Abstract: Abstract Multi-photon polymerization is a well-established, yet actively developing, additive manufacturing technique for 3D printing on the micro/nanoscale. Like all additive manufacturing techniques, determining the process parameters necessary to achieve dimensional accuracy for a structure 3D printed using this method is not always straightforward and can require time-consuming experimentation. In this work, an active machine learning based framework is presented for determining optimal process parameters for the recently developed, high-speed, layer-by-layer continuous projection 3D printing process. The proposed active learning framework uses Bayesian optimization to inform optimal experimentation in order to adaptively collect the most informative data for effective training of a Gaussian-process-regression-based machine learning model. This model then serves as a surrogate for the manufacturing process: predicting optimal process parameters for achieving a target geometry, e.g., the 2D geometry of each printed layer. Three representative 2D shapes at three different scales are used as test cases. In each case, the active learning framework improves the geometric accuracy, with drastic reductions of the errors to within the measurement accuracy in just four iterations of the Bayesian optimization using only a few hundred of total training data. The case studies indicate that the active learning framework developed in this work can be broadly applied to other additive manufacturing processes to increase accuracy with significantly reduced experimental data collection effort for optimization.

Abstract: An autonomous synthesis of organic flow battery molecules using flexible batch Bayesian optimization to handle varying variables sizes in a single batch.

Abstract: Bayesian optimization (BO) is an effective paradigm for the optimization of expensive-to-sample systems. Standard BO learns the performance of a system f(x) by using a Gaussian Process (GP) model; this treats the system as a black box and limits its ability to exploit available structural knowledge (e.g., physics and sparse interconnections in a complex system). Gray-box modeling, wherein the performance function is treated as a composition of known and unknown intermediate functions f(x, y(x)) (where y(x) is a GP model), offers a solution to this limitation; however, generating an analytical probability density for f from the Gaussian density of y(x) is often an intractable problem (e.g., when f is nonlinear). Previous work has handled this issue by using sampling techniques or by solving an auxiliary problem over an augmented space where the values of y(x) are constrained by confidence intervals derived from the GP models; such solutions are computationally intensive. In this work, we provide a detailed implementation of a recently proposed gray-box BO paradigm, BOIS, that uses adaptive linearizations of f to obtain analytical expressions for the statistical moments of the composite function. We show that the BOIS approach enables the exploitation of structural knowledge, such as that arising in interconnected systems as well as systems that embed multiple GP models and combinations of physics and GP models. We benchmark the effectiveness of BOIS against standard BO and existing gray-box BO algorithms using a pair of case studies focused on chemical process optimization and design. Our results indicate that BOIS performs as well as or better than existing gray-box methods, while also being less computationally intensive.

Abstract: We use Bayesian optimization in combination with three-dimensional particle-in-cell simulations to determine the optimal laser and plasma parameters that, for a given laser pulse energy, maximize the cut-off energy of an electron beam produced by laser wakefield accelerators. We assume a Gaussian laser driver with matched spot size and amplitude and investigate both self-guiding in a uniform-density plasma and guiding in a preformed plasma channel with matched radius. To interpret the simulation results quantitatively, we derive novel analytical expressions for the maximum electron energy and the corresponding acceleration distance, accounting for the effects of laser diffraction and energy depletion. Based on the results obtained, we discuss the potential scalability of the optimal input (plasma density, pulse duration, amplitude, spot size, and channel radius) and output (electron energy, electron charge, acceleration length, and acceleration efficiency) parameters to laser systems of arbitrary energy.

Abstract: Bayesian optimization (BO) is a sequential decision-making tool widely used for optimizing expensive black-box functions. Recently, Large Language Models (LLMs) have shown remarkable adaptability in low-data regimes, making them promising tools for black-box optimization by leveraging contextual knowledge to propose high-quality query points. However, relying solely on LLMs as optimization agents introduces risks due to their lack of explicit surrogate modeling and calibrated uncertainty, as well as their inherently opaque internal mechanisms. This structural opacity makes it difficult to characterize or control the exploration-exploitation trade-off, ultimately undermining theoretical tractability and reliability. To address this, we propose LLINBO: LLM-in-the-Loop BO, a hybrid framework for BO that combines LLMs with statistical surrogate experts (e.g., Gaussian Processes (GP)). The core philosophy is to leverage contextual reasoning strengths of LLMs for early exploration, while relying on principled statistical models to guide efficient exploitation. Specifically, we introduce three mechanisms that enable this collaboration and establish their theoretical guarantees. We end the paper with a real-life proof-of-concept in the context of 3D printing. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/LLM-in-the-Loop-BO.

