Highly accurate numerical or physical experiments are often very time-consuming or
expensive to obtain. When time or budget restrictions prohibit the generation of additional …

When evaluating quantities of interest that depend on the solutions to differential equations,
we inevitably face the trade-off between accuracy and efficiency. Especially for …

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation,
entail a huge computational complexity when dealing with input-output maps involving the …

Multi-fidelity data are common in various scientific and engineering fields. High-fidelity data,
often more accurate, come with greater expense, such as precision experimental testing or …

Heavy ion collisions performed at facilities such as the Large Hadron Collider (LHC) and the
Relativistic Heavy Ion Collider (RHIC) produce the hottest matter in the universe at∼ 10 12 …

Uncertainty quantification for physics-informed deep learning MATHEMATICS: KEY
ENABLING TECHNOLOGY FOR SCIENTIFIC MACHINE LEARNING — Page 2 Page 3 …