Multi-task Modeling for Engineering Applications with Sparse Data

Modern engineering and scientific workflows frequently require simultaneous prediction across related tasks and fidelity levels [1-6]. In such contexts, some outputs are scarce and expensive to obtain, while others are cheaper and more abundant. Multi-task Gaussian processes (MTGPs), also known as multi-output Gaussian processes, offer a principled Bayesian framework to exploit inter-task correlations, enabling knowledge sharing that improves predictive accuracy and reduces the demand for large high-fidelity datasets [7-9]. Over decades of development, MTGPs have been applied across diverse domains, including time series forecasting, multitask optimization, and multifidelity classification, demonstrating their broad utility wherever data cost asymmetries and cross-task dependencies are present [10-16]. The central motivation for MTGPs is to leverage dependencies among related tasks to enhance predictive quality when high-fidelity information is limited [17]. For example, predicting an airfoil's lift coefficient from limited, expensive high-fidelity computational fluid dynamics (CFD) simulations can benefit from correlating with sufficient low-fidelity simulations [3]. Recent work in joint multi-objective and multifidelity optimization has also utilized MT - GPs to balance exploration and exploitation across tasks, improving predictive performance and decision-making by explicitly modeling relationships among outputs and fidelities [12].