Abstract: Abstract The discovery of high‐performance electrocatalysts is crucial for advancing sustainable energy technologies. Compositionally complex solid solutions comprising multiple metals offer promising catalytic properties, yet their exploration is challenging due to the combinatorial explosion of possible compositions. In this work, human‐decision driven combinatorial sputtering of thin‐film materials libraries and high‐throughput characterization is combined with Bayesian optimization to efficiently explore the quaternary composition space Ni‐Pd‐Pt‐Ru for the oxygen evolution reaction (OER) in alkaline media. Using this method, the global activity optimum of pure Ru is identified after covering less than 20% of the complete composition space with six materials libraries. Six additional libraries are fabricated to validate the activity trend. The resulting dataset is used to formulate general guidelines for the efficient composition of space exploration with combinatorial synthesis paired with Bayesian optimization.

Abstract: This work presents a methodology to estimate tire parameters and their uncertainty using a Bayesian optimization approach. The literature mainly considers the estimation of tire parameters but lacks an evaluation of the parameter identification quality and the required slip ratios for an adequate model fit. Therefore, we examine the use of Stochastical Variational Inference as a methodology to estimate both - the parameters and their uncertainties. We evaluate the method compared to a state-of-the-art Neider-Mead algorithm for theoretical and real-world application. The theoretical study considers parameter fitting at different slip ratios to evaluate the required excitation for an adequate fitting of each parameter. The results are compared to a sensitivity analysis for a Pacejka Magic Formula tire model. We show the application of the algorithm on real-world data acquired during the Abu Dhabi Autonomous Racing League and highlight the uncertainties in identifying the curvature and shape parameters due to insufficient excitation. The gathered insights can help assess the acquired data's limitations and instead utilize standardized parameters until higher slip ratios are captured. We show that our proposed method can be used to assess the mean values and the uncertainties of tire model parameters in real-world conditions and derive actions for the tire modeling based on our simulative study.

Abstract: h-BCN is an intriguing material system where the bandgap varies considerably depending on the atomic configuration, even at a fixed composition. Exploring stable atomic configurations in this system is crucial for discussing the energetic formability and controllability of desirable configurations. In this study, this challenge is tackled by combining first-principles calculations with Bayesian optimization. An encoding method that represents the configurations as vectors, while incorporating information about the local atomic environments and domain knowledge, is proposed for the search. The proposed encoding method proved effective in the search, resulting in the discovery of two interesting and stable semiconductor configurations. Furthermore, the optimization behavior is discussed through principal component analysis, confirming that the ordered BN network and the C configuration features are well embedded in the search space. While our approach provided a tailored encoding for the h-BCN system in this study, it holds promise for broader application to other materials by adapting the domain knowledge matrix to each target system.

Abstract: Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the high computational complexity of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose the Bayesian Optimization by Kernel regression and density-based Exploration (BOKE) algorithm. BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and the improved kernel regression upper confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE and ensures its robustness. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.

Abstract: Many optimization problems in robotics involve the optimization of time-expensive black-box functions, such as those involving complex simulations or evaluation of real-world experiments. Furthermore, these functions are often stochastic as repeated experiments are subject to unmeasurable disturbances. Bayesian optimization can be used to optimize such methods in an efficient manner by deploying a probabilistic function estimator to estimate with a given confidence so that regions of the search space can be pruned away. Consequently, the success of the Bayesian optimization depends on the function estimator's ability to provide informative confidence bounds. Existing function estimators require many function evaluations to infer the underlying confidence or depend on modeling of the disturbances. In this paper, it is shown that the confidence bounds provided by the Wilson Score Kernel Density Estimator (WS-KDE) are applicable as excellent bounds to any stochastic function with an output confined to the closed interval [0;1] regardless of the distribution of the output. This finding opens up the use of WS-KDE for stable global optimization on a wider range of cost functions. The properties of WS-KDE in the context of Bayesian optimization are demonstrated in simulation and applied to the problem of automated trap design for vibrational part feeders.

