Finite element (FE) simulations of structures and materials are becoming increasingly accurate, but also more computationally expensive as a collateral result. This development occurs in parallel with a growing demand for data-driven design. To reconcile the two, a robust and data-efficient optimization method called Bayesian optimization (BO) has been previously established as a technique to optimize expensive objective functions. The mesh width of an FE model can be exploited to evaluate an objective at a lower or higher fidelity (cost & accuracy) level, which is the domain of multi-fidelity BO (MFBO) applications. However, BO and MFBO are usually not directly compared in the literature. Moreover, sampling quality and assessing design parameter sensitivity are often underrepresented parts of data-driven design. This paper combines global sensitivity analysis and (MF) BO into a novel, efficient Bayesian data-driven framework. We compare the performance of BO with that of MFBO by maximizing the energy absorption (EA) problem of spinodoid cellular structures. The findings show that similar or better designs are suggested by MFBO with 16% fewer expensive objective evaluations compared to BO when maximizing the EA. The results, which are made open-source, serve to support the utility of multi-fidelity techniques across expensive data-driven design problems.

Solder joint reliability related to failures due to thermomechanical loading is a critically important yet physically complex engineering problem. As a result, simulated behavior is oftentimes computationally expensive. In an increasingly data-driven world, it is popular to use efficient data-driven design schemes. Among the family of efficient optimization methods, Bayesian optimization with Gaussian process regression is a key representative. The authors argue that additional computational savings can be obtained from exploiting thorough surrogate modeling and selecting a design candidate based on multiple acquisition functions. This is feasible due to the relatively low computational cost, compared to the expensive simulation objective. This paper presents a novel heuristic framework for performing Bayesian optimization with adaptive hyperparameters across multiple optimization iterations. A comparative study shows the ability of adaptive Bayesian optimization to save on expensive objective evaluations with respect to the worst-performing regular Bayesian optimization scheme. As an engineering use case, the solder joint reliability problem is tackled by minimizing the accumulated non-linear creep strain under a cyclic thermal load. Results show that adaptive Bayesian optimization can at least match the performance of regular Bayesian optimization in terms of raw objective performance, but achieves this with half of the computational expense budget. This practical result underlines the methodological potential of the novel adaptive Bayesian data-driven methodology to achieve more efficient results and significantly cut optimization-related expenses. Lastly, to promote the reproducibility of the results, the data-driven implementations are made available on an open-source basis.

In the pursuit of designing safer and more efficient energy-absorbing structures, engineers must tackle the challenge of improving crush performance while balancing multiple conflicting objectives, such as maximising energy absorption and minimising peak impact forces. Accurately simulating real-world conditions necessitates the use of complex material models to replicate the non-linear behaviour of materials under impact, which comes at a significant computational cost. This study addresses these challenges by introducing a multi-objective Bayesian optimisation framework specifically developed to optimise spinodoid structures for crush energy absorption. Spinodoid structures, characterised by their scalable, non-periodic topologies and efficient stress distribution, offer a promising direction for advanced structural design. However, optimising design parameters to enhance crush performance is far from straightforward, particularly under realistic conditions. Conventional optimisation methods, although effective, often require a large number of costly simulations to identify suitable solutions, making the process both time-consuming and resource intensive. In this context, multi-objective Bayesian optimisation provides a clear advantage by intelligently navigating the design space, learning from each evaluation to reduce the number of simulations required, and efficiently addressing the complexities of non-linear material behaviour. By integrating finite element analysis with Bayesian optimisation, the framework developed in this study tackles the dual challenge of improving energy absorption and reducing peak force, particularly in scenarios where plastic deformation plays a critical role. Leveraging scalarisation and hypervolume-based techniques, the framework effectively identifies Pareto-optimal solutions that balance these conflicting objectives while accounting for the complexities of plastic material behaviour. Importantly, the approach also prevents problematic densification, ensuring structural integrity during impact. The results not only demonstrate the framework's ability to outperform the NSGA-II algorithm but also highlight its potential for wider applications in structural and material optimisation. The framework's adaptability to various design requirements underscores its capability to address complex, multi-objective optimisation challenges associated with real-world conditions.

High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies – comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.