Taiwo A. Adebiyi

Taiwo A. Adebiyi, Bach Do, Ruda Zhang

Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior sample paths, especially in higher dimensions. We introduce an efficient global optimization strategy for posterior samples based on global rootfinding. It provides gradient-based optimizers with two sets of judiciously selected starting points, designed to combine exploration and exploitation. The number of starting points can be kept small without sacrificing optimization quality. Remarkably, even with just one point from each set, the global optimum is discovered most of the time. The algorithm scales practically linearly to high dimensions, breaking the curse of dimensionality. For Gaussian process Thompson sampling (GP-TS), we demonstrate remarkable improvement in both inner- and outer-loop optimization, surprisingly outperforming alternatives like EI and GP-UCB in most cases. Our approach also improves the performance of other posterior sample-based acquisition functions, such as variants of entropy search. Furthermore, we propose a sample-average formulation of GP-TS, which has a parameter to explicitly control exploitation and can be computed at the cost of one posterior sample. Our implementation is available at https://github.com/UQUH/TSRoots .

Akash Yadav, Taiwo A. Adebiyi, Ruda Zhang

Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic Attention, a lightweight inference-time modification that randomizes attention by replacing softmax weights with normalized multinomial samples controlled by a single concentration parameter, and produces predictive ensembles without retraining. To set this parameter, we introduce a calibration objective that matches the stochastic attention output with the target, yielding an efficient univariate post-hoc tuning problem. We evaluate this mechanism on two scientific foundation models for weather and timeseries forecasting along with an additional regression task. Across benchmarks against uncertainty-aware baselines, we find that Stochastic Attention achieves the strongest native calibration and the sharpest prediction intervals at comparable coverage, while requiring only minutes of post-hoc tuning versus days of retraining for competitive baselines.

Taiwo A. Adebiyi, Nafeezat A. Ajenifuja, Ruda Zhang

Digital twin (DT) technology has received immense attention over the years due to the promises it presents to various stakeholders in science and engineering. As a result, different thematic areas of DT have been explored. This is no different in specific fields such as manufacturing, automation, oil and gas, and civil engineering, leading to fragmented approaches for field-specific applications. The civil engineering industry is further disadvantaged in this regard as it relies on external techniques by other engineering fields for its DT adoption. A rising consequence of these extensions is a concentrated application of DT to the operations and maintenance phase. On another spectrum, Building Information Modeling (BIM) is pervasively utilized in the planning/design phase, and the transient nature of the construction phase remains a challenge for its DT adoption. In this paper, we present a phase-based development of DT in the Architecture, Engineering, and Construction industry. We commence by presenting succinct expositions on DT as a concept and as a service, and establish a five-level scale system. Furthermore, we present separately a systematic literature review of the conventional techniques employed at each civil engineering phase. In this regard, we identified enabling technologies such as computer vision for extended sensing and the Internet of Things for reliable integration. Ultimately, we attempt to reveal DT as an important tool across the entire life cycle of civil engineering projects, and nudge researchers to think more holistically in their quest for the integration of DT for civil engineering applications.

Bach Do, Nafeezat A. Ajenifuja, Taiwo A. Adebiyi et al.

High-fidelity simulations and physical experiments are essential for engineering analysis and design. However, their high cost often limits their applications in two critical tasks: global sensitivity analysis (GSA) and optimization. This limitation motivates the common use of Gaussian processes (GPs) as proxy regression models to provide uncertainty-aware predictions based on a limited number of high-quality observations. GPs naturally enable efficient sampling strategies that support informed decision-making under uncertainty by extracting information from a subset of possible functions for the model of interest. Despite their popularity in machine learning and statistics communities, sampling from GPs has received little attention in the community of engineering optimization. In this paper, we present the formulation and detailed implementation of two notable sampling methods -- random Fourier features and pathwise conditioning -- for generating posterior samples from GPs. Alternative approaches are briefly described. Importantly, we detail how the generated samples can be applied in GSA, single-objective optimization, and multi-objective optimization. We show successful applications of these sampling methods through a series of numerical examples.