Abstract: Background/Objectives: Manual tuning of exoskeleton control parameters is tedious and often ineffective for adapting to individual users. Human-in-the-loop (HIL) optimization offers an automated approach, but existing methods typically rely on metabolic cost, which requires prolonged data collection times of at least 60 seconds. Surface electromyography (EMG) signals, as an alternative, enable faster optimization with reduced data acquisition times. This study develops a rapid EMG-based HIL Bayesian optimization framework to tune hip exoskeleton controllers for assisting free leg swinging. Methods: Eight participants are asked to perform leg swinging at two frequencies with assistance from a hip exoskeleton. EMG signals from four sensors, representing muscle activity during forward and backward swings, are dynamically processed into cost functions. Bayesian optimization with Gaussian processes tunes four controller parameters using an Expected Improvement acquisition function. Optimization outcomes are validated against no device, zero torque, and general control baselines. Results: Optimization converged within 142 ± 24 seconds, yielding muscle activity reductions of 16.1 compared to no device, 21.7% versus zero torque, and 15.1% versus general control (p < 0.001 for all). EMG-based tuning is faster than metabolic-cost-based methods and perceived as less effortful, with Borg scale reductions of up to 39.5%. Conclusions: EMG-based HIL optimization significantly enhances controller tuning speed and effectiveness, demonstrating its potential for scalable and user-specific exoskeleton applications.

Abstract: Designing modern industrial systems requires balancing several competing objectives, such as profitability, resilience, and sustainability, while accounting for complex interactions between technological, economic, and environmental factors. Multi-objective optimization (MOO) methods are commonly used to navigate these tradeoffs, but selecting the appropriate algorithm to tackle these problems is often unclear, particularly when system representations vary from fully equation-based (white-box) to entirely data-driven (black-box) models. While grey-box MOO methods attempt to bridge this gap, they typically impose rigid assumptions on system structure, requiring models to conform to the underlying structural assumptions of the solver rather than the solver adapting to the natural representation of the system of interest. In this chapter, we introduce a unifying approach to grey-box MOO by leveraging network representations, which provide a general and flexible framework for modeling interconnected systems as a series of function nodes that share various inputs and outputs. Specifically, we propose MOBONS, a novel Bayesian optimization-inspired algorithm that can efficiently optimize general function networks, including those with cyclic dependencies, enabling the modeling of feedback loops, recycle streams, and multi-scale simulations - features that existing methods fail to capture. Furthermore, MOBONS incorporates constraints, supports parallel evaluations, and preserves the sample efficiency of Bayesian optimization while leveraging network structure for improved scalability. We demonstrate the effectiveness of MOBONS through two case studies, including one related to sustainable process design. By enabling efficient MOO under general graph representations, MOBONS has the potential to significantly enhance the design of more profitable, resilient, and sustainable engineering systems.

Abstract: The predistortion model represented by the Volterra series can effectively compensate for the nonlinearity of power amplifiers (PAs). Traditional models require a large amount of samples to solve for the polynomial coefficients, which makes it difficult to meet the demands of green communication. Therefore, this letter proposes an improved genetic algorithm (GA) to select the smallest training sample subset that preserves the model’s features. However, due to the nonorthogonality of the basis functions, ill-conditioned matrix problems are likely to occur during few-sample learning (FSL). To address this, Bayesian learning is applied before sample selection to sparsify the basis functions. This not only further reduces the dimensionality of the polynomial but also accelerates the update process of the GA fitness function. Experimental results show that the convergence speed of this joint optimization strategy is 66% faster than that of the traditional GA, and even with an 80.5% reduction in training data, it can still achieve accuracy comparable to that of full-sample fitting.

Abstract: In this paper, we present a novel multi-objective Bayesian optimization approach for tactile feedback transmission and reconstruction in the NFV-based tactile Internet (NFV-based TI). For such a system, guaranteeing real-time and precise feedback performance is crucial for achieving seamless remote interactions. By optimizing the virtual network function (VNF) placement, routing paths, admission control strategies for each service function chain (SFC), and wireless resource allocation (e.g., resource blocks), this paper aims to optimize the feedback signal transmission and reconstruction, thereby ensuring a high-fidelity user experience. In contrast to existing work, we investigate the dynamic adjustment under uncertain network conditions and propose a multi-objective Bayesian optimization approach tailored for hybrid opaque-transparent model problems. Specifically, we design a hybrid kernel function surrogate model, which is combined with novel sampling strategies explicitly developed for the dynamic network conditions of NFV-based TI. Moreover, our proposed approach can adaptively adjust the parameters of tactile feedback transmission and reconstruction according to the current network conditions and changes in user requirements. This enables the system to find an optimal trade-off between tactile feedback delay and tactile feedback fidelity, ultimately achieving Pareto-optimal solutions. Simulation results validate the proposed solution and demonstrate its superiority over counterparts.

