implement the algorithm on a simulated electrochemical engineering optimization problem. 

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3. Machine Learning Enabled Design and Optimization for 3D‐Printing of High‐Fidelity Presurgical Organ Models

   https://doi.org/10.1002/admt.202400037  

   Chen, Eric_S; Ahmadianshalchi, Alaleh; Sparks, Sonja_S; Chen, Chuchu; Deshwal, Aryan; Doppa, Janardhan_R; Qiu, Kaiyan (August 2024, Advanced Materials Technologies)

   Abstract The development of a general‐purpose machine learning algorithm capable of quickly identifying optimal 3D‐printing settings can save manufacturing time and cost, reduce labor intensity, and improve the quality of 3D‐printed objects. Existing methods have limitations which focus on overall performance or one specific aspect of 3D‐printing quality. Here, for addressing the limitations, a multi‐objective Bayesian Optimization (BO) approach which uses a general‐purpose algorithm to optimize the black‐box functions is demonstrated and identifies the optimal input parameters of direct ink writing for 3D‐printing different presurgical organ models with intricate geometry. The BO approach enhances the 3D‐printing efficiency to achieve the best possible printed object quality while simultaneously addressing the inherent trade‐offs from the process of pursuing ideal outcomes relevant to requirements from practitioners. The BO approach also enables us to effectively explore 3D‐printing inputs inclusive of layer height, nozzle travel speed, and dispensing pressure, as well as visualize the trade‐offs between each set of 3D‐printing inputs in terms of the output objectives which consist of time, porosity, and geometry precisions through the Pareto front. 

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4. Direct Regret Optimization in Bayesian Optimization

   Zhang, F; Chen, Y (July 2025, First Exploration in AI Today Workshop at ICML (EXAIT at ICML 2025))

   Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate hand-crafted acquisition functions and surrogate models for the underlying function, and often operate in a myopic manner. In this paper, we propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition by distilling from a set of candidate models and acquisitions, and explicitly targets minimizing the multi-step regret. Our framework leverages an ensemble of Gaussian Processes (GPs) with varying hyperparameters to generate simulated BO trajectories, each guided by an acquisition function chosen from a pool of conventional choices, until a Bayesian early stop criterion is met. These simulated trajectories, capturing multi-step exploration strategies, are used to train an end-to-end decision transformer that directly learns to select next query points aimed at improving the ultimate objective. We further adopt a dense training–sparse learning paradigm: The decision transformer is trained offline with abundant simulated data sampled from ensemble GPs and acquisitions, while a limited number of real evaluations refine the GPs online. Experimental results on synthetic and real-world benchmarks suggest that our method consistently outperforms BO baselines, achieving lower simple regret and demonstrating more robust exploration in high-dimensional or noisy settings. 

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5. Bayesian optimization with adaptive surrogate models for automated experimental design

   https://doi.org/10.1038/s41524-021-00662-x  

   Lei, Bowen; Kirk, Tanner Quinn; Bhattacharya, Anirban; Pati, Debdeep; Qian, Xiaoning; Arroyave, Raymundo; Mallick, Bani K. (December 2021, npj Computational Materials)

   Abstract Bayesian optimization (BO) is an indispensable tool to optimize objective functions that either do not have known functional forms or are expensive to evaluate. Currently, optimal experimental design is always conducted within the workflow of BO leading to more efficient exploration of the design space compared to traditional strategies. This can have a significant impact on modern scientific discovery, in particular autonomous materials discovery, which can be viewed as an optimization problem aimed at looking for the maximum (or minimum) point for the desired materials properties. The performance of BO-based experimental design depends not only on the adopted acquisition function but also on the surrogate models that help to approximate underlying objective functions. In this paper, we propose a fully autonomous experimental design framework that uses more adaptive and flexible Bayesian surrogate models in a BO procedure, namely Bayesian multivariate adaptive regression splines and Bayesian additive regression trees. They can overcome the weaknesses of widely used Gaussian process-based methods when faced with relatively high-dimensional design space or non-smooth patterns of objective functions. Both simulation studies and real-world materials science case studies demonstrate their enhanced search efficiency and robustness. 

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