Tempone's expertise and research interests lie at the intersection of applied mathematics, computational science, and stochastic analysis, with a strong focus on developing and analyzing numerical methods for stochastic and deterministic problems. His work emphasizes adaptive algorithms and hierarchical and sparse approximation, Bayesian inverse problems and data assimilation, optimal experimental design, scientific machine learning, stochastic optimization, optimal control, and uncertainty quantification, aiming to push the boundaries of computational efficiency and accuracy in simulations. 
At the helm of the Stochastic Numerics Research Group at KAUST, Tempone is particularly interested in the development and analysis of numerical methods to advance applications spanning computational mechanics, quantitative finance, renewable energy sources management, biological and chemical modeling, and wireless communications.  
His approach is theoretical and highly applicable, addressing real-world problems across various domains while grounded in solid foundations of mathematical and computational techniques. His work is instrumental for those interested in the practical application of mathematics to solve complex, real-world issues, making his research group an ideal place for potential collaborators, postgraduate students, postdocs, and research scientists looking for cutting-edge projects at the nexus of uncertainty quantification and computational science.