Abstract: This paper presents a user-adaptive variable impedance control approach for robot-aided rehabilitation, initially focusing on an ankle rehabilitation application. The controller dynamically adjusts the impedance parameters based on the user's motion intent, thereby providing personalized assistance during motor tasks. Bayesian optimization is employed to enhance speed and accuracy during the motor tasks by minimizing an objective function formulated from the user's kinematic data. The optimization process incorporates a Gaussian process as a surrogate model to address uncertainties inherent in human behaviors. Furthermore, an outlier rejection method based on the Student-t process is integrated into Bayesian optimization to enhance its robustness. To evaluate the effectiveness of the proposed control approach, a goal-directed target-reaching study was conducted with 15 healthy participants using a wearable ankle robot. The performance metrics of speed, accuracy, task completion time, and user effort were used to compare the optimized variable impedance controller against an unoptimized counterpart. Results showed that the optimized controller achieved an average speed improvement of 9.9% and a 7.6% decrease in deviation from the target trajectory compared to the unoptimized controller. Additionally, the optimized controller reduced task completion time by 6.6% while maintaining a similar level of user effort. Notably, the optimal parameters for each individual varied significantly, highlighting the significance of the user-adaptive approach. Overall, this study demonstrates the effectiveness and feasibility of the proposed optimal variable impedance control approach for robot-aided rehabilitation applications, particularly in the context of ankle rehabilitation.

Abstract: The process of lead optimization in drug discovery is a complex, multi-objective challenge that remains a major bottleneck in the development of new therapeutics. Traditional approaches often struggle to efficiently explore the vast chemical space while simultaneously optimizing multiple, and sometimes conflicting, molecular properties. In this work, we present AutoLead, a novel framework that integrates Large Language Models (LLMs) with multi-objective Bayesian optimization to tackle this challenge. By leveraging the chemical reasoning capabilities of LLMs, AutoLead effectively guides the search for novel drug-like molecules that satisfy multiple objectives. We evaluate our approach on two molecule optimization tasks, achieving state-of-the-art results. Furthermore, we introduce a new benchmark dataset designed around a more realistic lead optimization scenario, where the task is to modify compounds that violate Lipinski's Rule of Five to simultaneously meet all criteria and improve their QED score. Through extensive experiments and a detailed case study, we demonstrate the potential of combining LLMs with black-box optimization techniques for more efficient and practical drug discovery.

Abstract: Purpose We propose an accelerated Bayesian optimization framework for tuning the learning rate of CNN+LSTM models in soil analysis, addressing the computational inefficiency of traditional Gaussian Process (GP)-based methods. This work bridges the gap between computational efficiency and probabilistic robustness, with broader implications for automated machine learning in geoscientific applications. Method The key innovation lies in a subspace-accelerated GP surrogate model that precomputes low-rank approximations of covariance matrices offline, thereby decoupling the costly hyperparameter tuning from the online acquisition function evaluations. By projecting the hyperparameter search space onto a dominant subspace derived from Nyström approximations, our method reduces the computational complexity from cubic to linear in the number of observations. The proposed system integrates seamlessly with existing CNN+LSTM pipelines, where the offline phase constructs the GP subspace using historical or synthetic data, while the online phase iteratively updates the subspace with rank-1 modifications. Moreover, the method’s adaptability to non-stationary response surfaces, facilitated by a Matérn-5/2 kernel with automatic relevance determination, makes it particularly suitable for soil data exhibiting multi-scale features. Results Empirical validation on soil spectral datasets demonstrates a 3–5× speedup in convergence compared to standard Bayesian optimization, with no loss in model accuracy. Experiments on soil spectral datasets show convergence in 23.4 min (3.8× faster than standard Bayesian optimization) with a test RMSE of 0.142, while maintaining equivalent accuracy across diverse CNN+LSTM architectures. Conclusion The reformulated approach not only overcomes the scalability limitations of conventional GP-based optimization but also preserves its theoretical guarantees, offering a practical solution for hyperparameter tuning in resource-constrained environments.